critical period case study

Critical Period In Brain Development and Childhood Learning

Charlotte Nickerson

Research Assistant at Harvard University

Undergraduate at Harvard University

Charlotte Nickerson is a student at Harvard University obsessed with the intersection of mental health, productivity, and design.

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Saul McLeod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul McLeod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.

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Key Takeaways

• Critical period is an ethological term that refers to a fixed and crucial time during the early development of an organism when it can learn things that are essential to survival. These influences impact the development of processes such as hearing and vision, social bonding, and language learning.
• The term is most often experienced in the study of imprinting, where it is thought that young birds could only develop an attachment to the mother during a fixed time soon after hatching.
• Neurologically, critical periods are marked by high levels of plasticity in the brain before neural connections become more solidified and stable. In particular, critical periods tend to end when synapses that inhibit the neurotransmitter GABA mature.
• In contrast to critical periods, sensitive periods, otherwise known as “weak critical periods,” happen when an organism is more sensitive than usual to outside factors influencing behavior, but this influence is not necessarily restricted to the sensitive period.
• Scholars have debated the extent to which older organisms can develop certain skills, such as natively-accented foreign languages, after the critical period.

The critical period is a biologically determined stage of development where an organism is optimally ready to acquire some pattern of behavior that is part of typical development. This period, by definition, will not recur at a later stage.

If an organism does not receive exposure to the appropriate stimulus needed to learn a skill during a critical period, it may be difficult or even impossible for that organism to develop certain functions associated with that skill later in life.

This happens because a range of functional and structural elements prevent passive experiences from eliciting significant changes in the brain (Cisneros-Franco et al., 2020).

The first strong proponent of the theory of critical periods was Charles Stockhard (1921), a biologist who attempted to experiment with the effects of various chemicals on the development of fish embryos, though he gave credit to Dareste for originating the idea 30 years earlier (Scott, 1962).

Stockhard’s experiments showed that applying almost any chemical to fish embryos at a certain stage of development would result in one-eyed fish.

These experiments established that the most rapidly growing tissues in an embryo are the most sensitive to any change in conditions, leading to effects later in development (Scott, 1962).

Meanwhile, psychologist Sigmund Freud attempted to explain the origins of neurosis in human patients as the result of early experiences, implying that infants are particularly sensitive to influences at certain points in their lives.

Lorenz (1935) later emphasized the importance of critical periods in the formation of primary social bonds (otherwise known as imprinting) in birds, remarking that this psychological imprinting was similar to critical periods in the development of the embryo.

Soon thereafter, McGraw (1946) pointed out the existence of critical periods for the optimal learning of motor skills in human infants (Scott, 1962).

Example: Infant-Parent Attachment

The concept of critical or sensitive periods can also be found in the domain of social development, for example, in the formation of the infant-parent attachment relationship (Salkind, 2005).

Attachment describes the strong emotional ties between the infant and caregiver, a reciprocal relationship developing over the first year of the child’s life and particularly during the second six months of the first year.

During this attachment period , the infant’s social behavior becomes increasingly focused on the principal caregivers (Salkind, 2005).

The 20th-century English psychiatrist John Bowlby formulated and presented a comprehensive theory of attachment influenced by evolutionary theory.

Bowlby argued that the infant-parent attachment relationship develops because it is important to the survival of the infant and that the period from six to twenty-four months of age is a critical period of attachment.

This coincides with an infant’s increasing tendency to approach familiar caregivers and to be wary of unfamiliar adults. After this critical period, it is still possible for a first attachment relationship to develop, albeit with greater difficulty (Salkind, 2005).

This has brought into question, in a similar vein to language development, whether there is actually a critical development period for infant-caregiver attachment.

Sources debating this issue typically include cases of infants who did not experience consistent caregiving due to being raised in institutions prior to adoption (Salkind, 2005).

Early research into the critical period of attachment, published in the 1940s, reports consistently that children raised in orphanages subsequently showed unusual and maladaptive patterns of social behavior, difficulty in forming close relationships, and being indiscriminately friendly toward unfamiliar adults (Salkind, 2005).

Later, research from the 1990s indicated that adoptees were actually still able to form attachment relationships after the first year of life and also made developmental progress following adoption.

Nonetheless, these children had an overall increased risk of insecure or maladaptive attachment relationships with their adoptive parents. This evidence supports the notion of a sensitive period, but not a critical period, in the development of first attachment relationships (Salkind, 2005).

Mechanisms for Critical Periods

Both genetics and sensory experiences from outside the body shape the brain as it develops (Knudsen, 2004). However, the developmental stage that an organism is in significantly impacts how much the brain can change based on these experiences.

In scientific terms, the brain’s plasticity changes over the course of a lifespan. The brain is very plastic in the early stages of life before many key connections take root, but less so later.

This is why researchers have shown that early experience is crucial for the development of, say, language and musical abilities, and these skills are more challenging to take up in adulthood (Skoe and Kraus, 2013; White et al., 2013; Hartshorne et al., 2018).

As brains mature, the connections in them become more fixed. The brain’s transitions from a more plastic to a more fixed state advantageously allow it to retain new and complex processes, such as perceptual, motor, and cognitive functions (Piaget, 1962).

Children’s gestures, for example, pride and predict how they will acquire oral language skills (Colonnesi et al., 2010), which in turn are important for developing executive functions (Marcovitch and Zelazo, 2009).

However, this formation of stable connections in the brain can limit how the brain’s neural circuitry can be revised in the future. For example, if a young organism has abnormal sensory experiences during the critical period – such as auditory or visual deprivation – the brain may not wire itself in a way that processes future sensory inputs properly (Gallagher et al., 2020).

One illustration of this is the timing of cochlear implants – a prosthesis that restores hearing in some deaf people. Children who receive cochlear implants before two years of age are more likely to benefit from them than those who are implanted later in life (Kral and Eggermont, 2007; Gallagher et al., 2020).

Similarly, the visual deprivation caused by cataracts in infants can cause similar consequences. When cataracts are removed during early infancy, individuals can develop relatively normal vision; however, when the cataracts are not removed until adulthood, this results in substantially poorer vision (Martins Rosa et al., 2013).

After the critical period closes, abnormal sensory experiences have a less drastic effect on the brain and lead to – barring direct damage to the central nervous system – reversible changes (Gallagher et al., 2020). Much of what scientists know about critical periods derives from animal studies , as these allow researchers greater control over the variables that they are testing.

This research has found that different sensory systems, such as vision, auditory processing, and spatial hearing, have different critical periods (Gallagher et al., 2020).

The brain regulates when critical periods open and close by regulating how much the brain’s synapses take up neurotransmitters , which are chemical substances that affect the transmission of electrical signals between neurons.

In particular, over time, synapses decrease their uptake of gamma-aminobutyric acid, better known as GABA. At the beginning of the critical period, outside sources become more effective at influencing changes and growth in the brain.

Meanwhile, as the inhibitory circuits of the brain mature, the mature brain becomes less sensitive to sensory experiences (Gallagher et al., 2020).

Critical Periods vs Sensitive Periods

Critical periods are similar to sensitive periods, and scholars have, at times, used them interchangeably. However, they describe distinct but overlapping developmental processes.

A sensitive period is a developmental stage where sensory experiences have a greater impact on behavioral and brain development than usual; however, this influence is not exclusive to this time period (Knudsen, 2004; Gallagher, 2020). These sensitive periods are important for skills such as learning a language or instrument.

In contrast, A critical period is a special type of sensitive period – a window where sensory experience is necessary to shape the neural circuits involved in basic sensory processing, and when this window opens and closes is well-defined (Gallagher, 2020).

Researchers also refer to sensitive periods as weak critical periods. Some examples of strong critical periods include the development of vision and hearing, while weak critical periods include phenome tuning – how children learn how to organize sounds in a language, grammar processing, vocabulary acquisition, musical training, and sports training (Gallagher et al., 2020).

Critical Period Hypothesis

One of the most notable applications of the concept of a critical period is in linguistics. Scholars usually trace the origins of the debate around age in language acquisition to Penfield and Robert’s (2014) book Speech and Brain Mechanisms.

In the 1950s and 1960s, Penfield was a staunch advocate of early immersion education (Kroll and De Groot, 2009). Nonetheless, it was Lenneberg, in his book Biological Foundations of Language, who coined the term critical period (1967) in describing the language period.

Lennenberg (1967) described a critical period as a period of automatic acquisition from mere exposure” that “seems to disappear after this age.” Scovel (1969) later summarized and narrowed Penfield’s and Lenneberg’s view on the critical period hypothesis into three main claims:

• Adult native speakers can identify non-natives by their accents immediately and accurately.
• The loss of brain plasticity at about the age of puberty accounts for the emergence of foreign accents./li>
• The critical period hypothesis only holds for speech (whether or not someone has a native accent) and does not affect other areas of linguistic competence.

Linguists have since attempted to find evidence for whether or not scientific evidence actually supports the critical period hypothesis, if there is a critical period for acquiring accentless speech, for “morphosyntactic” competence, and if these are true, how age-related differences can be explained on the neurological level (Scovel, 2000).

The critical period hypothesis applies to both first and second-language learning. Until recently, research around the critical period’s role in first language acquisition revolved around findings about so-called “feral” children who had failed to acquire language at an older age after having been deprived of normal input during the critical period.

However, these case studies did not account for the extent to which social deprivation, and possibly food deprivation or sensory deprivation, may have confounded with language input deprivation (Kroll and De Groot, 2009).

More recently, researchers have focused more systematically on deaf children born to hearing parents who are therefore deprived of language input until at least elementary school.

These studies have found the effects of lack of language input without extreme social deprivation: the older the age of exposure to sign language is, the worse its ultimate attainment (Emmorey, Bellugi, Friederici, and Horn, 1995; Kroll and De Groot, 2009).

However, Kroll and De Groot argue that the critical period hypothesis does not apply to the rate of acquisition of language. Adults and adolescents can learn languages at the same rate or even faster than children in their initial stage of acquisition (Slavoff and Johnson, 1995).

However, adults tend to have a more limited ultimate attainment of language ability (Kroll and De Groot, 2009).

There has been a long lineage of empirical findings around the age of acquisition. The most fundamental of this research comes from a series of studies since the late 1970s documenting a negative correlation between age of acquisition and ultimate language mastery (Kroll and De Grott, 2009).

Nonetheless, different periods correspond to sensitivity to different aspects of language. For example, shortly after birth, infants can perceive and discriminate speech sounds from any language, including ones they have not been exposed to (Eimas et al., 1971; Gallagher et al., 2020).

Around six months of age, exposure to the primary language in the infant’s environment guides phonetic representations of language and, subsequently, the neural representations of speech sounds of the native language while weakening those of unused sounds (McClelland et al., 1999; Gallagher et al., 2020).

Vocabulary learning experiences rapid growth at about 18 months of age (Kuhl, 2010).

Critical Evaluation

More than any other area of applied linguistics, the critical period hypothesis has impacted how teachers teach languages. Consequently, researchers have critiqued how important the critical period is to language learning.

For example, several studies in early language acquisition research showed that children were not necessarily superior to older learners in acquiring a second language, even in the area of pronunciation (Olson and Samuels, 1973; Snow and Hoefnagel-Hohle, 1978; Scovel, 2000).

In fact, the majority of researchers at the time appeared to be skeptical about the existence of a critical period, with some explicitly denying its existence.

Counter to one of the primary tenets of Scovel’s (1969) critical period hypothesis, there have been several cases of people who have acquired a second language in adulthood speaking with native accents.

For example, Moyer’s study of highly proficient English-speaking learners of German suggested that at least one of the participants was judged to have native-like pronunciation in his second language (1999), and several participants in Bongaerts (1999) study of highly proficient Dutch speakers of French spoke with accents judged to be native (Scovel, 2000).

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Cisneros-Franco, J. M., Voss, P., Thomas, M. E., & de Villers-Sidani, E. (2020). Critical periods of brain development. In Handbook of Clinical Neurolog y (Vol. 173, pp. 75-88). Elsevier.

Colonnesi, C., Stams, G. J. J., Koster, I., & Noom, M. J. (2010). The relation between pointing and language development: A meta-analysis. Developmental Review, 30 (4), 352-366.

Eimas, P. D., Siqueland, E. R., Jusczyk, P., & Vigorito, J. (1971). Speech perception in infants. Science, 171 (3968), 303-306.

Emmorey, K., Bellugi, U., Friederici, A., & Horn, P. (1995). Effects of age of acquisition on grammatical sensitivity: Evidence from on-line and off-line tasks. Applied Psycholinguistics, 16 (1), 1-23.

Knudsen, E. I. (2004). Sensitive periods in the development of the brain and behavior. Journal of cognitive neuroscience, 16 (8), 1412-1425.

Hartshorne, J. K., Tenenbaum, J. B., & Pinker, S. (2018). A critical period for second language acquisition: Evidence from 2/3 million English speakers. Cognition, 177 , 263-277.

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The Story of Genie Wiley

What her tragic story revealed about language and development

Who Was Genie Wiley?

Why was the genie wiley case so famous, did genie learn to speak, ethical concerns.

While there have been a number of cases of feral children raised in social isolation with little or no human contact, few have captured public and scientific attention, like that of Genie Wiley.

Genie spent almost her entire childhood locked in a bedroom, isolated, and abused for over a decade. Her case was one of the first to put the critical period theory to the test. Could a child reared in utter deprivation and isolation develop language? Could a nurturing environment make up for a horrifying past?

In order to understand Genie's story, it is important to look at what is known about her early life, the discovery of the abuse she had endured, and the subsequent efforts to treat and study her.

Early Life (1957-1970)

Genie's life prior to her discovery was one of utter deprivation. She spent most of her days tied naked to a potty chair, only able to move her hands and feet. When she made noise, her father would beat her. The rare times her father did interact with her, it was to bark or growl. Genie Wiley's brother, who was five years older than Genie, also suffered abuse under their father.

Discovery and Study (1970-1975)

Genie's story came to light on November 4, 1970, in Los Angeles, California. A social worker discovered the 13-year old girl after her mother sought out services for her own health. The social worker soon discovered that the girl had been confined to a small room, and an investigation by authorities quickly revealed that the child had spent most of her life in this room, often tied to a potty chair.

A Genie Wiley documentary was made in 1997 called "Secrets of the Wild Child." In it, Susan Curtiss, PhD, a linguist and researcher who worked with Genie, explained that the name Genie was used in case files to protect the girl's identity and privacy.

The case name is Genie. This is not the person's real name, but when we think about what a genie is, a genie is a creature that comes out of a bottle or whatever but emerges into human society past childhood. We assume that it really isn't a creature that had a human childhood.

Both parents were charged with abuse , but Genie's father died by suicide the day before he was due to appear in court, leaving behind a note stating that "the world will never understand."

The story of Genie's case soon spread, drawing attention from both the public and the scientific community. The case was important, said psycholinguist and author Harlan Lane, PhD, because "our morality doesn’t allow us to conduct deprivation experiments with human beings; these unfortunate people are all we have to go on."

With so much interest in her case, the question became what should be done to help her. A team of psychologists and language experts began the process of rehabilitating Genie.

The National Institute of Mental Health (NIMH) provided funding for scientific research on Genie’s case. Psychologist David Rigler, PhD, was part of the "Genie team" and he explained the process.

I think everybody who came in contact with her was attracted to her. She had a quality of somehow connecting with people, which developed more and more but was present, really, from the start. She had a way of reaching out without saying anything, but just somehow by the kind of look in her eyes, and people wanted to do things for her.

Genie's rehabilitation team also included graduate student Susan Curtiss and psychologist James Kent. Upon her initial arrival at UCLA, Genie weighed just 59 pounds and moved with a strange "bunny walk." She often spat and was unable to straighten her arms and legs. Silent, incontinent, and unable to chew, she initially seemed only able to recognize her own name and the word "sorry."

After assessing Genie's emotional and cognitive abilities, Kent described her as "the most profoundly damaged child I've ever seen … Genie's life is a wasteland." Her silence and inability to use language made it difficult to assess her mental abilities, but on tests, she scored at about the level of a 1-year-old.

Genie Wiley's Rehabilitation and the Forbidden Experiment

She soon began to rapidly progress in specific areas, quickly learning how to use the toilet and dress herself. Over the next few months, she began to experience more developmental progress but remained poor in areas such as language. She enjoyed going out on day trips outside of the hospital and explored her new environment with an intensity that amazed her caregivers and strangers alike.

Curtiss suggested that Genie had a strong ability to communicate nonverbally , often receiving gifts from total strangers who seemed to understand the young girl's powerful need to explore the world around her.

Psychiatrist Jay Shurley, MD, helped assess Genie after she was first discovered, and he noted that since situations like hers were so rare, she quickly became the center of a battle between the researchers involved in her case. Arguments over the research and the course of her treatment soon erupted. Genie occasionally spent the night at the home of Jean Butler, one of her teachers.

After an outbreak of measles, Genie was quarantined at her teacher's home. Butler soon became protective and began restricting access to Genie. Other members of the team felt that Butler's goal was to become famous from the case, at one point claiming that Butler had called herself the next Anne Sullivan, the teacher famous for helping Helen Keller learn to communicate.  

Genie was partially treated like an asset and an opportunity for recognition, significantly interfering with their roles, and the researchers fought with each other for access to their perceived power source.

Eventually, Genie was removed from Butler's care and went to live in the home of psychologist David Rigler, where she remained for the next four years. Despite some difficulties, she appeared to do well in the Rigler household. She enjoyed listening to classical music on the piano and loved to draw, often finding it easier to communicate through drawing than through other methods.

After Genie was discovered, a group of researchers began the process of rehabilitation. However, this work also coincided with research to study her ability to acquire and use language. These two interests led to conflicts in her treatment and between the researchers and therapists working on her case.

State Custody (1975-Present)

NIMH withdrew funding in 1974, due to the lack of scientific findings. Linguist Susan Curtiss had found that while Genie could use words, she could not produce grammar. She could not arrange these words in a meaningful way, supporting the idea of a critical period in language development.

Rigler's research was disorganized and largely anecdotal. Without funds to continue the research and care for Genie, she was moved from the Riglers' care.

In 1975, Genie returned to live with her birth mother. When her mother found the task too difficult, Genie was moved through a series of foster homes, where she was often subjected to further abuse and neglect .

Genie’s situation continued to worsen. After spending a significant amount of time in foster homes, she returned to Children’s Hospital. Unfortunately, the progress that had occurred during her first stay had been severely compromised by the subsequent treatment she received in foster care. Genie was afraid to open her mouth and had regressed back into silence.

Genie’s birth mother then sued the Children’s Hospital of Los Angeles and the research team, charging them with excessive testing. While the lawsuit was eventually settled, it raised important questions about the treatment and care of Genie. Did the research interfere with the girl's therapeutic treatment?

Psychiatrist Jay Shurley visited her on her 27th and 29th birthdays and characterized her as largely silent, depressed , and chronically institutionalized. Little is known about Genie's present condition, although an anonymous individual hired a private investigator to track her down in 2000 and described her as happy. But this contrasts with other reports.

Genie Wiley Today

Today, Genie Wiley's whereabouts are unknown; though, if she is still living, she is presumed to be a ward of the state of California, living in an adult care home. As of 2024, Genie would be 66-67 years old.

Part of the reason why Genie's case fascinated psychologists and linguists so deeply was that it presented a unique opportunity to study a hotly contested debate about language development.

Essentially, it boils down to the age-old nature versus nurture debate. Does genetics or environment play a greater role in the development of language?

Nativists believe that the capacity for language is innate, while empiricists suggest that environmental variables play a key role. Nativist Noam Chomsky suggested that acquiring language could not be fully explained by learning alone.

Instead, Chomsky proposed that children are born with a language acquisition device (LAD), an innate ability to understand the principles of language. Once exposed to language, the LAD allows children to learn the language at a remarkable pace.

Critical Periods

Linguist Eric Lenneberg suggests that like many other human behaviors, the ability to acquire language is subject to critical periods. A critical period is a limited span of time during which an organism is sensitive to external stimuli and capable of acquiring certain skills.

According to Lenneberg, the critical period for language acquisition lasts until around age 12. After the onset of puberty, he argued, the organization of the brain becomes set and no longer able to learn and use language in a fully functional manner.

Genie's case presented researchers with a unique opportunity. If given an enriched learning environment, could she overcome her deprived childhood and learn language even though she had missed the critical period?

If Genie could learn language, it would suggest that the critical period hypothesis of language development was wrong. If she could not, it would indicate that Lenneberg's theory was correct.

Despite scoring at the level of a 1-year-old upon her initial assessment, Genie quickly began adding new words to her vocabulary. She started by learning single words and eventually began putting two words together much the way young children do. Curtiss began to feel that Genie would be fully capable of acquiring language.

After a year of treatment, Genie started putting three words together occasionally. In children going through normal language development, this stage is followed by what is known as a language explosion. Children rapidly acquire new words and begin putting them together in novel ways.

Unfortunately, this never happened for Genie. Her language abilities remained stuck at this stage and she appeared unable to apply grammatical rules and use language in a meaningful way. At this point, her progress leveled off and her acquisition of new language halted.

While Genie was able to learn some language after puberty, her inability to use grammar (which Chomsky suggests is what separates human language from animal communication) offers evidence for the critical period hypothesis.

Of course, Genie's case is not so simple. Not only did she miss the critical period for learning language, but she was also horrifically abused. She was malnourished and deprived of cognitive stimulation for most of her childhood.

Researchers were also never able to fully determine if Genie had any pre-existing cognitive deficits. As an infant, a pediatrician had identified her as having some type of mental delay. So researchers were left to wonder whether Genie had experienced cognitive deficits caused by her years of abuse or if she had been born with some degree of intellectual disability.

There are many ethical concerns surrounding Genie's story. Arguments among those in charge of Genie's care and rehabilitation reflect some of these concerns.

"If you want to do rigorous science, then Genie's interests are going to come second some of the time. If you only care about helping Genie, then you wouldn't do a lot of the scientific research," suggested psycholinguist Harlan Lane in the NOVA documentary focused on her life.

In Genie's case, some of the researchers held multiple roles of caretaker-teacher-researcher-housemate. which, by modern standards, we would deem unethical. For example, the Riglers benefitted financially by taking Genie in (David received a large grant and was released from certain duties at the children's hospital without loss of pay). Butler also played a role in removing Genie from the Riglers' home, filing multiple complaints against him.

While Genie's story may be studied for its implications in our understanding of language acquisition and development, it is also a case that will continue to be studied over its serious ethical issues.

"I think future generations are going to study Genie's case not only for what it can teach us about human development but also for what it can teach us about the rewards and the risks of conducting 'the forbidden experiment,'" Lane explained.

Bottom Line

Genie Wiley's story perhaps leaves us with more questions than answers. Though it was difficult for Genie to learn language, she was able to communicate through body language, music, and art once she was in a safe home environment. Unfortunately, we don't know what her progress could have been had adequate care not been taken away from her.

Ultimately, her case is so important for the psychology and research field because we must learn from this experience not to revictimize and exploit the very people we set out to help. This is an important lesson because Genie's original abuse by her parents was perpetuated by the neglect and abandonment she faced later in her life. We must always strive to maintain objectivity and consider the best interest of the subject before our own.

Frequently Asked Questions

Genie, now in her 60s, is believed to be living in an adult care facility in California. Efforts by journalists to learn more about her location and current condition have been rejected by authorities due to confidentiality rules. Curtiss has also reported attempting to contact Genie without success.

Along with her husband, Irene Wiley was charged with abuse, but these charges were eventually dropped. Irene was blind and reportedly mentally ill, so it is believed that Genie's father was the child's primary caretaker. Genie's father, Clark Wiley, also abused his wife and other children. Two of the couple's children died in infancy under suspicious circumstances.

Genie's story suggests that the acquisition of language has a critical period of development. Her case is complex, however, since it is unclear if her language deficits were due to deprivation or if there was an underlying mental disability that played a role. The severe abuse she experienced may have also affected her mental development and language acquisition.

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Research Article

The Critical Period Hypothesis in Second Language Acquisition: A Statistical Critique and a Reanalysis

* E-mail: [email protected]

Affiliation Department of Multilingualism, University of Fribourg, Fribourg, Switzerland

• Jan Vanhove

• Published: July 25, 2013
• https://doi.org/10.1371/journal.pone.0069172
• Reader Comments

17 Jul 2014: The PLOS ONE Staff (2014) Correction: The Critical Period Hypothesis in Second Language Acquisition: A Statistical Critique and a Reanalysis. PLOS ONE 9(7): e102922. https://doi.org/10.1371/journal.pone.0102922 View correction

In second language acquisition research, the critical period hypothesis ( cph ) holds that the function between learners' age and their susceptibility to second language input is non-linear. This paper revisits the indistinctness found in the literature with regard to this hypothesis's scope and predictions. Even when its scope is clearly delineated and its predictions are spelt out, however, empirical studies–with few exceptions–use analytical (statistical) tools that are irrelevant with respect to the predictions made. This paper discusses statistical fallacies common in cph research and illustrates an alternative analytical method (piecewise regression) by means of a reanalysis of two datasets from a 2010 paper purporting to have found cross-linguistic evidence in favour of the cph . This reanalysis reveals that the specific age patterns predicted by the cph are not cross-linguistically robust. Applying the principle of parsimony, it is concluded that age patterns in second language acquisition are not governed by a critical period. To conclude, this paper highlights the role of confirmation bias in the scientific enterprise and appeals to second language acquisition researchers to reanalyse their old datasets using the methods discussed in this paper. The data and R commands that were used for the reanalysis are provided as supplementary materials.

Citation: Vanhove J (2013) The Critical Period Hypothesis in Second Language Acquisition: A Statistical Critique and a Reanalysis. PLoS ONE 8(7): e69172. https://doi.org/10.1371/journal.pone.0069172

Editor: Stephanie Ann White, UCLA, United States of America

Received: May 7, 2013; Accepted: June 7, 2013; Published: July 25, 2013

Copyright: © 2013 Jan Vanhove. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Funding: No current external funding sources for this study.

Competing interests: The author has declared that no competing interests exist.

Introduction

In the long term and in immersion contexts, second-language (L2) learners starting acquisition early in life – and staying exposed to input and thus learning over several years or decades – undisputedly tend to outperform later learners. Apart from being misinterpreted as an argument in favour of early foreign language instruction, which takes place in wholly different circumstances, this general age effect is also sometimes taken as evidence for a so-called ‘critical period’ ( cp ) for second-language acquisition ( sla ). Derived from biology, the cp concept was famously introduced into the field of language acquisition by Penfield and Roberts in 1959 [1] and was refined by Lenneberg eight years later [2] . Lenneberg argued that language acquisition needed to take place between age two and puberty – a period which he believed to coincide with the lateralisation process of the brain. (More recent neurological research suggests that different time frames exist for the lateralisation process of different language functions. Most, however, close before puberty [3] .) However, Lenneberg mostly drew on findings pertaining to first language development in deaf children, feral children or children with serious cognitive impairments in order to back up his claims. For him, the critical period concept was concerned with the implicit “automatic acquisition” [2, p. 176] in immersion contexts and does not preclude the possibility of learning a foreign language after puberty, albeit with much conscious effort and typically less success.

sla research adopted the critical period hypothesis ( cph ) and applied it to second and foreign language learning, resulting in a host of studies. In its most general version, the cph for sla states that the ‘susceptibility’ or ‘sensitivity’ to language input varies as a function of age, with adult L2 learners being less susceptible to input than child L2 learners. Importantly, the age–susceptibility function is hypothesised to be non-linear. Moving beyond this general version, we find that the cph is conceptualised in a multitude of ways [4] . This state of affairs requires scholars to make explicit their theoretical stance and assumptions [5] , but has the obvious downside that critical findings risk being mitigated as posing a problem to only one aspect of one particular conceptualisation of the cph , whereas other conceptualisations remain unscathed. This overall vagueness concerns two areas in particular, viz. the delineation of the cph 's scope and the formulation of testable predictions. Delineating the scope and formulating falsifiable predictions are, needless to say, fundamental stages in the scientific evaluation of any hypothesis or theory, but the lack of scholarly consensus on these points seems to be particularly pronounced in the case of the cph . This article therefore first presents a brief overview of differing views on these two stages. Then, once the scope of their cph version has been duly identified and empirical data have been collected using solid methods, it is essential that researchers analyse the data patterns soundly in order to assess the predictions made and that they draw justifiable conclusions from the results. As I will argue in great detail, however, the statistical analysis of data patterns as well as their interpretation in cph research – and this includes both critical and supportive studies and overviews – leaves a great deal to be desired. Reanalysing data from a recent cph -supportive study, I illustrate some common statistical fallacies in cph research and demonstrate how one particular cph prediction can be evaluated.

Delineating the scope of the critical period hypothesis

First, the age span for a putative critical period for language acquisition has been delimited in different ways in the literature [4] . Lenneberg's critical period stretched from two years of age to puberty (which he posits at about 14 years of age) [2] , whereas other scholars have drawn the cutoff point at 12, 15, 16 or 18 years of age [6] . Unlike Lenneberg, most researchers today do not define a starting age for the critical period for language learning. Some, however, consider the possibility of the critical period (or a critical period for a specific language area, e.g. phonology) ending much earlier than puberty (e.g. age 9 years [1] , or as early as 12 months in the case of phonology [7] ).

Second, some vagueness remains as to the setting that is relevant to the cph . Does the critical period constrain implicit learning processes only, i.e. only the untutored language acquisition in immersion contexts or does it also apply to (at least partly) instructed learning? Most researchers agree on the former [8] , but much research has included subjects who have had at least some instruction in the L2.

Third, there is no consensus on what the scope of the cp is as far as the areas of language that are concerned. Most researchers agree that a cp is most likely to constrain the acquisition of pronunciation and grammar and, consequently, these are the areas primarily looked into in studies on the cph [9] . Some researchers have also tried to define distinguishable cp s for the different language areas of phonetics, morphology and syntax and even for lexis (see [10] for an overview).

Fourth and last, research into the cph has focused on ‘ultimate attainment’ ( ua ) or the ‘final’ state of L2 proficiency rather than on the rate of learning. From research into the rate of acquisition (e.g. [11] – [13] ), it has become clear that the cph cannot hold for the rate variable. In fact, it has been observed that adult learners proceed faster than child learners at the beginning stages of L2 acquisition. Though theoretical reasons for excluding the rate can be posited (the initial faster rate of learning in adults may be the result of more conscious cognitive strategies rather than to less conscious implicit learning, for instance), rate of learning might from a different perspective also be considered an indicator of ‘susceptibility’ or ‘sensitivity’ to language input. Nevertheless, contemporary sla scholars generally seem to concur that ua and not rate of learning is the dependent variable of primary interest in cph research. These and further scope delineation problems relevant to cph research are discussed in more detail by, among others, Birdsong [9] , DeKeyser and Larson-Hall [14] , Long [10] and Muñoz and Singleton [6] .

Formulating testable hypotheses

Once the relevant cph 's scope has satisfactorily been identified, clear and testable predictions need to be drawn from it. At this stage, the lack of consensus on what the consequences or the actual observable outcome of a cp would have to look like becomes evident. As touched upon earlier, cph research is interested in the end state or ‘ultimate attainment’ ( ua ) in L2 acquisition because this “determines the upper limits of L2 attainment” [9, p. 10]. The range of possible ultimate attainment states thus helps researchers to explore the potential maximum outcome of L2 proficiency before and after the putative critical period.

One strong prediction made by some cph exponents holds that post- cp learners cannot reach native-like L2 competences. Identifying a single native-like post- cp L2 learner would then suffice to falsify all cph s making this prediction. Assessing this prediction is difficult, however, since it is not clear what exactly constitutes sufficient nativelikeness, as illustrated by the discussion on the actual nativelikeness of highly accomplished L2 speakers [15] , [16] . Indeed, there exists a real danger that, in a quest to vindicate the cph , scholars set the bar for L2 learners to match monolinguals increasingly higher – up to Swiftian extremes. Furthermore, the usefulness of comparing the linguistic performance in mono- and bilinguals has been called into question [6] , [17] , [18] . Put simply, the linguistic repertoires of mono- and bilinguals differ by definition and differences in the behavioural outcome will necessarily be found, if only one digs deep enough.

A second strong prediction made by cph proponents is that the function linking age of acquisition and ultimate attainment will not be linear throughout the whole lifespan. Before discussing how this function would have to look like in order for it to constitute cph -consistent evidence, I point out that the ultimate attainment variable can essentially be considered a cumulative measure dependent on the actual variable of interest in cph research, i.e. susceptibility to language input, as well as on such other factors like duration and intensity of learning (within and outside a putative cp ) and possibly a number of other influencing factors. To elaborate, the behavioural outcome, i.e. ultimate attainment, can be assumed to be integrative to the susceptibility function, as Newport [19] correctly points out. Other things being equal, ultimate attainment will therefore decrease as susceptibility decreases. However, decreasing ultimate attainment levels in and by themselves represent no compelling evidence in favour of a cph . The form of the integrative curve must therefore be predicted clearly from the susceptibility function. Additionally, the age of acquisition–ultimate attainment function can take just about any form when other things are not equal, e.g. duration of learning (Does learning last up until time of testing or only for a more or less constant number of years or is it dependent on age itself?) or intensity of learning (Do learners always learn at their maximum susceptibility level or does this intensity vary as a function of age, duration, present attainment and motivation?). The integral of the susceptibility function could therefore be of virtually unlimited complexity and its parameters could be adjusted to fit any age of acquisition–ultimate attainment pattern. It seems therefore astonishing that the distinction between level of sensitivity to language input and level of ultimate attainment is rarely made in the literature. Implicitly or explicitly [20] , the two are more or less equated and the same mathematical functions are expected to describe the two variables if observed across a range of starting ages of acquisition.

But even when the susceptibility and ultimate attainment variables are equated, there remains controversy as to what function linking age of onset of acquisition and ultimate attainment would actually constitute evidence for a critical period. Most scholars agree that not any kind of age effect constitutes such evidence. More specifically, the age of acquisition–ultimate attainment function would need to be different before and after the end of the cp [9] . According to Birdsong [9] , three basic possible patterns proposed in the literature meet this condition. These patterns are presented in Figure 1 . The first pattern describes a steep decline of the age of onset of acquisition ( aoa )–ultimate attainment ( ua ) function up to the end of the cp and a practically non-existent age effect thereafter. Pattern 2 is an “unconventional, although often implicitly invoked” [9, p. 17] notion of the cp function which contains a period of peak attainment (or performance at ceiling), i.e. performance does not vary as a function of age, which is often referred to as a ‘window of opportunity’. This time span is followed by an unbounded decline in ua depending on aoa . Pattern 3 includes characteristics of patterns 1 and 2. At the beginning of the aoa range, performance is at ceiling. The next segment is a downward slope in the age function which ends when performance reaches its floor. Birdsong points out that all of these patterns have been reported in the literature. On closer inspection, however, he concludes that the most convincing function describing these age effects is a simple linear one. Hakuta et al. [21] sketch further theoretically possible predictions of the cph in which the mean performance drops drastically and/or the slope of the aoa – ua proficiency function changes at a certain point.

• PPT PowerPoint slide
• PNG larger image
• TIFF original image

The graphs are based on based on Figure 2 in [9] .

https://doi.org/10.1371/journal.pone.0069172.g001

Although several patterns have been proposed in the literature, it bears pointing out that the most common explicit prediction corresponds to Birdsong's first pattern, as exemplified by the following crystal-clear statement by DeKeyser, one of the foremost cph proponents:

[A] strong negative correlation between age of acquisition and ultimate attainment throughout the lifespan (or even from birth through middle age), the only age effect documented in many earlier studies, is not evidence for a critical period…[T]he critical period concept implies a break in the AoA–proficiency function, i.e., an age (somewhat variable from individual to individual, of course, and therefore an age range in the aggregate) after which the decline of success rate in one or more areas of language is much less pronounced and/or clearly due to different reasons. [22, p. 445].

DeKeyser and before him among others Johnson and Newport [23] thus conceptualise only one possible pattern which would speak in favour of a critical period: a clear negative age effect before the end of the critical period and a much weaker (if any) negative correlation between age and ultimate attainment after it. This ‘flattened slope’ prediction has the virtue of being much more tangible than the ‘potential nativelikeness’ prediction: Testing it does not necessarily require comparing the L2-learners to a native control group and thus effectively comparing apples and oranges. Rather, L2-learners with different aoa s can be compared amongst themselves without the need to categorise them by means of a native-speaker yardstick, the validity of which is inevitably going to be controversial [15] . In what follows, I will concern myself solely with the ‘flattened slope’ prediction, arguing that, despite its clarity of formulation, cph research has generally used analytical methods that are irrelevant for the purposes of actually testing it.

Inferring non-linearities in critical period research: An overview

Group mean or proportion comparisons.

[T]he main differences can be found between the native group and all other groups – including the earliest learner group – and between the adolescence group and all other groups. However, neither the difference between the two childhood groups nor the one between the two adulthood groups reached significance, which indicates that the major changes in eventual perceived nativelikeness of L2 learners can be associated with adolescence. [15, p. 270].

Similar group comparisons aimed at investigating the effect of aoa on ua have been carried out by both cph advocates and sceptics (among whom Bialystok and Miller [25, pp. 136–139], Birdsong and Molis [26, p. 240], Flege [27, pp. 120–121], Flege et al. [28, pp. 85–86], Johnson [29, p. 229], Johnson and Newport [23, p. 78], McDonald [30, pp. 408–410] and Patowski [31, pp. 456–458]). To be clear, not all of these authors drew direct conclusions about the aoa – ua function on the basis of these groups comparisons, but their group comparisons have been cited as indicative of a cph -consistent non-continuous age effect, as exemplified by the following quote by DeKeyser [22] :

Where group comparisons are made, younger learners always do significantly better than the older learners. The behavioral evidence, then, suggests a non-continuous age effect with a “bend” in the AoA–proficiency function somewhere between ages 12 and 16. [22, p. 448].

The first problem with group comparisons like these and drawing inferences on the basis thereof is that they require that a continuous variable, aoa , be split up into discrete bins. More often than not, the boundaries between these bins are drawn in an arbitrary fashion, but what is more troublesome is the loss of information and statistical power that such discretisation entails (see [32] for the extreme case of dichotomisation). If we want to find out more about the relationship between aoa and ua , why throw away most of the aoa information and effectively reduce the ua data to group means and the variance in those groups?

Comparison of correlation coefficients.

Correlation-based inferences about slope discontinuities have similarly explicitly been made by cph advocates and skeptics alike, e.g. Bialystok and Miller [25, pp. 136 and 140], DeKeyser and colleagues [22] , [44] and Flege et al. [45, pp. 166 and 169]. Others did not explicitly infer the presence or absence of slope differences from the subset correlations they computed (among others Birdsong and Molis [26] , DeKeyser [8] , Flege et al. [28] and Johnson [29] ), but their studies nevertheless featured in overviews discussing discontinuities [14] , [22] . Indeed, the most recent overview draws a strong conclusion about the validity of the cph 's ‘flattened slope’ prediction on the basis of these subset correlations:

In those studies where the two groups are described separately, the correlation is much higher for the younger than for the older group, except in Birdsong and Molis (2001) [ =  [26] , JV], where there was a ceiling effect for the younger group. This global picture from more than a dozen studies provides support for the non-continuity of the decline in the AoA–proficiency function, which all researchers agree is a hallmark of a critical period phenomenon. [22, p. 448].

In Johnson and Newport's specific case [23] , their correlation-based inference that ua levels off after puberty happened to be largely correct: the gjt scores are more or less randomly distributed around a near-horizontal trend line [26] . Ultimately, however, it rests on the fallacy of confusing correlation coefficients with slopes, which seriously calls into question conclusions such as DeKeyser's (cf. the quote above).

https://doi.org/10.1371/journal.pone.0069172.g002

Lower correlation coefficients in older aoa groups may therefore be largely due to differences in ua variance, which have been reported in several studies [23] , [26] , [28] , [29] (see [46] for additional references). Greater variability in ua with increasing age is likely due to factors other than age proper [47] , such as the concomitant greater variability in exposure to literacy, degree of education, motivation and opportunity for language use, and by itself represents evidence neither in favour of nor against the cph .

Regression approaches.

Having demonstrated that neither group mean or proportion comparisons nor correlation coefficient comparisons can directly address the ‘flattened slope’ prediction, I now turn to the studies in which regression models were computed with aoa as a predictor variable and ua as the outcome variable. Once again, this category of studies is not mutually exclusive with the two categories discussed above.

In a large-scale study using self-reports and approximate aoa s derived from a sample of the 1990 U.S. Census, Stevens found that the probability with which immigrants from various countries stated that they spoke English ‘very well’ decreased curvilinearly as a function of aoa [48] . She noted that this development is similar to the pattern found by Johnson and Newport [23] but that it contains no indication of an “abruptly defined ‘critical’ or sensitive period in L2 learning” [48, p. 569]. However, she modelled the self-ratings using an ordinal logistic regression model in which the aoa variable was logarithmically transformed. Technically, this is perfectly fine, but one should be careful not to read too much into the non-linear curves found. In logistic models, the outcome variable itself is modelled linearly as a function of the predictor variables and is expressed in log-odds. In order to compute the corresponding probabilities, these log-odds are transformed using the logistic function. Consequently, even if the model is specified linearly, the predicted probabilities will not lie on a perfectly straight line when plotted as a function of any one continuous predictor variable. Similarly, when the predictor variable is first logarithmically transformed and then used to linearly predict an outcome variable, the function linking the predicted outcome variables and the untransformed predictor variable is necessarily non-linear. Thus, non-linearities follow naturally from Stevens's model specifications. Moreover, cph -consistent discontinuities in the aoa – ua function cannot be found using her model specifications as they did not contain any parameters allowing for this.

Using data similar to Stevens's, Bialystok and Hakuta found that the link between the self-rated English competences of Chinese- and Spanish-speaking immigrants and their aoa could be described by a straight line [49] . In contrast to Stevens, Bialystok and Hakuta used a regression-based method allowing for changes in the function's slope, viz. locally weighted scatterplot smoothing ( lowess ). Informally, lowess is a non-parametrical method that relies on an algorithm that fits the dependent variable for small parts of the range of the independent variable whilst guaranteeing that the overall curve does not contain sudden jumps (for technical details, see [50] ). Hakuta et al. used an even larger sample from the same 1990 U.S. Census data on Chinese- and Spanish-speaking immigrants (2.3 million observations) [21] . Fitting lowess curves, no discontinuities in the aoa – ua slope could be detected. Moreover, the authors found that piecewise linear regression models, i.e. regression models containing a parameter that allows a sudden drop in the curve or a change of its slope, did not provide a better fit to the data than did an ordinary regression model without such a parameter.

To sum up, I have argued at length that regression approaches are superior to group mean and correlation coefficient comparisons for the purposes of testing the ‘flattened slope’ prediction. Acknowledging the reservations vis-à-vis self-estimated ua s, we still find that while the relationship between aoa and ua is not necessarily perfectly linear in the studies discussed, the data do not lend unequivocal support to this prediction. In the following section, I will reanalyse data from a recent empirical paper on the cph by DeKeyser et al. [44] . The first goal of this reanalysis is to further illustrate some of the statistical fallacies encountered in cph studies. Second, by making the computer code available I hope to demonstrate how the relevant regression models, viz. piecewise regression models, can be fitted and how the aoa representing the optimal breakpoint can be identified. Lastly, the findings of this reanalysis will contribute to our understanding of how aoa affects ua as measured using a gjt .

Summary of DeKeyser et al. (2010)

I chose to reanalyse a recent empirical paper on the cph by DeKeyser et al. [44] (henceforth DK et al.). This paper lends itself well to a reanalysis since it exhibits two highly commendable qualities: the authors spell out their hypotheses lucidly and provide detailed numerical and graphical data descriptions. Moreover, the paper's lead author is very clear on what constitutes a necessary condition for accepting the cph : a non-linearity in the age of onset of acquisition ( aoa )–ultimate attainment ( ua ) function, with ua declining less strongly as a function of aoa in older, post- cp arrivals compared to younger arrivals [14] , [22] . Lastly, it claims to have found cross-linguistic evidence from two parallel studies backing the cph and should therefore be an unsuspected source to cph proponents.

The authors set out to test the following hypotheses:

• Hypothesis 1: For both the L2 English and the L2 Hebrew group, the slope of the age of arrival–ultimate attainment function will not be linear throughout the lifespan, but will instead show a marked flattening between adolescence and adulthood.
• Hypothesis 2: The relationship between aptitude and ultimate attainment will differ markedly for the young and older arrivals, with significance only for the latter. (DK et al., p. 417)

Both hypotheses were purportedly confirmed, which in the authors' view provides evidence in favour of cph . The problem with this conclusion, however, is that it is based on a comparison of correlation coefficients. As I have argued above, correlation coefficients are not to be confused with regression coefficients and cannot be used to directly address research hypotheses concerning slopes, such as Hypothesis 1. In what follows, I will reanalyse the relationship between DK et al.'s aoa and gjt data in order to address Hypothesis 1. Additionally, I will lay bare a problem with the way in which Hypothesis 2 was addressed. The extracted data and the computer code used for the reanalysis are provided as supplementary materials, allowing anyone interested to scrutinise and easily reproduce my whole analysis and carry out their own computations (see ‘supporting information’).

Data extraction

In order to verify whether we did in fact extract the data points to a satisfactory degree of accuracy, I computed summary statistics for the extracted aoa and gjt data and checked these against the descriptive statistics provided by DK et al. (pp. 421 and 427). These summary statistics for the extracted data are presented in Table 1 . In addition, I computed the correlation coefficients for the aoa – gjt relationship for the whole aoa range and for aoa -defined subgroups and checked these coefficients against those reported by DK et al. (pp. 423 and 428). The correlation coefficients computed using the extracted data are presented in Table 2 . Both checks strongly suggest the extracted data to be virtually identical to the original data, and Dr DeKeyser confirmed this to be the case in response to an earlier draft of the present paper (personal communication, 6 May 2013).

https://doi.org/10.1371/journal.pone.0069172.t001

https://doi.org/10.1371/journal.pone.0069172.t002

Results and Discussion

Modelling the link between age of onset of acquisition and ultimate attainment.

I first replotted the aoa and gjt data we extracted from DK et al.'s scatterplots and added non-parametric scatterplot smoothers in order to investigate whether any changes in slope in the aoa – gjt function could be revealed, as per Hypothesis 1. Figures 3 and 4 show this not to be the case. Indeed, simple linear regression models that model gjt as a function of aoa provide decent fits for both the North America and the Israel data, explaining 65% and 63% of the variance in gjt scores, respectively. The parameters of these models are given in Table 3 .

The trend line is a non-parametric scatterplot smoother. The scatterplot itself is a near-perfect replication of DK et al.'s Fig. 1.

https://doi.org/10.1371/journal.pone.0069172.g003

The trend line is a non-parametric scatterplot smoother. The scatterplot itself is a near-perfect replication of DK et al.'s Fig. 5.

https://doi.org/10.1371/journal.pone.0069172.g004

https://doi.org/10.1371/journal.pone.0069172.t003

To ensure that both segments are joined at the breakpoint, the predictor variable is first centred at the breakpoint value, i.e. the breakpoint value is subtracted from the original predictor variable values. For a blow-by-blow account of how such models can be fitted in r , I refer to an example analysis by Baayen [55, pp. 214–222].

Solid: regression with breakpoint at aoa 18 (dashed lines represent its 95% confidence interval); dot-dash: regression without breakpoint.

https://doi.org/10.1371/journal.pone.0069172.g005

Solid: regression with breakpoint at aoa 18 (dashed lines represent its 95% confidence interval); dot-dash (hardly visible due to near-complete overlap): regression without breakpoint.

https://doi.org/10.1371/journal.pone.0069172.g006

https://doi.org/10.1371/journal.pone.0069172.t004

https://doi.org/10.1371/journal.pone.0069172.g007

Solid: regression with breakpoint at aoa 16 (dashed lines represent its 95% confidence interval); dot-dash: regression without breakpoint.

https://doi.org/10.1371/journal.pone.0069172.g008

Solid: regression with breakpoint at aoa 6 (dashed lines represent its 95% confidence interval); dot-dash (hardly visible due to near-complete overlap): regression without breakpoint.

https://doi.org/10.1371/journal.pone.0069172.g009

https://doi.org/10.1371/journal.pone.0069172.t005

https://doi.org/10.1371/journal.pone.0069172.t006

https://doi.org/10.1371/journal.pone.0069172.t007

https://doi.org/10.1371/journal.pone.0069172.t008

In sum, a regression model that allows for changes in the slope of the the aoa – gjt function to account for putative critical period effects provides a somewhat better fit to the North American data than does an everyday simple regression model. The improvement in model fit is marginal, however, and including a breakpoint does not result in any detectable improvement of model fit to the Israel data whatsoever. Breakpoint models therefore fail to provide solid cross-linguistic support in favour of critical period effects: across both data sets, gjt can satisfactorily be modelled as a linear function of aoa .

On partialling out ‘age at testing’

As I have argued above, correlation coefficients cannot be used to test hypotheses about slopes. When the correct procedure is carried out on DK et al.'s data, no cross-linguistically robust evidence for changes in the aoa – gjt function was found. In addition to comparing the zero-order correlations between aoa and gjt , however, DK et al. computed partial correlations in which the variance in aoa associated with the participants' age at testing ( aat ; a potentially confounding variable) was filtered out. They found that these partial correlations between aoa and gjt , which are given in Table 9 , differed between age groups in that they are stronger for younger than for older participants. This, DK et al. argue, constitutes additional evidence in favour of the cph . At this point, I can no longer provide my own analysis of DK et al.'s data seeing as the pertinent data points were not plotted. Nevertheless, the detailed descriptions by DK et al. strongly suggest that the use of these partial correlations is highly problematic. Most importantly, and to reiterate, correlations (whether zero-order or partial ones) are actually of no use when testing hypotheses concerning slopes. Still, one may wonder why the partial correlations differ across age groups. My surmise is that these differences are at least partly the by-product of an imbalance in the sampling procedure.

https://doi.org/10.1371/journal.pone.0069172.t009

The upshot of this brief discussion is that the partial correlation differences reported by DK et al. are at least partly the result of an imbalance in the sampling procedure: aoa and aat were simply less intimately tied for the young arrivals in the North America study than for the older arrivals with L2 English or for all of the L2 Hebrew participants. In an ideal world, we would like to fix aat or ascertain that it at most only weakly correlates with aoa . This, however, would result in a strong correlation between aoa and another potential confound variable, length of residence in the L2 environment, bringing us back to square one. Allowing for only moderate correlations between aoa and aat might improve our predicament somewhat, but even in that case, we should tread lightly when making inferences on the basis of statistical control procedures [61] .

On estimating the role of aptitude

Having shown that Hypothesis 1 could not be confirmed, I now turn to Hypothesis 2, which predicts a differential role of aptitude for ua in sla in different aoa groups. More specifically, it states that the correlation between aptitude and gjt performance will be significant only for older arrivals. The correlation coefficients of the relationship between aptitude and gjt are presented in Table 10 .

https://doi.org/10.1371/journal.pone.0069172.t010

The problem with both the wording of Hypothesis 2 and the way in which it is addressed is the following: it is assumed that a variable has a reliably different effect in different groups when the effect reaches significance in one group but not in the other. This logic is fairly widespread within several scientific disciplines (see e.g. [62] for a discussion). Nonetheless, it is demonstrably fallacious [63] . Here we will illustrate the fallacy for the specific case of comparing two correlation coefficients.

Apart from not being replicated in the North America study, does this difference actually show anything? I contend that it does not: what is of interest are not so much the correlation coefficients, but rather the interactions between aoa and aptitude in models predicting gjt . These interactions could be investigated by fitting a multiple regression model in which the postulated cp breakpoint governs the slope of both aoa and aptitude. If such a model provided a substantially better fit to the data than a model without a breakpoint for the aptitude slope and if the aptitude slope changes in the expected direction (i.e. a steeper slope for post- cp than for younger arrivals) for different L1–L2 pairings, only then would this particular prediction of the cph be borne out.

Using data extracted from a paper reporting on two recent studies that purport to provide evidence in favour of the cph and that, according to its authors, represent a major improvement over earlier studies (DK et al., p. 417), it was found that neither of its two hypotheses were actually confirmed when using the proper statistical tools. As a matter of fact, the gjt scores continue to decline at essentially the same rate even beyond the end of the putative critical period. According to the paper's lead author, such a finding represents a serious problem to his conceptualisation of the cph [14] ). Moreover, although modelling a breakpoint representing the end of a cp at aoa 16 may improve the statistical model slightly in study on learners of English in North America, the study on learners of Hebrew in Israel fails to confirm this finding. In fact, even if we were to accept the optimal breakpoint computed for the Israel study, it lies at aoa 6 and is associated with a different geometrical pattern.

Diverging age trends in parallel studies with participants with different L2s have similarly been reported by Birdsong and Molis [26] and are at odds with an L2-independent cph . One parsimonious explanation of such conflicting age trends may be that the overall, cross-linguistic age trend is in fact linear, but that fluctuations in the data (due to factors unaccounted for or randomness) may sometimes give rise to a ‘stretched L’-shaped pattern ( Figure 1, left panel ) and sometimes to a ‘stretched 7’-shaped pattern ( Figure 1 , middle panel; see also [66] for a similar comment).

Importantly, the criticism that DeKeyser and Larsson-Hall levy against two studies reporting findings similar to the present [48] , [49] , viz. that the data consisted of self-ratings of questionable validity [14] , does not apply to the present data set. In addition, DK et al. did not exclude any outliers from their analyses, so I assume that DeKeyser and Larsson-Hall's criticism [14] of Birdsong and Molis's study [26] , i.e. that the findings were due to the influence of outliers, is not applicable to the present data either. For good measure, however, I refitted the regression models with and without breakpoints after excluding one potentially problematic data point per model. The following data points had absolute standardised residuals larger than 2.5 in the original models without breakpoints as well as in those with breakpoints: the participant with aoa 17 and a gjt score of 125 in the North America study and the participant with aoa 12 and a gjt score of 117 in the Israel study. The resultant models were virtually identical to the original models (see Script S1 ). Furthermore, the aoa variable was sufficiently fine-grained and the aoa – gjt curve was not ‘presmoothed’ by the prior aggregation of gjt across parts of the aoa range (see [51] for such a criticism of another study). Lastly, seven of the nine “problems with supposed counter-evidence” to the cph discussed by Long [5] do not apply either, viz. (1) “[c]onfusion of rate and ultimate attainment”, (2) “[i]nappropriate choice of subjects”, (3) “[m]easurement of AO”, (4) “[l]eading instructions to raters”, (6) “[u]se of markedly non-native samples making near-native samples more likely to sound native to raters”, (7) “[u]nreliable or invalid measures”, and (8) “[i]nappropriate L1–L2 pairings”. Problem No. 5 (“Assessments based on limited samples and/or “language-like” behavior”) may be apropos given that only gjt data were used, leaving open the theoretical possibility that other measures might have yielded a different outcome. Finally, problem No. 9 (“Faulty interpretation of statistical patterns”) is, of course, precisely what I have turned the spotlights on.

Conclusions

The critical period hypothesis remains a hotly contested issue in the psycholinguistics of second-language acquisition. Discussions about the impact of empirical findings on the tenability of the cph generally revolve around the reliability of the data gathered (e.g. [5] , [14] , [22] , [52] , [67] , [68] ) and such methodological critiques are of course highly desirable. Furthermore, the debate often centres on the question of exactly what version of the cph is being vindicated or debunked. These versions differ mainly in terms of its scope, specifically with regard to the relevant age span, setting and language area, and the testable predictions they make. But even when the cph 's scope is clearly demarcated and its main prediction is spelt out lucidly, the issue remains to what extent the empirical findings can actually be marshalled in support of the relevant cph version. As I have shown in this paper, empirical data have often been taken to support cph versions predicting that the relationship between age of acquisition and ultimate attainment is not strictly linear, even though the statistical tools most commonly used (notably group mean and correlation coefficient comparisons) were, crudely put, irrelevant to this prediction. Methods that are arguably valid, e.g. piecewise regression and scatterplot smoothing, have been used in some studies [21] , [26] , [49] , but these studies have been criticised on other grounds. To my knowledge, such methods have never been used by scholars who explicitly subscribe to the cph .

I suspect that what may be going on is a form of ‘confirmation bias’ [69] , a cognitive bias at play in diverse branches of human knowledge seeking: Findings judged to be consistent with one's own hypothesis are hardly questioned, whereas findings inconsistent with one's own hypothesis are scrutinised much more strongly and criticised on all sorts of points [70] – [73] . My reanalysis of DK et al.'s recent paper may be a case in point. cph exponents used correlation coefficients to address their prediction about the slope of a function, as had been done in a host of earlier studies. Finding a result that squared with their expectations, they did not question the technical validity of their results, or at least they did not report this. (In fact, my reanalysis is actually a case in point in two respects: for an earlier draft of this paper, I had computed the optimal position of the breakpoints incorrectly, resulting in an insignificant improvement of model fit for the North American data rather than a borderline significant one. Finding a result that squared with my expectations, I did not question the technical validity of my results – until this error was kindly pointed out to me by Martijn Wieling (University of Tübingen).) That said, I am keen to point out that the statistical analyses in this particular paper, though suboptimal, are, as far as I could gather, reported correctly, i.e. the confirmation bias does not seem to have resulted in the blatant misreportings found elsewhere (see [74] for empirical evidence and discussion). An additional point to these authors' credit is that, apart from explicitly identifying their cph version's scope and making crystal-clear predictions, they present data descriptions that actually permit quantitative reassessments and have a history of doing so (e.g. the appendix in [8] ). This leads me to believe that they analysed their data all in good conscience and to hope that they, too, will conclude that their own data do not, in fact, support their hypothesis.

I end this paper on an upbeat note. Even though I have argued that the analytical tools employed in cph research generally leave much to be desired, the original data are, so I hope, still available. This provides researchers, cph supporters and sceptics alike, with an exciting opportunity to reanalyse their data sets using the tools outlined in the present paper and publish their findings at minimal cost of time and resources (for instance, as a comment to this paper). I would therefore encourage scholars to engage their old data sets and to communicate their analyses openly, e.g. by voluntarily publishing their data and computer code alongside their articles or comments. Ideally, cph supporters and sceptics would join forces to agree on a protocol for a high-powered study in order to provide a truly convincing answer to a core issue in sla .

Supporting Information

Dataset s1..

aoa and gjt data extracted from DeKeyser et al.'s North America study.

https://doi.org/10.1371/journal.pone.0069172.s001

Dataset S2.

aoa and gjt data extracted from DeKeyser et al.'s Israel study.

https://doi.org/10.1371/journal.pone.0069172.s002

Script with annotated R code used for the reanalysis. All add-on packages used can be installed from within R.

https://doi.org/10.1371/journal.pone.0069172.s003

Acknowledgments

I would like to thank Irmtraud Kaiser (University of Fribourg) for helping me to get an overview of the literature on the critical period hypothesis in second language acquisition. Thanks are also due to Martijn Wieling (currently University of Tübingen) for pointing out an error in the R code accompanying an earlier draft of this paper.

Author Contributions

Analyzed the data: JV. Wrote the paper: JV.

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Genie Wiley, the Feral Child

Tom Need / Getty Images

• Archaeology

• Ph.D., Psychology, Fielding Graduate University
• M.A., Psychology, Fielding Graduate University
• B.A., Film Studies, Cornell University

Genie Wiley (born April 1957) was a severely neglected and abused child who was discovered and taken into custody by authorities when she was 13 years old. While her circumstances until that point were undeniably tragic, they also presented an opportunity for psychologists, linguists, and other researchers to study psychosocial, emotional, and cognitive development in an individual who had suffered from severe social isolation and deprivation. In particular, the discovery of Genie presented an opportunity to study whether a child who was past the so-called "critical period" for language acquisition could learn to speak a first language.

Key Takeaways: Genie Wiley

• Genie Wiley was abused and neglected for over a decade until she was discovered in 1970 when she was 13 years old.
• Known as the feral child, Genie became an important subject of research. Of special interest was whether she could acquire language, as she was no longer within the "critical period" for language development.
• Genie's case presented an ethical dilemma between prioritizing her care or prioritizing research on her development.

Early Life and Discovery

The case of Genie Wiley came to light on November 4, 1970. Genie was discovered by a social worker when her mother, who was partially blind, went to apply for social services. Genie had been isolated in a small room starting at the age of 20 months until her discovery at 13 years and 9 months old. She spent most of her time naked and tied to a potty chair where she was given limited use of her hands and feet. She was completely cut off from any kind of stimulation. The windows were curtained and the door was kept closed. She was only fed cereal and baby food and wasn’t spoken to. Although she lived with her father, mother, and brother, her father and brother would only bark or growl at her and her mother was only permitted very brief interactions. Genie’s father was intolerant of noise, so no TV or radio was played in the house. If Genie made any noise, she was physically beaten.

Upon her discovery, Genie was admitted to Children’s Hospital of Los Angeles for evaluation. She was severely underdeveloped. She was thin and looked like a child of six or seven. She couldn’t stand up straight and could only walk with a hunched “bunny walk.” She was unable to chew, had trouble swallowing, and spat frequently. She was incontinent and mute. At first, the only words she recognized were her name and “sorry.” Testing shortly after she came to the hospital revealed that her social maturity and mental abilities were at the level of a one-year-old.

Genie didn’t walk at a normal age, so her father came to believe she was developmentally disabled. However, the researchers brought onto the case after Genie’s discovery found little evidence of this in her early history. It appeared she never suffered from brain damage, mental disability, or autism. Therefore, the impairments and developmental delays Genie exhibited upon being assessed were the result of the isolation and deprivation she was subjected to.

Both of Genie’s parents were charged with abuse , but Genie’s 70-year-old father committed suicide the day he was supposed to appear in court. The note he left said, “The world will never understand.”

The Rush to Research

Genie’s case drew media attention as well as great interest from the research community, which considered it a rare opportunity to discover whether it was possible for Genie to mentally develop after such severe deprivation. Researchers would never deliberately conduct deprivation experiments with people on moral grounds. So, Genie’s sad case was ripe for study. Genie was not the child’s real name, but the name given to the case in order to protect her privacy.

The National Institute of Mental Health (NIMH) provided funding for research and a team was assembled whose goal was to rehabilitate and study Genie’s progress. Genie soon learned basic social skills like using the toilet and dressing herself. She was fascinated by her environment and would study it intensely. She especially enjoyed visiting places outside the hospital. She was talented at nonverbal communication, but her ability to use language did not proceed rapidly. As a result, psychologist David Rigler decided to focus the research on Genie's language acquisition.

Language Acquisition

The discovery of Genie coincided with a debate about language acquisition in the scholarly community. Linguist Noam Chomsky, from the Massachusetts Institute of Technology, claimed humans are born with an innate ability to develop language. He believed language isn’t acquired because we learn it, but because it’s part of our genetic inheritance. Then, neuropsychologist Eric Lenneberg added a caveat to Chomsky’s ideas. Lenneberg agreed that humans are born with the ability to develop language, but suggested that if a language wasn’t acquired by puberty, it might never be. Lenneberg’s proposal was called the “critical period hypothesis.” Yet, there was no ability to test the theory until Genie came along.

Within the first seven months after her discovery, Genie learned many new words . She had even begun to speak but only in single words. By July 1971, Genie could put two words together and by November she could put together three. Despite signs of progress, Genie never learned to ask questions and she didn’t seem to understand the rules of grammar.

After beginning to speak in two-word phrases, normal children experience a language “explosion” a few weeks later in which speech develops quickly. Genie never experienced such an explosion. Her speech seemed to plateau at creating two to three-word strings, despite four years of additional work and research with her.

Genie demonstrated that it’s possible for an individual to learn some language after the critical period. Yet, her inability to learn grammar, which Chomsky believed was key to human language, indicated that passing the critical period was detrimental to the complete acquisition of a first language.

Arguments and Ethical Considerations

During Genie’s treatment, there were disputes amongst the members of her team. In the early days after her discovery, she entered her first foster home with her teacher Jean Butler. Butler claimed she felt that Genie was being subject to too many tests and attempted to make changes to Genie’s treatment. She wouldn’t allow the linguist Susan Curtiss or the psychologist James Kent into her house to see Genie. Other team members claimed Butler thought she could become famous through her work with Genie and didn’t want anyone else to get credit. Butler’s application to become Genie’s permanent foster parent was rejected about a month later.

Psychologist David Rigler and his wife Marilyn stepped in and fostered Genie for the next four years. They continued to work with her and let others continue their research throughout that time. However, Genie left the Riglers’ home after NIMH stopped funding the project due to problems with data collection.

Throughout the four years in which Genie was being tested and studied, there was debate about whether she could be a research subject and a rehabilitation patient at the same time. The ethics of the situation were murky.

In 1975, Genie’s mother regained custody after being acquitted of all charges of child abuse. Genie’s care quickly became too much for her to handle, though, so Genie began to bounce from foster home to foster home. She was once again subjected to abuse in those homes. Soon, she stopped talking and refused to open her mouth entirely.

Meanwhile, Genie’s mother filed a lawsuit against Genie’s team and the Children's Hospital alleging that the researchers prioritized testing Genie over her welfare. She contended that they pushed Genie to the point of exhaustion. The case was eventually settled but the debate continues. Some believe the researchers exploited Genie, and therefore, didn’t help her as much as they could have. However, the researchers say they treated Genie to the best of their ability.

Historian and psychologist Harlan Lane points out that “there's an ethical dilemma in this kind of research. If you want to do rigorous science, then Genie's interests are going to come second some of the time. If you only care about helping Genie, then you wouldn't do a lot of the scientific research. So, what are you going to do?”

Genie Today

Genie is believed to be alive and living in an adult foster home as a ward of the state of California. While the linguist who worked with Genie, Susan Curtiss, has attempted to get in touch with her, she’s been repeatedly rebuffed. However, she said that when she calls the authorities, they inform her that Genie is well. Yet, when journalist Russ Rymer saw Genie at her 27 th birthday party, he painted a much bleaker picture. Similarly, psychiatrist Jay Shurley, who was at Genie’s 27 th and 29 th birthdays, claimed Genie was depressed and had withdrawn into herself.

• Cherry, Kendra. “Overview of Feral Child Genie Wiley.” Verywell Mind , 9 March 2019. https://www.verywellmind.com/genie-the-story-of-the-wild-child-2795241
• Pines, Maya. "The Civilizing of Genie." Teaching English Through the Disciplines: Psychology , edited by Loretta F. Kasper. Whittier Publications, 1997. http://kccesl.tripod.com/genie.html
• NOVA. "Secret of the Wild Child." PBS , 4 March, 1997. https://www.pbs.org/wgbh/nova/transcripts/2112gchild.html
• Fromkin, Victoria, Krashen, Stephen, Curtiss, Susan, Rigler, David, and Rigler, Marilyn. "The Development of Language in Genie: A Case of Language Acquisition Beyond the 'Critical Period'" Brain and Language , vol. 1, no. 1, 1974, pp. 81-107. http://dx.doi.org/10.1016/0093-934X(74)90027-3
• Carroll, Rory. "Starved, Tortured, Forgotten: Genie, the Feral Child Who Left a Mark on Researchers." The Guardian , 14 July 2016. https://www.theguardian.com/society/2016/jul/14/genie-feral-child-los-angeles-researchers
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Genie Wiley’s Case Study: Implications for Critical Period Hypothesis and Child Abuse and Neglect

Genie wiley- case study.

Genie Wiley was a young girl who was kept in severe isolation and abuse for most of her childhood, restricting her ability to learn language, social skills, and normal emotional expressions. As a result, she suffered from severe mental and physical disabilities that lasted throughout her life. Her case study is often cited in studies related to the critical period hypothesis and the importance of early childhood experiences on cognitive and emotional development.

1) What is the critical period hypothesis?

The critical period hypothesis is a theory that states that there is a time during early childhood when the brain is most susceptible to developing certain cognitive and physical abilities. It is believed that if experiences critical to development do not occur during this period, it may be difficult or impossible for individuals to acquire certain skills later in life.

2) How did Genie’s early childhood experiences affect her cognitive development?

Genie’s early childhood experiences had a significant impact on her cognitive development. She was deprived of language stimulation and normal social interactions during her crucial developmental years, resulting in a lack of basic cognitive and social skills. As a result, she suffered from severe developmental delays, intellectual disabilities, and a limited ability to communicate with verbal language. Genie’s case is often used to study the effects of deprivation, neglect, and abuse on child development.

3) How might Genie’s case study inform our understanding of child abuse and neglect?

Genie’s case highlights the severe consequences of child abuse and neglect on a child’s cognitive, social, and emotional development. It is evident from her case that prolonged deprivation of normal social interactions can have a lasting impact on a child’s cognitive abilities. Her case emphasizes the importance of providing children with safe and nurturing environments where they can receive proper care and positive stimulation, particularly during their early childhood years.

4) What might have been done differently to help Genie during her childhood years?

In hindsight, several things could have been done differently to help Genie during her childhood years. She needed a safe, nurturing, and stimulating environment that provided her with love, attention, and social interaction. If she had been discovered earlier, she could have been placed in a foster home where she could have received specialized support and therapy. Furthermore, social workers and psychologists could have provided language and cognitive therapy to help her overcome her developmental setbacks.

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The Critical Period Hypothesis in Second Language Acquisition: A Statistical Critique and a Reanalysis

Jan vanhove.

Department of Multilingualism, University of Fribourg, Fribourg, Switzerland

Analyzed the data: JV. Wrote the paper: JV.

Associated Data

In second language acquisition research, the critical period hypothesis ( cph ) holds that the function between learners' age and their susceptibility to second language input is non-linear. This paper revisits the indistinctness found in the literature with regard to this hypothesis's scope and predictions. Even when its scope is clearly delineated and its predictions are spelt out, however, empirical studies–with few exceptions–use analytical (statistical) tools that are irrelevant with respect to the predictions made. This paper discusses statistical fallacies common in cph research and illustrates an alternative analytical method (piecewise regression) by means of a reanalysis of two datasets from a 2010 paper purporting to have found cross-linguistic evidence in favour of the cph . This reanalysis reveals that the specific age patterns predicted by the cph are not cross-linguistically robust. Applying the principle of parsimony, it is concluded that age patterns in second language acquisition are not governed by a critical period. To conclude, this paper highlights the role of confirmation bias in the scientific enterprise and appeals to second language acquisition researchers to reanalyse their old datasets using the methods discussed in this paper. The data and R commands that were used for the reanalysis are provided as supplementary materials.

Introduction

In the long term and in immersion contexts, second-language (L2) learners starting acquisition early in life – and staying exposed to input and thus learning over several years or decades – undisputedly tend to outperform later learners. Apart from being misinterpreted as an argument in favour of early foreign language instruction, which takes place in wholly different circumstances, this general age effect is also sometimes taken as evidence for a so-called ‘critical period’ ( cp ) for second-language acquisition ( sla ). Derived from biology, the cp concept was famously introduced into the field of language acquisition by Penfield and Roberts in 1959 [1] and was refined by Lenneberg eight years later [2] . Lenneberg argued that language acquisition needed to take place between age two and puberty – a period which he believed to coincide with the lateralisation process of the brain. (More recent neurological research suggests that different time frames exist for the lateralisation process of different language functions. Most, however, close before puberty [3] .) However, Lenneberg mostly drew on findings pertaining to first language development in deaf children, feral children or children with serious cognitive impairments in order to back up his claims. For him, the critical period concept was concerned with the implicit “automatic acquisition” [2, p. 176] in immersion contexts and does not preclude the possibility of learning a foreign language after puberty, albeit with much conscious effort and typically less success.

sla research adopted the critical period hypothesis ( cph ) and applied it to second and foreign language learning, resulting in a host of studies. In its most general version, the cph for sla states that the ‘susceptibility’ or ‘sensitivity’ to language input varies as a function of age, with adult L2 learners being less susceptible to input than child L2 learners. Importantly, the age–susceptibility function is hypothesised to be non-linear. Moving beyond this general version, we find that the cph is conceptualised in a multitude of ways [4] . This state of affairs requires scholars to make explicit their theoretical stance and assumptions [5] , but has the obvious downside that critical findings risk being mitigated as posing a problem to only one aspect of one particular conceptualisation of the cph , whereas other conceptualisations remain unscathed. This overall vagueness concerns two areas in particular, viz. the delineation of the cph 's scope and the formulation of testable predictions. Delineating the scope and formulating falsifiable predictions are, needless to say, fundamental stages in the scientific evaluation of any hypothesis or theory, but the lack of scholarly consensus on these points seems to be particularly pronounced in the case of the cph . This article therefore first presents a brief overview of differing views on these two stages. Then, once the scope of their cph version has been duly identified and empirical data have been collected using solid methods, it is essential that researchers analyse the data patterns soundly in order to assess the predictions made and that they draw justifiable conclusions from the results. As I will argue in great detail, however, the statistical analysis of data patterns as well as their interpretation in cph research – and this includes both critical and supportive studies and overviews – leaves a great deal to be desired. Reanalysing data from a recent cph -supportive study, I illustrate some common statistical fallacies in cph research and demonstrate how one particular cph prediction can be evaluated.

Delineating the scope of the critical period hypothesis

First, the age span for a putative critical period for language acquisition has been delimited in different ways in the literature [4] . Lenneberg's critical period stretched from two years of age to puberty (which he posits at about 14 years of age) [2] , whereas other scholars have drawn the cutoff point at 12, 15, 16 or 18 years of age [6] . Unlike Lenneberg, most researchers today do not define a starting age for the critical period for language learning. Some, however, consider the possibility of the critical period (or a critical period for a specific language area, e.g. phonology) ending much earlier than puberty (e.g. age 9 years [1] , or as early as 12 months in the case of phonology [7] ).

Second, some vagueness remains as to the setting that is relevant to the cph . Does the critical period constrain implicit learning processes only, i.e. only the untutored language acquisition in immersion contexts or does it also apply to (at least partly) instructed learning? Most researchers agree on the former [8] , but much research has included subjects who have had at least some instruction in the L2.

Third, there is no consensus on what the scope of the cp is as far as the areas of language that are concerned. Most researchers agree that a cp is most likely to constrain the acquisition of pronunciation and grammar and, consequently, these are the areas primarily looked into in studies on the cph [9] . Some researchers have also tried to define distinguishable cp s for the different language areas of phonetics, morphology and syntax and even for lexis (see [10] for an overview).

Fourth and last, research into the cph has focused on ‘ultimate attainment’ ( ua ) or the ‘final’ state of L2 proficiency rather than on the rate of learning. From research into the rate of acquisition (e.g. [11] – [13] ), it has become clear that the cph cannot hold for the rate variable. In fact, it has been observed that adult learners proceed faster than child learners at the beginning stages of L2 acquisition. Though theoretical reasons for excluding the rate can be posited (the initial faster rate of learning in adults may be the result of more conscious cognitive strategies rather than to less conscious implicit learning, for instance), rate of learning might from a different perspective also be considered an indicator of ‘susceptibility’ or ‘sensitivity’ to language input. Nevertheless, contemporary sla scholars generally seem to concur that ua and not rate of learning is the dependent variable of primary interest in cph research. These and further scope delineation problems relevant to cph research are discussed in more detail by, among others, Birdsong [9] , DeKeyser and Larson-Hall [14] , Long [10] and Muñoz and Singleton [6] .

Formulating testable hypotheses

Once the relevant cph 's scope has satisfactorily been identified, clear and testable predictions need to be drawn from it. At this stage, the lack of consensus on what the consequences or the actual observable outcome of a cp would have to look like becomes evident. As touched upon earlier, cph research is interested in the end state or ‘ultimate attainment’ ( ua ) in L2 acquisition because this “determines the upper limits of L2 attainment” [9, p. 10]. The range of possible ultimate attainment states thus helps researchers to explore the potential maximum outcome of L2 proficiency before and after the putative critical period.

One strong prediction made by some cph exponents holds that post- cp learners cannot reach native-like L2 competences. Identifying a single native-like post- cp L2 learner would then suffice to falsify all cph s making this prediction. Assessing this prediction is difficult, however, since it is not clear what exactly constitutes sufficient nativelikeness, as illustrated by the discussion on the actual nativelikeness of highly accomplished L2 speakers [15] , [16] . Indeed, there exists a real danger that, in a quest to vindicate the cph , scholars set the bar for L2 learners to match monolinguals increasingly higher – up to Swiftian extremes. Furthermore, the usefulness of comparing the linguistic performance in mono- and bilinguals has been called into question [6] , [17] , [18] . Put simply, the linguistic repertoires of mono- and bilinguals differ by definition and differences in the behavioural outcome will necessarily be found, if only one digs deep enough.

A second strong prediction made by cph proponents is that the function linking age of acquisition and ultimate attainment will not be linear throughout the whole lifespan. Before discussing how this function would have to look like in order for it to constitute cph -consistent evidence, I point out that the ultimate attainment variable can essentially be considered a cumulative measure dependent on the actual variable of interest in cph research, i.e. susceptibility to language input, as well as on such other factors like duration and intensity of learning (within and outside a putative cp ) and possibly a number of other influencing factors. To elaborate, the behavioural outcome, i.e. ultimate attainment, can be assumed to be integrative to the susceptibility function, as Newport [19] correctly points out. Other things being equal, ultimate attainment will therefore decrease as susceptibility decreases. However, decreasing ultimate attainment levels in and by themselves represent no compelling evidence in favour of a cph . The form of the integrative curve must therefore be predicted clearly from the susceptibility function. Additionally, the age of acquisition–ultimate attainment function can take just about any form when other things are not equal, e.g. duration of learning (Does learning last up until time of testing or only for a more or less constant number of years or is it dependent on age itself?) or intensity of learning (Do learners always learn at their maximum susceptibility level or does this intensity vary as a function of age, duration, present attainment and motivation?). The integral of the susceptibility function could therefore be of virtually unlimited complexity and its parameters could be adjusted to fit any age of acquisition–ultimate attainment pattern. It seems therefore astonishing that the distinction between level of sensitivity to language input and level of ultimate attainment is rarely made in the literature. Implicitly or explicitly [20] , the two are more or less equated and the same mathematical functions are expected to describe the two variables if observed across a range of starting ages of acquisition.

But even when the susceptibility and ultimate attainment variables are equated, there remains controversy as to what function linking age of onset of acquisition and ultimate attainment would actually constitute evidence for a critical period. Most scholars agree that not any kind of age effect constitutes such evidence. More specifically, the age of acquisition–ultimate attainment function would need to be different before and after the end of the cp [9] . According to Birdsong [9] , three basic possible patterns proposed in the literature meet this condition. These patterns are presented in Figure 1 . The first pattern describes a steep decline of the age of onset of acquisition ( aoa )–ultimate attainment ( ua ) function up to the end of the cp and a practically non-existent age effect thereafter. Pattern 2 is an “unconventional, although often implicitly invoked” [9, p. 17] notion of the cp function which contains a period of peak attainment (or performance at ceiling), i.e. performance does not vary as a function of age, which is often referred to as a ‘window of opportunity’. This time span is followed by an unbounded decline in ua depending on aoa . Pattern 3 includes characteristics of patterns 1 and 2. At the beginning of the aoa range, performance is at ceiling. The next segment is a downward slope in the age function which ends when performance reaches its floor. Birdsong points out that all of these patterns have been reported in the literature. On closer inspection, however, he concludes that the most convincing function describing these age effects is a simple linear one. Hakuta et al. [21] sketch further theoretically possible predictions of the cph in which the mean performance drops drastically and/or the slope of the aoa – ua proficiency function changes at a certain point.

The graphs are based on based on Figure 2 in [9] .

Although several patterns have been proposed in the literature, it bears pointing out that the most common explicit prediction corresponds to Birdsong's first pattern, as exemplified by the following crystal-clear statement by DeKeyser, one of the foremost cph proponents:

[A] strong negative correlation between age of acquisition and ultimate attainment throughout the lifespan (or even from birth through middle age), the only age effect documented in many earlier studies, is not evidence for a critical period…[T]he critical period concept implies a break in the AoA–proficiency function, i.e., an age (somewhat variable from individual to individual, of course, and therefore an age range in the aggregate) after which the decline of success rate in one or more areas of language is much less pronounced and/or clearly due to different reasons. [22, p. 445].

DeKeyser and before him among others Johnson and Newport [23] thus conceptualise only one possible pattern which would speak in favour of a critical period: a clear negative age effect before the end of the critical period and a much weaker (if any) negative correlation between age and ultimate attainment after it. This ‘flattened slope’ prediction has the virtue of being much more tangible than the ‘potential nativelikeness’ prediction: Testing it does not necessarily require comparing the L2-learners to a native control group and thus effectively comparing apples and oranges. Rather, L2-learners with different aoa s can be compared amongst themselves without the need to categorise them by means of a native-speaker yardstick, the validity of which is inevitably going to be controversial [15] . In what follows, I will concern myself solely with the ‘flattened slope’ prediction, arguing that, despite its clarity of formulation, cph research has generally used analytical methods that are irrelevant for the purposes of actually testing it.

Inferring non-linearities in critical period research: An overview

Group mean or proportion comparisons

[T]he main differences can be found between the native group and all other groups – including the earliest learner group – and between the adolescence group and all other groups. However, neither the difference between the two childhood groups nor the one between the two adulthood groups reached significance, which indicates that the major changes in eventual perceived nativelikeness of L2 learners can be associated with adolescence. [15, p. 270].

Similar group comparisons aimed at investigating the effect of aoa on ua have been carried out by both cph advocates and sceptics (among whom Bialystok and Miller [25, pp. 136–139], Birdsong and Molis [26, p. 240], Flege [27, pp. 120–121], Flege et al. [28, pp. 85–86], Johnson [29, p. 229], Johnson and Newport [23, p. 78], McDonald [30, pp. 408–410] and Patowski [31, pp. 456–458]). To be clear, not all of these authors drew direct conclusions about the aoa – ua function on the basis of these groups comparisons, but their group comparisons have been cited as indicative of a cph -consistent non-continuous age effect, as exemplified by the following quote by DeKeyser [22] :

Where group comparisons are made, younger learners always do significantly better than the older learners. The behavioral evidence, then, suggests a non-continuous age effect with a “bend” in the AoA–proficiency function somewhere between ages 12 and 16. [22, p. 448].

The first problem with group comparisons like these and drawing inferences on the basis thereof is that they require that a continuous variable, aoa , be split up into discrete bins. More often than not, the boundaries between these bins are drawn in an arbitrary fashion, but what is more troublesome is the loss of information and statistical power that such discretisation entails (see [32] for the extreme case of dichotomisation). If we want to find out more about the relationship between aoa and ua , why throw away most of the aoa information and effectively reduce the ua data to group means and the variance in those groups?

Comparison of correlation coefficients

Correlation-based inferences about slope discontinuities have similarly explicitly been made by cph advocates and skeptics alike, e.g. Bialystok and Miller [25, pp. 136 and 140], DeKeyser and colleagues [22] , [44] and Flege et al. [45, pp. 166 and 169]. Others did not explicitly infer the presence or absence of slope differences from the subset correlations they computed (among others Birdsong and Molis [26] , DeKeyser [8] , Flege et al. [28] and Johnson [29] ), but their studies nevertheless featured in overviews discussing discontinuities [14] , [22] . Indeed, the most recent overview draws a strong conclusion about the validity of the cph 's ‘flattened slope’ prediction on the basis of these subset correlations:

In those studies where the two groups are described separately, the correlation is much higher for the younger than for the older group, except in Birdsong and Molis (2001) [ =  [26] , JV], where there was a ceiling effect for the younger group. This global picture from more than a dozen studies provides support for the non-continuity of the decline in the AoA–proficiency function, which all researchers agree is a hallmark of a critical period phenomenon. [22, p. 448].

In Johnson and Newport's specific case [23] , their correlation-based inference that ua levels off after puberty happened to be largely correct: the gjt scores are more or less randomly distributed around a near-horizontal trend line [26] . Ultimately, however, it rests on the fallacy of confusing correlation coefficients with slopes, which seriously calls into question conclusions such as DeKeyser's (cf. the quote above).

It can then straightforwardly be deduced that, other things equal, the aoa – ua correlation in the older group decreases as the ua variance in the older group increases relative to the ua variance in the younger group (Eq. 3).

Lower correlation coefficients in older aoa groups may therefore be largely due to differences in ua variance, which have been reported in several studies [23] , [26] , [28] , [29] (see [46] for additional references). Greater variability in ua with increasing age is likely due to factors other than age proper [47] , such as the concomitant greater variability in exposure to literacy, degree of education, motivation and opportunity for language use, and by itself represents evidence neither in favour of nor against the cph .

Regression approaches

Having demonstrated that neither group mean or proportion comparisons nor correlation coefficient comparisons can directly address the ‘flattened slope’ prediction, I now turn to the studies in which regression models were computed with aoa as a predictor variable and ua as the outcome variable. Once again, this category of studies is not mutually exclusive with the two categories discussed above.

In a large-scale study using self-reports and approximate aoa s derived from a sample of the 1990 U.S. Census, Stevens found that the probability with which immigrants from various countries stated that they spoke English ‘very well’ decreased curvilinearly as a function of aoa [48] . She noted that this development is similar to the pattern found by Johnson and Newport [23] but that it contains no indication of an “abruptly defined ‘critical’ or sensitive period in L2 learning” [48, p. 569]. However, she modelled the self-ratings using an ordinal logistic regression model in which the aoa variable was logarithmically transformed. Technically, this is perfectly fine, but one should be careful not to read too much into the non-linear curves found. In logistic models, the outcome variable itself is modelled linearly as a function of the predictor variables and is expressed in log-odds. In order to compute the corresponding probabilities, these log-odds are transformed using the logistic function. Consequently, even if the model is specified linearly, the predicted probabilities will not lie on a perfectly straight line when plotted as a function of any one continuous predictor variable. Similarly, when the predictor variable is first logarithmically transformed and then used to linearly predict an outcome variable, the function linking the predicted outcome variables and the untransformed predictor variable is necessarily non-linear. Thus, non-linearities follow naturally from Stevens's model specifications. Moreover, cph -consistent discontinuities in the aoa – ua function cannot be found using her model specifications as they did not contain any parameters allowing for this.

Using data similar to Stevens's, Bialystok and Hakuta found that the link between the self-rated English competences of Chinese- and Spanish-speaking immigrants and their aoa could be described by a straight line [49] . In contrast to Stevens, Bialystok and Hakuta used a regression-based method allowing for changes in the function's slope, viz. locally weighted scatterplot smoothing ( lowess ). Informally, lowess is a non-parametrical method that relies on an algorithm that fits the dependent variable for small parts of the range of the independent variable whilst guaranteeing that the overall curve does not contain sudden jumps (for technical details, see [50] ). Hakuta et al. used an even larger sample from the same 1990 U.S. Census data on Chinese- and Spanish-speaking immigrants (2.3 million observations) [21] . Fitting lowess curves, no discontinuities in the aoa – ua slope could be detected. Moreover, the authors found that piecewise linear regression models, i.e. regression models containing a parameter that allows a sudden drop in the curve or a change of its slope, did not provide a better fit to the data than did an ordinary regression model without such a parameter.

To sum up, I have argued at length that regression approaches are superior to group mean and correlation coefficient comparisons for the purposes of testing the ‘flattened slope’ prediction. Acknowledging the reservations vis-à-vis self-estimated ua s, we still find that while the relationship between aoa and ua is not necessarily perfectly linear in the studies discussed, the data do not lend unequivocal support to this prediction. In the following section, I will reanalyse data from a recent empirical paper on the cph by DeKeyser et al. [44] . The first goal of this reanalysis is to further illustrate some of the statistical fallacies encountered in cph studies. Second, by making the computer code available I hope to demonstrate how the relevant regression models, viz. piecewise regression models, can be fitted and how the aoa representing the optimal breakpoint can be identified. Lastly, the findings of this reanalysis will contribute to our understanding of how aoa affects ua as measured using a gjt .

Summary of DeKeyser et al. (2010)

I chose to reanalyse a recent empirical paper on the cph by DeKeyser et al. [44] (henceforth DK et al.). This paper lends itself well to a reanalysis since it exhibits two highly commendable qualities: the authors spell out their hypotheses lucidly and provide detailed numerical and graphical data descriptions. Moreover, the paper's lead author is very clear on what constitutes a necessary condition for accepting the cph : a non-linearity in the age of onset of acquisition ( aoa )–ultimate attainment ( ua ) function, with ua declining less strongly as a function of aoa in older, post- cp arrivals compared to younger arrivals [14] , [22] . Lastly, it claims to have found cross-linguistic evidence from two parallel studies backing the cph and should therefore be an unsuspected source to cph proponents.

The authors set out to test the following hypotheses:

• Hypothesis 1: For both the L2 English and the L2 Hebrew group, the slope of the age of arrival–ultimate attainment function will not be linear throughout the lifespan, but will instead show a marked flattening between adolescence and adulthood.
• Hypothesis 2: The relationship between aptitude and ultimate attainment will differ markedly for the young and older arrivals, with significance only for the latter. (DK et al., p. 417)

Both hypotheses were purportedly confirmed, which in the authors' view provides evidence in favour of cph . The problem with this conclusion, however, is that it is based on a comparison of correlation coefficients. As I have argued above, correlation coefficients are not to be confused with regression coefficients and cannot be used to directly address research hypotheses concerning slopes, such as Hypothesis 1. In what follows, I will reanalyse the relationship between DK et al.'s aoa and gjt data in order to address Hypothesis 1. Additionally, I will lay bare a problem with the way in which Hypothesis 2 was addressed. The extracted data and the computer code used for the reanalysis are provided as supplementary materials, allowing anyone interested to scrutinise and easily reproduce my whole analysis and carry out their own computations (see ‘supporting information’).

Data extraction

In order to verify whether we did in fact extract the data points to a satisfactory degree of accuracy, I computed summary statistics for the extracted aoa and gjt data and checked these against the descriptive statistics provided by DK et al. (pp. 421 and 427). These summary statistics for the extracted data are presented in Table 1 . In addition, I computed the correlation coefficients for the aoa – gjt relationship for the whole aoa range and for aoa -defined subgroups and checked these coefficients against those reported by DK et al. (pp. 423 and 428). The correlation coefficients computed using the extracted data are presented in Table 2 . Both checks strongly suggest the extracted data to be virtually identical to the original data, and Dr DeKeyser confirmed this to be the case in response to an earlier draft of the present paper (personal communication, 6 May 2013).

Results and Discussion

Modelling the link between age of onset of acquisition and ultimate attainment.

I first replotted the aoa and gjt data we extracted from DK et al.'s scatterplots and added non-parametric scatterplot smoothers in order to investigate whether any changes in slope in the aoa – gjt function could be revealed, as per Hypothesis 1. Figures 3 and ​ and4 4 show this not to be the case. Indeed, simple linear regression models that model gjt as a function of aoa provide decent fits for both the North America and the Israel data, explaining 65% and 63% of the variance in gjt scores, respectively. The parameters of these models are given in Table 3 .

The trend line is a non-parametric scatterplot smoother. The scatterplot itself is a near-perfect replication of DK et al.'s Fig. 1.

The trend line is a non-parametric scatterplot smoother. The scatterplot itself is a near-perfect replication of DK et al.'s Fig. 5.

To ensure that both segments are joined at the breakpoint, the predictor variable is first centred at the breakpoint value, i.e. the breakpoint value is subtracted from the original predictor variable values. For a blow-by-blow account of how such models can be fitted in r , I refer to an example analysis by Baayen [55, pp. 214–222].

Solid: regression with breakpoint at aoa 18 (dashed lines represent its 95% confidence interval); dot-dash: regression without breakpoint.

Solid: regression with breakpoint at aoa 18 (dashed lines represent its 95% confidence interval); dot-dash (hardly visible due to near-complete overlap): regression without breakpoint.

Solid: regression with breakpoint at aoa 16 (dashed lines represent its 95% confidence interval); dot-dash: regression without breakpoint.

Solid: regression with breakpoint at aoa 6 (dashed lines represent its 95% confidence interval); dot-dash (hardly visible due to near-complete overlap): regression without breakpoint.

In sum, a regression model that allows for changes in the slope of the the aoa – gjt function to account for putative critical period effects provides a somewhat better fit to the North American data than does an everyday simple regression model. The improvement in model fit is marginal, however, and including a breakpoint does not result in any detectable improvement of model fit to the Israel data whatsoever. Breakpoint models therefore fail to provide solid cross-linguistic support in favour of critical period effects: across both data sets, gjt can satisfactorily be modelled as a linear function of aoa .

On partialling out ‘age at testing’

As I have argued above, correlation coefficients cannot be used to test hypotheses about slopes. When the correct procedure is carried out on DK et al.'s data, no cross-linguistically robust evidence for changes in the aoa – gjt function was found. In addition to comparing the zero-order correlations between aoa and gjt , however, DK et al. computed partial correlations in which the variance in aoa associated with the participants' age at testing ( aat ; a potentially confounding variable) was filtered out. They found that these partial correlations between aoa and gjt , which are given in Table 9 , differed between age groups in that they are stronger for younger than for older participants. This, DK et al. argue, constitutes additional evidence in favour of the cph . At this point, I can no longer provide my own analysis of DK et al.'s data seeing as the pertinent data points were not plotted. Nevertheless, the detailed descriptions by DK et al. strongly suggest that the use of these partial correlations is highly problematic. Most importantly, and to reiterate, correlations (whether zero-order or partial ones) are actually of no use when testing hypotheses concerning slopes. Still, one may wonder why the partial correlations differ across age groups. My surmise is that these differences are at least partly the by-product of an imbalance in the sampling procedure.

The upshot of this brief discussion is that the partial correlation differences reported by DK et al. are at least partly the result of an imbalance in the sampling procedure: aoa and aat were simply less intimately tied for the young arrivals in the North America study than for the older arrivals with L2 English or for all of the L2 Hebrew participants. In an ideal world, we would like to fix aat or ascertain that it at most only weakly correlates with aoa . This, however, would result in a strong correlation between aoa and another potential confound variable, length of residence in the L2 environment, bringing us back to square one. Allowing for only moderate correlations between aoa and aat might improve our predicament somewhat, but even in that case, we should tread lightly when making inferences on the basis of statistical control procedures [61] .

On estimating the role of aptitude

Having shown that Hypothesis 1 could not be confirmed, I now turn to Hypothesis 2, which predicts a differential role of aptitude for ua in sla in different aoa groups. More specifically, it states that the correlation between aptitude and gjt performance will be significant only for older arrivals. The correlation coefficients of the relationship between aptitude and gjt are presented in Table 10 .

The problem with both the wording of Hypothesis 2 and the way in which it is addressed is the following: it is assumed that a variable has a reliably different effect in different groups when the effect reaches significance in one group but not in the other. This logic is fairly widespread within several scientific disciplines (see e.g. [62] for a discussion). Nonetheless, it is demonstrably fallacious [63] . Here we will illustrate the fallacy for the specific case of comparing two correlation coefficients.

Apart from not being replicated in the North America study, does this difference actually show anything? I contend that it does not: what is of interest are not so much the correlation coefficients, but rather the interactions between aoa and aptitude in models predicting gjt . These interactions could be investigated by fitting a multiple regression model in which the postulated cp breakpoint governs the slope of both aoa and aptitude. If such a model provided a substantially better fit to the data than a model without a breakpoint for the aptitude slope and if the aptitude slope changes in the expected direction (i.e. a steeper slope for post- cp than for younger arrivals) for different L1–L2 pairings, only then would this particular prediction of the cph be borne out.

Using data extracted from a paper reporting on two recent studies that purport to provide evidence in favour of the cph and that, according to its authors, represent a major improvement over earlier studies (DK et al., p. 417), it was found that neither of its two hypotheses were actually confirmed when using the proper statistical tools. As a matter of fact, the gjt scores continue to decline at essentially the same rate even beyond the end of the putative critical period. According to the paper's lead author, such a finding represents a serious problem to his conceptualisation of the cph [14] ). Moreover, although modelling a breakpoint representing the end of a cp at aoa 16 may improve the statistical model slightly in study on learners of English in North America, the study on learners of Hebrew in Israel fails to confirm this finding. In fact, even if we were to accept the optimal breakpoint computed for the Israel study, it lies at aoa 6 and is associated with a different geometrical pattern.

Diverging age trends in parallel studies with participants with different L2s have similarly been reported by Birdsong and Molis [26] and are at odds with an L2-independent cph . One parsimonious explanation of such conflicting age trends may be that the overall, cross-linguistic age trend is in fact linear, but that fluctuations in the data (due to factors unaccounted for or randomness) may sometimes give rise to a ‘stretched L’-shaped pattern ( Figure 1, left panel ) and sometimes to a ‘stretched 7’-shaped pattern ( Figure 1 , middle panel; see also [66] for a similar comment).

Importantly, the criticism that DeKeyser and Larsson-Hall levy against two studies reporting findings similar to the present [48] , [49] , viz. that the data consisted of self-ratings of questionable validity [14] , does not apply to the present data set. In addition, DK et al. did not exclude any outliers from their analyses, so I assume that DeKeyser and Larsson-Hall's criticism [14] of Birdsong and Molis's study [26] , i.e. that the findings were due to the influence of outliers, is not applicable to the present data either. For good measure, however, I refitted the regression models with and without breakpoints after excluding one potentially problematic data point per model. The following data points had absolute standardised residuals larger than 2.5 in the original models without breakpoints as well as in those with breakpoints: the participant with aoa 17 and a gjt score of 125 in the North America study and the participant with aoa 12 and a gjt score of 117 in the Israel study. The resultant models were virtually identical to the original models (see Script S1 ). Furthermore, the aoa variable was sufficiently fine-grained and the aoa – gjt curve was not ‘presmoothed’ by the prior aggregation of gjt across parts of the aoa range (see [51] for such a criticism of another study). Lastly, seven of the nine “problems with supposed counter-evidence” to the cph discussed by Long [5] do not apply either, viz. (1) “[c]onfusion of rate and ultimate attainment”, (2) “[i]nappropriate choice of subjects”, (3) “[m]easurement of AO”, (4) “[l]eading instructions to raters”, (6) “[u]se of markedly non-native samples making near-native samples more likely to sound native to raters”, (7) “[u]nreliable or invalid measures”, and (8) “[i]nappropriate L1–L2 pairings”. Problem No. 5 (“Assessments based on limited samples and/or “language-like” behavior”) may be apropos given that only gjt data were used, leaving open the theoretical possibility that other measures might have yielded a different outcome. Finally, problem No. 9 (“Faulty interpretation of statistical patterns”) is, of course, precisely what I have turned the spotlights on.

Conclusions

The critical period hypothesis remains a hotly contested issue in the psycholinguistics of second-language acquisition. Discussions about the impact of empirical findings on the tenability of the cph generally revolve around the reliability of the data gathered (e.g. [5] , [14] , [22] , [52] , [67] , [68] ) and such methodological critiques are of course highly desirable. Furthermore, the debate often centres on the question of exactly what version of the cph is being vindicated or debunked. These versions differ mainly in terms of its scope, specifically with regard to the relevant age span, setting and language area, and the testable predictions they make. But even when the cph 's scope is clearly demarcated and its main prediction is spelt out lucidly, the issue remains to what extent the empirical findings can actually be marshalled in support of the relevant cph version. As I have shown in this paper, empirical data have often been taken to support cph versions predicting that the relationship between age of acquisition and ultimate attainment is not strictly linear, even though the statistical tools most commonly used (notably group mean and correlation coefficient comparisons) were, crudely put, irrelevant to this prediction. Methods that are arguably valid, e.g. piecewise regression and scatterplot smoothing, have been used in some studies [21] , [26] , [49] , but these studies have been criticised on other grounds. To my knowledge, such methods have never been used by scholars who explicitly subscribe to the cph .

I suspect that what may be going on is a form of ‘confirmation bias’ [69] , a cognitive bias at play in diverse branches of human knowledge seeking: Findings judged to be consistent with one's own hypothesis are hardly questioned, whereas findings inconsistent with one's own hypothesis are scrutinised much more strongly and criticised on all sorts of points [70] – [73] . My reanalysis of DK et al.'s recent paper may be a case in point. cph exponents used correlation coefficients to address their prediction about the slope of a function, as had been done in a host of earlier studies. Finding a result that squared with their expectations, they did not question the technical validity of their results, or at least they did not report this. (In fact, my reanalysis is actually a case in point in two respects: for an earlier draft of this paper, I had computed the optimal position of the breakpoints incorrectly, resulting in an insignificant improvement of model fit for the North American data rather than a borderline significant one. Finding a result that squared with my expectations, I did not question the technical validity of my results – until this error was kindly pointed out to me by Martijn Wieling (University of Tübingen).) That said, I am keen to point out that the statistical analyses in this particular paper, though suboptimal, are, as far as I could gather, reported correctly, i.e. the confirmation bias does not seem to have resulted in the blatant misreportings found elsewhere (see [74] for empirical evidence and discussion). An additional point to these authors' credit is that, apart from explicitly identifying their cph version's scope and making crystal-clear predictions, they present data descriptions that actually permit quantitative reassessments and have a history of doing so (e.g. the appendix in [8] ). This leads me to believe that they analysed their data all in good conscience and to hope that they, too, will conclude that their own data do not, in fact, support their hypothesis.

I end this paper on an upbeat note. Even though I have argued that the analytical tools employed in cph research generally leave much to be desired, the original data are, so I hope, still available. This provides researchers, cph supporters and sceptics alike, with an exciting opportunity to reanalyse their data sets using the tools outlined in the present paper and publish their findings at minimal cost of time and resources (for instance, as a comment to this paper). I would therefore encourage scholars to engage their old data sets and to communicate their analyses openly, e.g. by voluntarily publishing their data and computer code alongside their articles or comments. Ideally, cph supporters and sceptics would join forces to agree on a protocol for a high-powered study in order to provide a truly convincing answer to a core issue in sla .

Supporting Information

aoa and gjt data extracted from DeKeyser et al.'s North America study.

aoa and gjt data extracted from DeKeyser et al.'s Israel study.

Script with annotated R code used for the reanalysis. All add-on packages used can be installed from within R.

Acknowledgments

I would like to thank Irmtraud Kaiser (University of Fribourg) for helping me to get an overview of the literature on the critical period hypothesis in second language acquisition. Thanks are also due to Martijn Wieling (currently University of Tübingen) for pointing out an error in the R code accompanying an earlier draft of this paper.

Funding Statement

No current external funding sources for this study.

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What are the main arguments for and against the critical period hypothesis, and what are alternative explanations?

Why is the critical period hypothesis so heavily disputed, yet widely accepted; what are its major strengths and weaknesses; what other explanations exist for the perceived "critical period", if it does not exist?

• critical-period

Let us start with a simple, relatively informal statement: “in most cases, those who start learning a language as children become ultimately become more proficient in a language than those who start learning it later”. This is uncontroversial, and something I think the vast majority of second-language acquisition researchers would agree on. However, this is not how the Critical Period Hypothesis (CPH) is understood within the field of Second Language Acquisition (SLA). CPH is a large subject, and your question is hard to answer in a few paragraphs. Therefore, I am reusing large fragments of an assignment I wrote on this very topic for an SLA course a few years ago. Let me know if something is unclear or the style is too terse at some points.

Summary (TL;DR)

There is no universally accepted definition of a critical period within linguistics and some of the controversies are caused by the fact that different researchers use different definitions.

There are a few key findings that are not controversial:

• early learners perform consistently well in all aspects of language use,
• as we move the starting age, they perform statistically worse and worse until puberty,
• however, the decrease in performance is not uniform.

An explanation, provided by Bialystok (1997) as an alternative to CPH, is the different learning style of children, compared to late learners.

Paradoxically, the differences (or lack thereof) between those who learn a foreign language as adults is the key factor in deciding whether CPH is true or not, and a controversial one:

• Some studies found correlations between the age adult learners started learning a language and their ultimate attainment. In other words, these studies suggest that if we compare people who have been learning a language for a very long time, the ultimate attainment of those who started at the age of 20 is statistically higher than the ultimate attainment of those who started at the age of 40. These studies argue that there is no CPH in the childhood, but rather that our abilities in learning a new language consistently decrease throughout our whole lives.
• Other studies found no clear correlations between the starting age and the ultimate attainment among adult language learners. They point out that the correlation between the starting age and ultimate attainment is clear for those who started before puberty. Based on that, they argue that there is something qualitatively different about starting to learn in an early age, and therefore conclude that it is an argument for CPH.

Definitions of the critical period used by those who argue against CPH

Controversies with the Critical Period Hypothesis (CPH) are related to the issue of ultimate attainment of early and late language learners, that is, the highest language proficiency level they can attain. The patterns in ultimate attainment may be explained by CPH, but they may also have different explanations. Some researchers support some form of the Critical Period Hypothesis (Johnson and Newport 1989, DeKeyser and Larson-Hall 2005, Patkowsky 1994, Scovel 1988), while others argue against it (Bialystok 1997).

A major problem with the Critical Period Hypothesis is that there appears to be no universally accepted definition of a critical period within linguistics . Bialystok (1997) bases her discussion of the critical/sensitive period (which she takes to be synonymous 1 ) on a specific technical definition used in ethology, which includes 14 essential structural characteristics that describe such a period (Bornstein 1989). She argues that one of these characteristics is especially problematic – the system: “structure or function altered in the sensitive period” (Bornstein 1989:184). In other words, she argues that there is no period where a structure in the brain is modified in a way that makes subsequent language learning harder or impossible. Bialystok does, however, agree that there is an optimal period for language learning – something that can be characterised by the statement “ On average, children are more successful than adults when faced with the task of learning a second language ” (Bialystok 1997:117). Despite the controversy around other issues, this fact is uncontested and has been verified by numerous studies .

Bialystok (1997) rejects the existence of a critical period, because of lack of postulated structure that is modified when the period is over. She postulates that an important factor that causes differences in ultimate attainment between early and late starters is learning style: children prefer accommodation (creating new concepts) over assimilation (extending existing concepts). The question remains: why do they prefer accommodation? She suggests that “[t]his may be because children are in the process of creating new categories all the time as they are learning new information” (Bialystok 1997:132).

Definitions of the critical period used by supporters of CPH

The researchers who support some form of the Critical Period Hypothesis (Johnson and Newport 1989, DeKeyser and Larson-Hall 2005), formulate it in a form that is much weaker than Bialystok's (1997) formulation. What they postulate often resembles what Bialystok calls the optimal age.

Johnson and Newport (1989) reformulated CPH into two alternative hypotheses, in order to fit second language acquisition into the picture:

The exercise hypothesis : “Early in life, humans have a superior capacity for acquiring languages. If the capacity is not exercised during this time, it will disappear or decline with maturation. If the capacity is exercised, however, further language learning abilities will remain intact throughout life.” (Johnson and Newport 1989:64)

The maturational state hypothesis : “Early in life, humans have a superior capacity for acquiring languages. This capacity disappears or declines with maturation.” (Johnson and Newport 1989:64)

We can see that if a critical period was found for second language acquisition, we could be almost sure that it exists for L1 acquisition as well (the maturational state hypothesis). However, we cannot deduce in this way in case of the exercise hypothesis – non-existence of a critical period for L2 acquisition does not exclude in any way a possibility of such period for the first language (Bialystok 1997).

DeKeyser and Larson-Hall (2005) formulate the hypothesis as: “language acquisition from mere exposure (i.e. implicit learning) […] is severely limited in older adolescents and adults”. Their formulation is quite vague, as is the constatation that there is a “qualitative change in language learning capacities somewhere between 4 and 18 years”.

There are also definitions that restrict the Critical Period Hypothesis to specific subareas of the language faculty. The most commonly mentioned area is phonology, see e.g. Patkowsky (1994, cited in Bialystok 1997), Scovel (1988, cited in Bialystok 1997).

Age effects before and after puberty

The current consensus is that early learners perform consistently well in all aspects of language use. As we move the starting age, they perform statistically worse and worse until puberty. The decrease in performance is not uniform, and in some areas (such as phonology) it is particularly visible. Performance on the same level as early bilinguals is possible, but rare.

Probably the most controversial aspect is the performance of adult learners. After puberty there is much bigger variance in the performance, so data are more prone to different interpretations. The results obtained by Derwing and Munro (2013) suggest that comprehensibility and good accent are negatively correlated with the age of arrival, that is, the age when English language immersion started. Johnson and Newport (1989) found no correlation of starting age after puberty with ultimate language proficiency, while Bialystok (1997) re-analysed these data and found some negative correlation. A meta-analysis by DeKeyser and Larson-Hall (2005) downplays the role of post-adolescent correlations. As we can see, the jury is still out on this debate.

1 In neuroscience critical period and sensitive period are two separate concepts, see Knudsen (2004).

Bibliography

• Bialystok, E. 1997. The structure of age: in search of barriers to second language acquisition. Second Language Research 13(2): 116-137.
• Bornstein, M.H. 1989. Sensitive periods in development: structural characteristics and causal interpretations. Psychological Bulletin 105,179–97.
• DeKeyser, R. and J. Larson-Hall. 2005. What does the critical period really mean? In J. F. Kroll and A. M. B. de Groot. 2005. Handbook of bilingualism: Psycholinguistic approaches . Cary, NC: Oxford University Press. Pp. 109–27.
• Derwing, T. M., & Munro, M. J. 2013. The development of L2 oral language skills in two L1 groups: A 7-year study. Language Learning 63, 163-185.
• Johnson, J.S., & Newport, E.L. 1989. Critical period effects in second language learning: The influence of maturational state on the acquisition of English as a second language. Cognitive Psychology , 21, 60-99.
• Knudsen, E. I. 2004. Sensitive periods in the development of the brain and behavior. Journal of Cognitive Neuroscience , 16, 1412-25
• Newport, E. L., & Supalla, T. 1987. A critical period effect in the acquisition of a primary language .
• Patkowsky, M. 1980. The sensitive period for the acquisition of syntax in a second language. Language Learning 30, 449–72
• Scovel, T. 1988. A time to speak: a psycholinguistic inquiry into the critical period for human speech . New York: Newbury House

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Poly-methyl-methacrylate rods in light-transmitting concrete: a critical investigation into sustainable implementation.

1. Introduction

2. materials, mix design, and casting process, 2.1. materials, 2.1.1. cement, 2.1.2. fly ash, 2.1.3. coarse aggregates, 2.1.4. fine aggregates, 2.1.5. water, 2.1.6. superplasticiser, 2.1.7. pmma rods, 2.2. mix design, 2.3. casting process, 3. experimental program, 3.1. fresh properties, 3.2. strength properties, 3.3. microstructural imaging, imagej image processing, 3.4. thermal characteristics, 3.5. behaviour in artificial illumination, 3.6. behaviour in natural sunlight, 3.7. modelling and simulation, 3.7.1. integrated environmental solutions—virtual environment, 3.7.2. nine-point method of transmittance, 3.8. estimation and costing, 3.9. projection and forecasting, 3.10. carbon emission characteristics, 4.1. fresh properties, 4.2. compressive strength, 4.3. flexural strength, 4.4. microscopic photography, 4.5. thermal behaviour, 4.6. testing under artificial light, 4.7. testing in natural light, 4.8. coefficient of transmission, 4.9. modelling analysis, 4.10. costing analysis, 4.11. energy characteristics, 4.12. predictive modelling, 4.13. carbon emission calculations, 5. conclusions.

• The use of PMMA rods as a transmission media in light-transmitting concrete is suitable for non-structural use of concrete.
• The surface roughness has been an important factor in improving the friction and area of contact between fibre and paste, which impacts the behaviour of these fibres in strength tests, as illustrated in steel fibres [ 62 , 63 ]. The smooth surface finish of PMMA rods reduces friction and increases the void concentration, causing a loss in bond strength as seen in the image analysis. This leads to the presence of failure surfaces in the concrete and negatively impacts the strength performance.
• The best orientation of fibres to enhance the tensile properties is if the fibres are placed along the direction of tensile loads, as demonstrated with steel fibres [ 64 , 65 ]. In the case of light-transmitting concrete, the rod orientation is along the cross-section of the beam samples tested for flexure, which does not contribute to improving the strength. Combined with the lack of bonding, the effect of unidirectional orientation is detrimental to the strength properties, as evident from the results.
• The thermal transmission behaviour indicates that the use of PMMA rods does not cause a considerable increase in the ambient temperature as the thermal transmittance is similar to concrete. This is indicative that the cooling or heating loads of the built environment employing light-transmitting concrete will be comparable to that of a structure built conventionally. There is no adverse impact of using light-transmitting concrete on the heating and cooling loads; hence, the material is suitable for use in construction, irrespective of weather conditions.
• A linear trend was observed between the area available for light and transmittance, which was in line with various historical studies using other transmitting materials like optic fibres [ 27 , 45 , 66 ].
• Annual transmittance characteristics indicated the transmittance being highest in the months of April and May, during summer when the cloud cover was minimal. Conversely, the monsoon months of July and August were the months with the least transmittance. The best performance was seen in P21, with a maximum monthly average transmittance of 721 lux in the month of May between 12.00 and 01.00 p.m., and the least average monthly transmittance observed between 12.00 and 01.00 p.m. for P21 was 427 lux. The percentage reduction in transmittance was 40.77% in this specific instance. Generally, for all variants, the percentage difference between the highest and lowest transmittance for the same time of testing varied between 38.21% and 56.74%.
• The cost of construction for the use of materials increased between 91% and 217% based on the different variations of rods as well as the different room dimensions and configurations. A major increase in the cost was due to the addition of PMMA rods, which was slightly offset by the deduction of plastering and painting costs, as the light-transmitting concrete variants cannot be plastered or painted.
• The IESVE modelling of the variants indicated the transmittance behaviour and provided evidence of the suitability of the use of the different variants throughout the year, considering the weather conditions of Manipal. Variant P12 exhibited lower average luminance levels compared to P11, P21, and P22, with the annual average being below 300 lux for all three applications. This indicates that the use of P12 needs to be supported by artificial illumination for adequate functionality.
• Projected operational cost and cost saving indicate that all variants are feasible in construction. The return of the increased cost varies between 9 and 31 years, based on the variant used.
• The environmental impact and reduction in CO 2 emissions are significant, as observed in this study. With operational emission reductions estimated as high as 97.33% or even as low as 39.02%, there is an immense impact on sustainable construction. The CO 2 emissions were increased in the construction phase for all cases as the use of PMMA has an increased footprint. That being said, it was offset by the reduction in emissions resulting from the omission of plastering and painting. The major difference in emission was in operational emissions, as some of the variants had zero daylighting emissions, and the average illuminations ranged above the minimum stipulated criteria.

Author Contributions

Institutional review board statement, informed consent statement, data availability statement, conflicts of interest.

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Shenoy, A.; Nayak, G.; Tantri, A.; Shetty, K.K.; Maxwell, J.A.; Pai, B.H.V.; Kudva, L.P. Poly-Methyl-Methacrylate Rods in Light-Transmitting Concrete: A Critical Investigation into Sustainable Implementation. Sustainability 2024 , 16 , 8033. https://doi.org/10.3390/su16188033

Shenoy A, Nayak G, Tantri A, Shetty KK, Maxwell JA, Pai BHV, Kudva LP. Poly-Methyl-Methacrylate Rods in Light-Transmitting Concrete: A Critical Investigation into Sustainable Implementation. Sustainability . 2024; 16(18):8033. https://doi.org/10.3390/su16188033

Shenoy, Adithya, Gopinatha Nayak, Adithya Tantri, Kiran K. Shetty, Jasmin Anna Maxwell, B. H. Venkataram Pai, and Laxman P. Kudva. 2024. "Poly-Methyl-Methacrylate Rods in Light-Transmitting Concrete: A Critical Investigation into Sustainable Implementation" Sustainability 16, no. 18: 8033. https://doi.org/10.3390/su16188033

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