hypothesis function r

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Hypothesis Testing in R Programming

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Four Step Process of Hypothesis Testing

There are 4 major steps in hypothesis testing:

State the hypothesis- This step is started by stating null and alternative hypothesis which is presumed as true.
Formulate an analysis plan and set the criteria for decision- In this step, a significance level of test is set. The significance level is the probability of a false rejection in a hypothesis test.
Analyze sample data- In this, a test statistic is used to formulate the statistical comparison between the sample mean and the mean of the population or standard deviation of the sample and standard deviation of the population.
Interpret decision- The value of the test statistic is used to make the decision based on the significance level. For example, if the significance level is set to 0.1 probability, then the sample mean less than 10% will be rejected. Otherwise, the hypothesis is retained to be true.

One Sample T-Testing

One sample T-Testing approach collects a huge amount of data and tests it on random samples. To perform T-Test in R, normally distributed data is required. This test is used to test the mean of the sample with the population. For example, the height of persons living in an area is different or identical to other persons living in other areas.

Syntax: t.test(x, mu) Parameters: x: represents numeric vector of data mu: represents true value of the mean

To know about more optional parameters of t.test() , try the below command:

Example:

Data: The dataset ‘x’ was used for the test.
The determined t-value is -49.504.
Degrees of Freedom (df): The t-test has 99 degrees of freedom.
The p-value is 2.2e-16, which indicates that there is substantial evidence refuting the null hypothesis.
Alternative hypothesis: The true mean is not equal to five, according to the alternative hypothesis.
95 percent confidence interval: (-0.1910645, 0.2090349) is the confidence interval’s value. This range denotes the values that, with 95% confidence, correspond to the genuine population mean.

Two Sample T-Testing

In two sample T-Testing, the sample vectors are compared. If var. equal = TRUE, the test assumes that the variances of both the samples are equal.

Syntax: t.test(x, y) Parameters: x and y: Numeric vectors

Directional Hypothesis

Using the directional hypothesis, the direction of the hypothesis can be specified like, if the user wants to know the sample mean is lower or greater than another mean sample of the data.

Syntax: t.test(x, mu, alternative) Parameters: x: represents numeric vector data mu: represents mean against which sample data has to be tested alternative: sets the alternative hypothesis

One Sample -Test

This type of test is used when comparison has to be computed on one sample and the data is non-parametric. It is performed using wilcox.test() function in R programming.

Syntax: wilcox.test(x, y, exact = NULL) Parameters: x and y: represents numeric vector exact: represents logical value which indicates whether p-value be computed

To know about more optional parameters of wilcox.test() , use below command:

The calculated test statistic or V value is 2555.
P-value: The null hypothesis is weakly supported by the p-value of 0.9192.
The alternative hypothesis asserts that the real location is not equal to 0. This indicates that there is a reasonable suspicion that the distribution’s median or location parameter is different from 0.

Two Sample -Test

This test is performed to compare two samples of data. Example:

Correlation Test

This test is used to compare the correlation of the two vectors provided in the function call or to test for the association between the paired samples.

Syntax: cor.test(x, y) Parameters: x and y: represents numeric data vectors

To know about more optional parameters in cor.test() function, use below command:

Data: The variables’mtcars$mpg’ and’mtcars$hp’ from the ‘mtcars’ dataset were subjected to a correlation test.
t-value: The t-value that was determined is -6.7424.
Degrees of Freedom (df): The test has 30 degrees of freedom.
The p-value is 1.788e-07, indicating that there is substantial evidence that rules out the null hypothesis.
The alternative hypothesis asserts that the true correlation is not equal to 0, indicating that “mtcars$mpg” and “mtcars$hp” are significantly correlated.
95 percent confidence interval: (-0.8852686, -0.5860994) is the confidence interval. This range denotes the values that, with a 95% level of confidence, represent the genuine population correlation coefficient.
Correlation coefficient sample estimate: The correlation coefficient sample estimate is -0.7761684.