A hypothesis is made by the researchers about the data collected for any experiment or data set. A hypothesis is an assumption made by the researchers that are not mandatory true. In simple words, a hypothesis is a decision taken by the researchers based on the data of the population collected. Hypothesis Testing in R Programming is a process of testing the hypothesis made by the researcher or to validate the hypothesis. To perform hypothesis testing, a random sample of data from the population is taken and testing is performed. Based on the results of testing, the hypothesis is either selected or rejected. This concept is known as Statistical Inference. In this article, we’ll discuss the four-step process of hypothesis testing, One sample T-Testing, Two-sample T-Testing, Directional Hypothesis, one sample -test, two sample -test and correlation test in R programming.
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, 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)
x: represents numeric vector of data
mu: represents true value of the mean
To know about more optional parameters of t.test(), try below command:
One Sample t-test data: x t = -49.504, df = 99, p-value < 2.2e-16 alternative hypothesis: true mean is not equal to 5 95 percent confidence interval: -0.1910645 0.2090349 sample estimates: mean of x 0.008985172
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)
x and y: Numeric vectors
Welch Two Sample t-test data: x and y t = -1.0601, df = 197.86, p-value = 0.2904 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: -0.4362140 0.1311918 sample estimates: mean of x mean of y -0.05075633 0.10175478
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)
x: represents numeric vector data
mu: represents mean against which sample data has to be tested
alternative: sets the alternative hypothesis
One Sample t-test data: x t = -20.708, df = 99, p-value = 1 alternative hypothesis: true mean is greater than 2 95 percent confidence interval: -0.2307534 Inf sample estimates: mean of x -0.0651628
One Sample -Test
This type of test is used when comparison has to 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)
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:
Wilcoxon signed rank test with continuity correction data: x V = 2555, p-value = 0.9192 alternative hypothesis: true location is not equal to 0
Two Sample -Test
This test is performed to compare two samples of data.
Wilcoxon rank sum test with continuity correction data: x and y W = 5300, p-value = 0.4643 alternative hypothesis: true location shift is not equal to 0
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)
x and y: represents numeric data vectors
To know about more optional parameters in cor.test() function, use below command:
Pearson's product-moment correlation data: mtcars$mpg and mtcars$hp t = -6.7424, df = 30, p-value = 1.788e-07 alternative hypothesis: true correlation is not equal to 0 95 percent confidence interval: -0.8852686 -0.5860994 sample estimates: cor -0.7761684