Student's T-test
Explore the use of Student's t-test in R to compare means between two groups. Understand when to use independent versus paired samples t-tests, interpret p-values and t-values, and apply these concepts to real datasets for statistical significance testing.
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We use the Student’s t-test to compare the means of two normal populations. It is useful when we have a small sample (typically less than 30), and the population standard deviation is unknown.
The t-test takes the difference and variability of sample means into account and then makes inferences about the test issue. There are two types of Student’s t-tests: the independent samples t-test and the paired samples t-test.
Independent samples t-test
The independent samples t-test compares the means of two independent groups. We assume that the groups are unrelated, meaning that there is no relationship between the observations. It calculates the p-value based on the difference between the sample means and standard deviations. We use the independent samples t-test to determine if the null value should be rejected. For example, we can decide if two distinct learning methods have distinguishable effects on comprehension. The formula of the independent t-test is as follows:
The notation is as follows:
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: The mean of the first sample
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