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We use Paired sample t-test when we are determined to find the differences between two variables belonging to the same subject. The Paired sample t-test compares the mean of these two variables or measurements.
Like all the statistical procedures, Paired sample t-test formulates the hypothesis and there are two competing hypothesis: null hypothesis and alternative hypothesis.
Example of Paired sample t-test
Let’s say we wish to study the diabetic patients from 1952 to 1962. The Paired sample t-test would look like:
For α = 0.05, the critical value of t is 2.093. Since | -6.7| > 2.093, we will reject the null hypothesis (H0) and state that we have significant evidence that the average difference in diabetic patients from 1952 to 1962 is NOT 0. Specifically, there was an average decrease of 69.8 from 1952 to 1962.
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The Paired sample t-test makes some assumptions and it is advised to derive the degree of deviation from these assumptions to make sure the quality of your results is preserved. Each of the assumptions refers to the observations which further define the differences in the sample measurements.