Two-sample t-tests for a difference in means involve independent samples (unpaired samples) or paired samples. The significance level is 5% and the number of cases is 60. The simulated random numbers originate from a bivariate normal distribution with a variance of 1 and a deviation of the expected value of 0.4. Power of unpaired and paired two-sample t-tests as a function of the correlation. ![]() The simulated random numbers originate from a bivariate normal distribution with a variance of 1. Unpaired and paired two-sample t-tests Type I error of unpaired and paired two-sample t-tests as a function of the correlation. Z may be sensitive to the alternative hypothesis (i.e., its magnitude tends to be larger when the alternative hypothesis is true), whereas s is a scaling parameter that allows the distribution of t to be determined. Most test statistics have the form t = Z/ s, where Z and s are functions of the data. These tests are often referred to as unpaired or independent samples t-tests, as they are typically applied when the statistical units underlying the two samples being compared are non-overlapping. All such tests are usually called Student's t-tests, though strictly speaking that name should only be used if the variances of the two populations are also assumed to be equal the form of the test used when this assumption is dropped is sometimes called Welch's t-test.
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