Let’s say you want to know if two different brands of batteries have the same average life. The pairwise t-test will be dealt with in different blog. However, two-sample T-test can also be used for pairwise comparisons when the “two” samples represent the same items tested in different scenarios. The independent samples mean that the two samples cannot be from the same group of people and they cannot be related in any way. In order to use a two-sample T-test as desccribed in this blog, you need to have two independent samples. The two-sample T-test is used when the two samples are independent and have normal distributions. That said, the size of the sample is not a strict condition for using T-test.

The size of sample 30 or less is considered as small sample. The two-sample T-test is used when the standard deviations of the populations to be compared are unknown and the sample size is small. When two-sample T-test instead of two-sample Z-test?Ī two-sample T-test is defined as statistical hypothesis testing technique in which two independent samples are compared to determine if the means of two populations are statistically different.T-statistics when population variances or standard deviations are equal.T-statistics when population variances or standard deviations are unequal.Statistical Principles in Experimental Design (2nd Ed.). The third edition(s) of Winer may have additional and more recent material. However, the references there may provide more detail. Winer (1971) has a discussion on the test on pages 41-44 with an example (although not with the extreme difference in sample size that you discussed. We do not have material at hand on the robustness of the unequal-variance t-test to very small or very unbalanced sample sizes or suggestions for a minimum size. However, when one group has 0 variance, ONEWAY will not calculate the Brown-Forsythe and Welch tests, whereas T-TEST will calculate the unequal variance t-test significance.) (Note that the Brown-Forsythe and Welch tests give the same significance level as the unequal variance t-test. The interpretation of the test results is the same as with a t-test for equality of means with equal variances assumed. Both the Brown-Forsythe and Welch tests, which are available in the ONEWAY procedure as tests that are robust for unequal variance, collapse to this t-test when there are only two groups, but this modification of the standard t-test predates both of these, and thus doesn't generally carry either name. There is apparently no formal name for this test. When the groups in an independent samples t-test have unequal variances, the option that SPSS gives is simply called a t-test with a Satterthwaite approximation for the degrees of freedom.

Two sample unequal variance t test