One sample comprises students who learned using Method A while the other sample learned using Method B. Our hypothetical scenario is that we are comparing scores from two teaching methods. Click the link to learn more about its hypotheses, assumptions, and interpretation. Let’s conduct a two-sample t-test! This test is also known as the independent samples t-test. If you have unequal variances and unequal samples sizes, it’s vital to use the unequal variances version of the 2-sample t-test! Step-by-Step Instructions for Running the Two-Sample t-Test in Excel If you use this approach when the variances are equal, you lose a trivial amount of statistical power, but you’ll be better off when the variances are not equal. Other analysts suggest always using the form of the t-test that assumes unequal variances. If you find one group has twice the variance of another group, it might be time to worry! However, you don’t need to worry about smaller differences. When you have an equal, or nearly equal, number of observations in both groups and a moderate sample size, t-tests are robust to differences between variances. Conversely, small sample sizes can fail to detect a substantial difference between variances. That’s the difference between practical significance and statistical significance. This condition can cause the test to identify an inconsequential difference as being statistically significant. However, using additional tests always increases the probability of both false positives and false negatives (a.k.a, Type I and Type II errors).Īdditionally, if you have a large sample size, the f-test has more statistical power. And, Excel does offer the F-test Two-Sample for Variances. Some analysts advise using an F-test to determine whether the variances are unequal. Which One to Use?Īdvice for using either the equal or unequal variances form of the 2-sample t-test varies because this issue is more complicated than it first appears. Another form of the test, known as Welch’s t-test, does not assume equal variances.Īs an aside, thanks to the central limit theorem, you can safely use t-tests to analyze nonnormal data when have ~20 or more observations per group. However, the conventional t-test also assumes the standard deviations/variances for both groups are equal. All t-tests assume you obtained data from normally distributed populations. Variances and the closely related standard deviation are measures of variability. One that assumes equal variances and the other that assumes unequal variances. You’ll notice that Excel has two forms of the two-sample t-test. The standard form tests the following hypotheses: To learn more about unstandardized and standardized effect sizes, read my post about Effect Sizes in Statistics. Effect sizes help you understand how important the findings are in a practical sense. Cohen’s d is the corresponding standardized effect size and it’s appropriate to report in some cases. Statisticians consider differences between group means to be an unstandardized effect size because these values indicate the strength of the relationship using values that retain the natural units of the dependent variable. In other words, each group contains a unique set of people or items. For example, do students who learn using Method A have a different mean score than those who learn using Method B? This form of the test uses independent samples. Two-sample t-tests compare the means of precisely two groups-no more and no less! Typically, you perform this test to determine whether two population means are different.
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