The Difference Between t and z and the Difference It Makes

Tests of the null hypothesis for comparisons involving sample means use the t test when the conditions of the z test cannot be met. The 2 tests have different rationales and can lead to different conclusions regarding significance. In the present study, the authors compared the properties of t and z in simulation runs. The differences in the results are a result of fluctuations in the t test sample variances that do not exist in the z test, and those differences lead to differences in designating the significance of comparisons.