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The difference between t and z and the difference it makes.

David C Blouin·Arthur J Riopelle
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Abstract

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.

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David C Blouin, Arthur J Riopelle. 2004. The difference between t and z and the difference it makes.. https://doi.org/10.3200/genp.131.1.77-84

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