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Related Experiment Videos

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

David C Blouin1, Arthur J Riopelle

  • 1Department of Experimental Statistics, Louisiana State University, Baton Rouge 70803, USA. dblouin@lsu.edu

The Journal of General Psychology
|February 24, 2004
PubMed
Summary

The t test and z test differ in statistical significance due to sample variance fluctuations. Simulations show these differences impact hypothesis testing conclusions when z test conditions aren't met.

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Functional anatomy of the null hypothesis and of tests of it.

The Journal of general psychology·2003

Area of Science:

  • Statistics
  • Hypothesis Testing

Background:

  • The t test and z test are statistical methods for null hypothesis testing of sample means.
  • These tests have different underlying assumptions and can yield distinct conclusions regarding statistical significance.

Purpose of the Study:

  • To compare the statistical properties of the t test and z test.
  • To investigate how differences in these tests affect the designation of significance in comparisons.

Main Methods:

  • The study employed simulation runs to analyze the behavior of both t and z tests.
  • Key focus was on comparing outcomes when the conditions for the z test were not satisfied.

Main Results:

  • The t test exhibited fluctuations in sample variances, unlike the z test.

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  • These variances in the t test led to discrepancies in determining the significance of statistical comparisons.

    • Conclusions:

    • The inherent differences in sample variance behavior between the t test and z test can lead to divergent conclusions in hypothesis testing.
    • Understanding these properties is crucial for accurate statistical analysis when sample sizes are small or population variance is unknown.