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A Statistical Test for Means of Samples from Skew Populations

Published online by Cambridge University Press:  01 January 2025

Leon Festinger
Leon Festinger*
Affiliation:
Iowa Child Welfare Research Station, State University of Iowa
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Abstract

This paper presents a test for determining significance of differences between means of samples which are drawn from positively skewed populations, more specifically, those having a Pearson Type III distribution function. The quantity 2npxg/xp (where p equals the mean squared divided by the variance and n is the number of cases in the sample), which distributes itself as Chi Square for 2np degrees of freedom, may be referred to the tables of Chi Square for testing hypotheses about the value of the true mean. For two independent samples, the larger mean divided by the smaller mean, which distributes itself as F for 2n1p1 and 2n2p2 degrees of freedom, may be referred to the F distribution tables for testing significance of difference between means. The test assumes that the range of possible scores is from zero to infinity. When a lower theoretical score limit (c) exists which is not zero, the quantity (Mean − c) should be used instead of the mean in all calculations.

Type
Original Paper
Information
Psychometrika , Volume 8 , Issue 4 , December 1943 , pp. 205 - 210
Copyright
Copyright © 1943 The Psychometric Society

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References

Craig, C. C. Sampling when the parent population is of Pearson's Type III. Biometrika, 1929, 21, 287–293.CrossRefGoogle Scholar
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