Functional anatomy of the null hypothesis and of tests of it |
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Authors: | Riopelle Arthur J |
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Institution: | Department of Psychology, Louisiana State University, Baton Rouge 70803, USA. ariope@lsu.edu |
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Abstract: | The author compared simulations of the "true" null hypothesis (zeta) test, in which sigma was known and fixed, with the t test, in which s, an estimate of sigma, was calculated from the sample because the t test was used to emulate the "true" test. The true null hypothesis test bears exclusively on calculating the probability that a sample distance (mean) is larger than a specified value. The results showed that the value of t was sensitive to sampling fluctuations in both distance and standard error. Large values of t reflect small standard errors when n is small. The value of t achieves sensitivity primarily to distance only when the sample sizes are large. One cannot make a definitive statement about the probability or "significance" of a distance solely on the basis of the value of t. |
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