Accession Number:

AD0422649

Title:

STUDIES IN RESEARCH METHODOLOGY. IV. A SAMPLING STUDY OF THE CENTRAL LIMIT THEOREM AND THE ROBUSTNESS OF ONE-SAMPLE PARAMETRIC TESTS,

Descriptive Note:

Corporate Author:

AEROSPACE MEDICAL RESEARCH LABS WRIGHT-PATTERSON AFB OHIO

Personal Author(s):

Report Date:

1963-03-01

Pagination or Media Count:

305.0

Abstract:

As a natural consequence of the type of task required, the time to operate an instrument control is likely to have a distribution with a distinctive, extremely nonnormal shape. The effect of this particular variety of nonnormality upon a the rapidity of the approach to normality by the distribution of the sample mean as sample size increases, and b the approximate validity of certain normality-assuming statistical tests at various sample sizes, was investigated by performing a large sampling study upon a population representing time scores for the operation of a push button. Ten thousand samples were drawn at each of the sample sizes, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, and for each sample Z, t, and chi-square were calculated. The sampling distributions of Z, t, and chi-square departed from their normal-theory distributions to a degree which could only be described as iconoclastic. Even at N1024 these departures were quite appreciable at the testing tails, being greatest for chi-square and least for Z, and becoming worse in all cases at increasingly extreme tail areas. Author

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Distribution Statement:

APPROVED FOR PUBLIC RELEASE