A computer program for calculating the sample size necessary to control for both Type I and Type II errors in chi-square tests for hypotheses concerning multinomial probabilities is described. Based on numerical analysis, this program evaluates any noncentral chi-square distribution formed by considering a specific alternative hypothesis. Two unique features of the program are its interactive/ tutorial mode and the calculation of the chi-square noncentrality factor (X) and Cohen's "effect size" index (w).
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References
1.
Bradley, J. V.Probability; decision; statistics . Englewood Cliffs, N. J.: Prentice-Hall , 1976.
2.
Cohen, J.Statistical power analysis for the behavioral sciences (revised ed). New York: Academic Press, 1977.
3.
Cramer, H.Mathematical methods of statistics . Princeton, N. J.: Princeton University Press, 1958.
4.
Fix, E.Tables of the noncentral χ 2. University of California Publication in Statistics , 1949, 1, 15-19.
5.
Guenther, W. C.Power and sample size for approximate chi-square tests. The American Statistician, 1977, 31, 83-85.
6.
Haynam, G. E., Gouindarajulu, Z., and Leone, F. C. In H. L. Harter and D. B. Owen (Eds.) Tables of the cumulative noncentral chi-square distribution, selected tables in mathematical statistics. Vol. 1. Providence, R. I.: American Mathematical Society, 1973.
7.
Hays, W. F.Statistics for the social sciences (2nd ed.). New York: Holt, Rinehart and Winston , 1973.
8.
Mood, A. M. and Graybill, F. A.Introduction to the theory of statistics (2nd ed.). New York: McGraw-Hill, 1963.
9.
Pearson, K.On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. Philosophical Magazine, 1900 , 50, 157-172.
10.
Wonnacott, T. H. and Wonnacott, R. J.Introductory statistics for business and economics . New York: Wiley, 1972.