Sage Journals: Discover world-class research

Abstract

The chi-square test of independence is a frequently used nonparametric test. Although the Type I error estimates for small-sample chi-square statistics applied to 2 x 2 tables have been relatively thoroughly studied, the Type II error rate (or power) has not been as extensively investigated. Additionally, most of the previous research has been limited to 2 x 2 tables and has not been extended to tables of larger dimensions. The objectives of the present research were (a) to investigate the small-sample power of several statistical tests in 2 x 2 and 3 x 3 contingency tables, and (b) to examine the Type I error rates for these tests under studied conditions. Various marginal distributions, sample sizes, and effect sizes were examined.

Get full access to this article

View all access options for this article.

References

Agresti, A. (1992). A survey of exact inference for contingency tables. Statistical Science, 7, 131-177.

Bradley, J. V. (1978). Robustness? British Journal of Mathematical and Statistical Psychology, 31, 144-152.

Camilli, G. (1990). The test of homogeneity for 2 x 2 contingency tables: Areview of and some personal observations on the controversy. Psychological Bulletin, 108, 135-145.

Camilli, G. , & Hopkins, K. D. (1978). Applicability of chi-square to 2 x 2 contingency tables with small expected cell frequencies. Psychological Bulletin, 85, 163-167.

Camilli, G. , & Hopkins, K. D. (1979). Testing for association in 2 x 2 contingency tables with very small sample sizes. Psychological Bulletin, 86, 1011-1014.

Cohen, J. (1988). Statistical power analysis for the behavioral sciences. New York: Academic Press.

D'Agostino, R. B. , Chase, W. , & Belanger, A. (1988). The appropriateness of some common procedures for testing the equality of two independent binomial populations. American Statistician, 42, 198-201.

Fienberg, S. E. (1977). The analysis of cross-classified categorical data. Cambridge: MIT Press.

Lamtz, K. (1978). Small-sample comparisons of exact levels for chi-squared goodness-of-fit statistics. Journal of the American Statistical Association, 73, 253-263.

10.

Little, R.J.A. (1989). Testing the equality of two independent binomial proportions. American Statistician, 43, 283-288.

11.

Mantel, N. , & Greenhouse, S. W. (1968). What is the continuity correction? American Statistician, 22, 27-30.

12.

Martin Andres, A. , Herranz Tejedor, I. , & Luna del Castillo, J. D. (1992). Optimal correction for continuity in the chi-squared test in 2 x 2 tables conditioned method. Communication in Statistics, 21, 1077-1101.

13.

Mehta, C. R. , & Hilton, J. F. (1993). Exact power of conditional and unconditional tests: Going beyond the 2 x 2 contingency table. American Statistician, 47, 91-98.

14.

Mehta, C. R. , & Patel, N. R. (1983). A network algorithm for performing Fisher's Exact Test in r x c contingency tables. Journal of the American Statistical Association, 78, 427-434.

15.

Milligan, G. W. (1980). Factors that affect Type I and Type II error rates in the analysis of multidimensional contingency tables. Psychological Bulletin, 87, 238-244.

16.

Roscoe, J. T. , & Byars, J. A. (1971). An investigation of the restraints with respect to sample size commonly imposed on the use of the chi-square statistic. Journal of the American Statistical Association, 66, 755-759.

17.

Suissa, S. , & Schuster, J. J. (1985). Exact unconditional sample sizes for the 2 x 2 binomial test. Journal of the Royal Statistical Society (Ser. A), 148, 317-327.

18.

Thompson, B. (1988). Misuse of chi-square contingency table test statistics. Educational and Psychological Research, 8, 39-49.

19.

Upton, G. J. G. (1978). The analysis of cross-tabulated data. New York: Wiley.

Tests of Independence in Contingency Tables with Small Samples: A Comparison of Statistical Power

Abstract

Get full access to this article

References