A Handbook for Data Analysis in the Behavioral Sciences: Statistical Issues

By Gideon Keren; Charles Lewis | Go to book overview

There is general agreement, however, that the correction often results in an overly conservative test when the margins in a table are generated from random variables.

There are a number of supplementary and alternative approaches to the use of Pearson's chi-square that the researcher should know. Often the questions one asks of data may be more directly or efficiently answered by planned contrasts of proportions, partitioning of the total chi-square, or the use of log-linear models. A useful paper on this subject was written by Cochran ( 1954). He presented methods for dealing with some specific contingency table designs and probability distributions. In addition to the previously mentioned recommendations regarding minimum expected values, he discussed testing goodness-of-fit hypotheses in different distributions, degrees of freedom in 2 × N tables, and combining 2 × 2 tables.


ACKNOWLEDGMENTS

This chapter was written while the author was a research associate at the Developmental Studies Center. He is now senior statistician at the Treatment Research Unit, University of California, San Francisco.

The author would like to acknowledge and thank Drs. Patricia Busk and Ron Serlin for helpful discussions, Drs. Daniel Solomon, Victor Battistich, and an anonymous reviewer for many helpful suggestions and the late Dr. Leonard Marascuilo who suggested this topic to the author many years ago.


REFERENCES

Agresti, A. ( 1990). Categorical data analysis. New York: John Wiley & Sons.

Agresti, A., & Wackerly, D. ( 1977). "Some exact conditional tests of independence for R × C cross- classification tables". Psychometrika, 42, 111-125.

Baker, R. J. ( 1977). "Algorithm AS 112. Exact distributions derived from two-way tables". Applied Statistics, 26, 199-206.

Baker, F. B. ( 1981). "A criticism of Scheuneman's item bias technique". Journal of Educational Measurement, 18, 59-62.

Berkson, J. ( 1938). "Some difficulties in interpretation of the chi-square test". Journal of the American Statistical Association, 33, 526-536.

Berkson, J. ( 1978). "In dispraise of exact tests". Journal of Statistical Planning and Inference, 2, 27- 42.

Bishop, Y. M. M., Fienberg, S. E., & Holland, P. W. ( 1975). Discrete multivariate analysis: Theory and practice. Cambridge, MA: MIT Press.

Boardman, T. J. ( 1977). "Graphical contributions to the X2 statistics for two-way contingency tables". Communications in Statistics: Theory and Methods, A6, 1437-1451.

Bradely, D. R., Bradely, T. D., McGrath, S. G., & Cutcomb, S. D. ( 1979). "Type I error rate of the chi-square test of independence in R × C tables that have small expected frequencies". Psychological Bulletin, 86, 1920-1927.

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