The thesis of this article is that the multitude of procedures for testing hypotheses about mean contrasts often presented in statistical methods textbooks is seemingly unwarranted. Nearly all research situations calling for the study of contrasts can be handled with a single contrast test statistic, that often attributed to R. A. Fisher. By jointly considering a probability value and an eta-squared value and by keeping in mind the total number of contrasts studied, one finds that a single contrast test procedure evolves.
Get full access to this article
View all access options for this article.
References
1.
Alt, F. and Spruill, C. (1977). A comparison of confidence intervals generated by the Scheffe and Bonferroni methods. Communications in Statistics, A6, 1503-1510.
2.
Bernhardson, C. S. (1975). Type I error rates when multiple comparison procedures follow a significant F test of ANOVA. Biometrics, 31, 229-232.
3.
Bohrer, R. , Chow, W., Faith, R., Joshi, V. M., and Wu, C. F. (1973). Multiple three-decision rules for factorial simple effects: Bonferroni wins again. Journal of the American Statistical Association, 76, 119-124.
4.
Brown, M. B. and Forsythe, A. B. (1974). The ANOVA and multiple comparisons for data with heterogeneous variances. Biometrics, 30, 719-724.
5.
Carmer, S. G. and Swanson, M. R. (1973). Evaluation of ten pairwise multiple procedures by Monte Carlo methods. Journal of the American Statistical Association, 68, 66-74.
6.
Cohen, J. and Cohen, P. (1983). Applied multiple regression/ correlation analysis for the behavioral sciences. Hillsdale, N J: Erlbaum.
7.
Davis, C. , and Gaito, J. (1984). Multiple comparison procedures within experimental research. Canadian Psychology, 25, 1-13.
8.
de Cani, J. S. (1984) Balancing Type I risk and loss of power in ordered Bonferroni procedures. Journal of Educational Psychology, 76, 1035-1037.
9.
Dunn, O. J. (1961). Multiple comparisons among means. Journal of the American Statistical Association, 56, 52-64.
10.
Gaito, J. (1978). Multiple comparisons within ANOVA using orthogonal or nonorthogonal components. EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT, 38, 901-904.
11.
Games, P. A. (1971). Multiple comparisons of means. American Educational Research Journal, 8, 531-565.
12.
Games, P. A. (1983). Use of contrasts in a design of experiments-ANOVA course. Bulletin in Applied Statistics, 10, 1-17.
13.
Harris, R. J. (1985). A primer of multivariate statistics. Orlando, FL: Academic Press.
14.
Huberty, R. J. (1987). On statistical testing. Educational Researcher, 16(8), 4-9.
15.
Jaccard, J. , Becker, M. A., and Wood, G. (1984). Pairwise multiple comparison procedures: A review. Psychological Bulletin, 96, 589-596.
16.
Jaspen, N. (1965). The calculation of probabilities corresponding to values of z, t, F, and chi-square. EDUCATIONAL AND PSYCHOLOGICAL MEASUREMENT, 25, 877-880.
17.
Jones, D. (1984). Use, misuse, and role of multiple-comparison procedures in ecological and agricultural entomology. Environmental Entomology, 13, 635-649.
18.
Keppel, G. (1982). Design and analysis. Englewood Cliffs, NJ: Prentice-Hall.
19.
Kirk, R. E. (1982). Experimental design. Belmont, CA: Brooks/Cole.
20.
Kohr, R. L. and Games, P. A. (1977). Testing complex a priori contrasts on means from independent samples. Journal of Educational Statistics, 2, 207-216.
21.
Maxwell, S. E. (1980). Pairwise multiple comparisons in repeated measures designs. Journal of Educational Statistics, 5, 269-287.
22.
Miller, R. G. (1977). Developments in multiple comparisons 1966-1976. Journal of the American Statistical Association, 72, 779-788.
23.
Miller, R. G. (1981). Simultaneous statistical inference. New York: Springer-Verlag.
24.
Morrison, D. F. (1976). Multivariate statistical methods. New York: McGraw-Hill.
25.
Myers, J. L. (1979). Fundamentals of experimental design. Boston: Allyn and Bacon.
26.
Neter, J. , Wasserman, W., and Kutner, M. H. (1985). Applied linear statistical methods. Homewood, I L: Irwin.
27.
O'Neill, R. and Wetherill, G. B. (1971). The present state of multiple comparison methods. Journal of the Royal Statistical Society (Series B), 33, 218-250 (with discussion).
28.
Pedhazur, E. J. (1982). Multiple regression in behavioral research. New York: Holt, Rinehart and Winston.
29.
Rosenthal, R. and Rubin, D. B. (1983). Ensemble-adjusted p values. Psychological Bulletin, 94, 540-541.
30.
Rosenthal, R. and Rubin, D. B. (1984). Multiple contrasts and ordered Bonferroni procedures. Journal of Educational Psychology, 76, 1028-1034.
31.
Ryan, T. A. (1959). Multiple comparisons in psychological research. Psychological Bulletin, 56, 26-47.
32.
Tatsuoka, M. M. (1982). Statistical methods. In H. E. Mitzel (Ed.), Encyclopedia of educational research (5th ed., pp. 1780-1808). New York: Free Press.
33.
Ware, J. H. , Mosteller, F., and Ingelfinger, J. A. (1986). P values. In J. C. Bailar and F. Mosteller (Eds.), Medical uses of statistics (pp. 149-169). Waltham, M A: NEJM.
34.
Zwick, R. and Marascuilo, L. A. (1984). Selection of pairwise multiple comparison procedures for parametric and nonparametric analysis of variance models. Psychological Bulletin95, 148-155.