Multiple comparison procedures based on the maximal component of the cumulative chi-squared statistic

SUMMARY Multiple comparison procedures based on the maximal component of the cumulative chi-squared statistic are discussed. The Markov properties for the successive components of the cumulative chi-squared statistic are proved and applied for obtaining the p-value of the maximal component in each of the one-way and the two-way analysis of variance models and the two-way contingency table. The power of the multiple comparison procedure is compared with those for some well-known procedures in the setting of Williams (1971) for detecting the change point from the zero level.

[1]  K. Gabriel,et al.  On closed testing procedures with special reference to ordered analysis of variance , 1976 .

[2]  D. Siegmund,et al.  Maximally Selected Chi Square Statistics , 1982 .

[3]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[4]  Stephen J. Ruberg,et al.  Contrasts for Identifying the Minimum Effective Dose , 1989 .

[5]  F. Graybill,et al.  Matrices with Applications in Statistics. , 1984 .

[6]  R. Marcus,et al.  The powers of some tests of the equality of normal means against an ordered alternative , 1976 .

[7]  Chihiro Hirotsu,et al.  Defining the pattern of association in two-way contingency tables , 1983 .

[8]  Christopher Jennison,et al.  Exact calculations for sequential t, X2 and F tests , 1991 .

[9]  Eryl A. C. Shirley.  The Comparison of Treatment with Control Group Means in Toxicological Studies , 1979 .

[10]  D. A. Williams,et al.  A test for differences between treatment means when several dose levels are compared with a zero dose control. , 1971, Biometrics.

[11]  J W Tukey,et al.  Testing the statistical certainty of a response to increasing doses of a drug. , 1985, Biometrics.

[12]  Chihiro Hirotsu,et al.  Ordered alternatives for interaction effects , 1978 .

[13]  D. J. Bartholomew,et al.  A TEST OF HOMOGENEITY FOR ORDERED ALTERNATIVES. II , 1959 .

[14]  John W. Tukey,et al.  Efficient Utilization of Non-Numerical Information in Quantitative Analysis General Theory and the Case of Simple Order , 1963 .

[15]  Philip Solomon,et al.  Discussion of the Paper , 1961 .