Simultaneous Confidence Intervals for Product-Type Interaction Contrasts

• Published in: Journal of the Royal Statistical Society. Series B, Methodological Methodological, 1973-01, Vol.35 (2), p.234-244
• Main Authors: Gabriel, K. R., Putter, J., Wax, Y.
• Format: Article
• Language: English
• Subjects: Analysis of variance; Confidence interval; contrasts; Degrees of freedom; Direct products; Eigenvalues; Estimators; interaction; Mathematical vectors; Matrices; maximum characteristic root; multiple comparisons; simultaneous confidence intervals; Statistical discrepancies
• ISSN: 0035-9246; 1369-7412; 2517-6161; 1467-9868
• DOI: 10.1111/j.2517-6161.1973.tb00954.x

The set of product-type interaction contrasts, which contains the subsets of interaction residuals, tetrad contrasts, double-dichotomy contrasts and pooled-tetrad contrasts, is discussed. In the Normal case with equal and known variances, simultaneous confidence intervals for a given set of such contrasts can be constructed in several ways. Five such methods (the Scheffe method, the Tukey method, the Dunn method, a method based on Roy's maximum-root statistic and a modification of Tukey's method) are presented and compared in terms of the widths of the resulting 95 and 99 per cent confidence intervals. The Dunn method is found to yield the shortest intervals for interaction residuals, for tetrad contrasts and for double-dichotomy contrasts. On the other hand, for the set of pooled-tetrad contrasts, and therefore also for any larger set of product-type interaction contrasts, the maximum-root method yields the shortest intervals. A table of the half-widths of the intervals given by the recommended methods is provided.