Experiment-wise Type I error rates in nested (hierarchical) study designs

Controlling Experiment-wise Type I Error of Meta-analysis in the Solomon Four-group Design

Stouffer=s Z, a meta-analytic technique, was proposed by W. Braver and Braver (1988) for analyzing data collected from a Solomon Four-group Design. Sawilowsky, Kelley, Blair, and Markman (1994) showed that this technique produces inflated Type I error rates. Recommendations are made to control the false positive inflation of their procedure. According to Campbell and Stanley (1963), the Solomon...

Constructions of 3-resolvable nested 3-designs and 3-wise balanced designs

Kruskal-Wallis and Friedman type tests for nested effects in hierarchical designs

In hierarchical-design experiments researchers need to test for nested effects, but sometimes parametric assumptions are violated. We show that the Kruskal-Wallis (K-W) rank test can be extended to test for such effects. Let B = b1 . . . bh be the tested effect, and A = a1 . . . ag be the effect immediately above it in the hierarchy. If one calculates separate K-W statistics for the effect B at...

Nested Designs

1. Nested Block Designs Heterogeneity in the experimental material is the most important problem to be reckoned within the statistical design of scientific experiments. If it is not suitably taken care of, in designing of an experiment, is likely to over shadow the real treatment differences making them remain undetected, unless they are large enough. Occasionally, one can find a certain factor...

t-Wise Balanced Designs

Steiner 3-wise balanced designs are constructed for parameters 3-(3n − 1, {4, 8}, 1), 3(qnm− qm, {q− 1, q, q+ 1}, 1), 3-(qnm− 2qm− 1, {qm− 3, qm− 2, qm− 1, qm, qm+ 1}, 1), 3-(qnm − 2qm, {qm − 3, qm − 2, qm − 1, qm, qm + 1}, 1), 3-(qnm − 2qm + 1, {qm − 3, qm − 2, qm−1, qm, qm+1}, 1), where q is a prime power and n ≥ 2, m ≥ 1 are integers. Further designs are obtained from these. © 2008 Elsevier ...