Abstract

Unbalanced split-plot experiments present many analysis problems. This paper discusses some of the difficulties by comparing the results of the analysis recommended by Milliken and Johnson (1984) to a set of minimal sufficient statistics using a small experiment from Milliken and Johnson as a case study. The estimators used by Milliken and Johnson are not necessarily the best (smallest variance) estimators. A set of minimal sufficient statistics is used to show that the whole plot error term suggested by Milliken and Johnson does not have a distribution that is proportional to an exact chi-square distribution and is not always independent of parameter function estimators. Other options for analyzing unbalanced split-plot experiments and unbalanced repeated measures experiments in which the repeated measures satisfy the Huyhn-Feldt (1970) conditions are proposed.

Keywords

random effect, mixed model, variance component, Huyhn-Feldt

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Apr 26th, 2:30 PM

OPTIONS FOR ANALYZING UNBALANCED SPLIT-PLOT EXPERIMENTS: A CASE STUDY

Unbalanced split-plot experiments present many analysis problems. This paper discusses some of the difficulties by comparing the results of the analysis recommended by Milliken and Johnson (1984) to a set of minimal sufficient statistics using a small experiment from Milliken and Johnson as a case study. The estimators used by Milliken and Johnson are not necessarily the best (smallest variance) estimators. A set of minimal sufficient statistics is used to show that the whole plot error term suggested by Milliken and Johnson does not have a distribution that is proportional to an exact chi-square distribution and is not always independent of parameter function estimators. Other options for analyzing unbalanced split-plot experiments and unbalanced repeated measures experiments in which the repeated measures satisfy the Huyhn-Feldt (1970) conditions are proposed.