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
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.
Recommended Citation
Remmenga, Marta D. and Johnson, Dallas E.
(1992).
"OPTIONS FOR ANALYZING UNBALANCED SPLIT-PLOT EXPERIMENTS: A CASE STUDY,"
Conference on Applied Statistics in Agriculture.
https://doi.org/10.4148/2475-7772.1403
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.
