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ANALYSIS OF UNREPLICATED EXPERIMENTS (SYMPOSIUM)

A Method for Analyzing Unreplicated Agricultural Experiments

^a Program of Applied Statistics and Research Methods, Univ. of Northern Colorado, Greeley, CO 80639
^b Dep. of Statistics, Kansas State Univ., Manhattan, KS 66506

^* Corresponding author (jamis.perrett{at}unco.edu)

Many studies are conducted in which replication of units is prohibitive. Traditional methods of hypothesis testing do not allow for analysis of unreplicated experiments. An abundance of subsampling allows for accurate estimation of within-treatment variance, but does not constitute experimental error. The intraclass correlation coefficient (ICC) is a ratio involving both the within-treatment variance and the between-treatment variance. We propose a method for analyzing unreplicated experiments that exploits the relationship among the ICC, within-treatment variance, and between-treatment variance by placing a reasonable upper bound on the ICC (from prior research) and using subsampling to carry out classical tests of significance that have conservative levels of significance. The methodology has wide applicability for analyzing unreplicated experiments and may be implemented in SAS (Cary, NC) using the MIXED procedure. As a demonstration of the methodology, the authors used data from an unpublished study in which a researcher tested the effectiveness of four different treatments [(i) control; (ii) sample-dependent release of the predacious phytoseiid mite (Phytoseiulus persimilis Athias-Henriot, PP); (iii) scheduled release of PP; (iv) Floramite {2-(4-methoxy-[1,1-biphenyl]-3-yl)-1-methylethyl ester; UniRoyal Chemical Company, Inc., Middlesbury, CT} pesticide application] controlling two-spotted spider mites (hereafter refered to as just mites) in commercial greenhouses. Four greenhouses were used for the study. Within each greenhouse, eight potted ivy geranium [Pelargonium peltatum (L.) L'Hér. ex Ait., ‘Summer-Rose Red’] plants were inoculated with mites. One of the four treatments was applied in each of the four greenhouses. At the end of 1 wk, the number of mites was counted on each potted plant in each greenhouse. Using the proposed methodology, one-factor ANOVA was performed with follow-up tests identifying significant differences among the treatment means.

Abbreviations: ICC, intraclass correlation coefficient • PP, Phytoseiulus persimilis