Degree Type

Creative Component

Semester of Graduation

Summer 2020

Department

Statistics

First Major Professor

Annette O'Connor

Second Major Professor

Chong Wang

Degree(s)

Master of Science (MS)

Major(s)

Statistics

Abstract

The split plot design (SPD) has at least two types of experimental units and at least two levels of complete random design. As a result of this SPD structure, a method of analysis that accounts for the different levels of experimental unit is required, which is commonly a mixed model or a split-plot ANOVA. The design is utilized when it is not feasible to randomize the multiple interventions to the same level. The classic example of a split plot arises from agronomy, and gives name to the design, where the effects of two irrigation methods (factor 1) that must be applied to the entire (whole) plot are investigated with the effect of two different fertilizer types (factor 2) that are applied to sub plots within the whole plot.

In toxicology and nutrition, the split plot design is also employed to investigate the impact of exposure to toxins or nutrients during pregnancy and after birth. In these split plot experiments, the whole plot is the dam and the offspring are the subplots. Our objective is to evaluate the impact of choice of statistical approaches on the type I and type II error rates in hypothesis testing of effects as well as the precision of the estimation. Firstly, we assessed the reporting of SPD of 20 rat research studies and 25 agricultural studies where anecdotally the design appears to be better recognized. For the second objective, we used simulation modelling to evaluate the influences of two analysis approaches on the statistical inference obtained. For the Three scenarios included I) empirical mean parameters, II) null whole-plot main effect mean parameters and III) null effects mean parameters. And two variance conditions were i) empirical variance of random effects from research data and ii) sequential variance magnitude pairs of random effects at whole-plot and split-plot levels. The simulation study shown that although the misusage of two-way ANOVA on SPD data would provided a higher power for hypothesis testing, it was meanwhile at a risk of greater type I error rate. Furthermore, type I error introduced by two-way ANOVA rose with the increase of ratio of variance of whole-plot random effect to split-plot random effect. On the contrast, split ANOVA offered a stable type I error which around 0.05. This is a solid evidence of necessary of correct application of mixed model and split ANOVA on split-plot data.

Copyright Owner

Liu, Pu

File Format

PDF

Embargo Period (admin only)

7-23-2020

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