Defense Date


Document Type


Degree Name

Doctor of Philosophy



First Advisor

R.K. Elswick, Jr.


Power analysis is becoming standard in inference based research proposals and is used to support the proposed design and sample size. The choice of an appropriate power analysis depends on the choice of the research question, measurement procedures, design, and analysis plan. The "best" power analysis, however, will have many features of a sound data analysis. First, it addresses the study hypothesis, and second, it yields a credible answer.

Power calculations for standard statistical hypotheses based on normal theory have been defined for t-tests through the univariate and multivariate general linear models. For these statistical methods, the approaches to power calculations have been presented based on the exact or approximate distributions of the test statistics in question. Through the methods proposed by O'Brien and Muller (1993), the noncentrality parameter for the noncentral distribution of the test statistics for the univariate and multivariate general linear models is expressed in terms of its distinct components. This in tum leads to methods for calculating power which are efficient and easy to implement.

As more complex research questions are studied, more involved methods have been proposed to analyze data. One such method includes the mixed linear model. This research extends the approach to power calculation used for the general linear model to the mixed linear model. Power calculations for the mixed linear model will be based on the approximate F statistic for testing the mixed model's fixed effects proposed by Helms (1992). The noncentrality parameter of the approximate noncentral F for the mixed model will be written in terms of its distinct components so that a useful and efficient method for calculating power in the mixed model setting will be achieved. In this research, it has been found that the rewriting of the noncentrality parameter varies depending on study design. Thus, the noncentrality parameter for three specific cases of study design are derived.


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