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Date of Award

Spring 2012

Degree Type

Thesis

Degree Name

Master of Science (MSc)

Department

Statistics

Supervisor

Jemila Hamid

Co-Supervisor

Roman Viveros-Aguilera

Language

English

Committee Member

Narayanaswamy Balakrishnan

Abstract

Craniofacial variability index (CVI), estimated by the standard deviation of z-scores obtained from craniofacial measurements of one or more individuals, is considered in the medical literature as a useful and relatively simple quantitative measure of the degree of dysmorphogenesis in the head and face.

CVI obtained from patients diagnosed with syndromes such as Smith-Lemli-Opitz Syndrome (SLOLS) is often compared with CVI for healthy individuals. Moreover, CVI is commonly used to compare degree of dysmorphogenesis among individuals and groups characterized by the presence or absence of certain syndromes and abnormalities. However, the type of comparison provided is often subjective with no statistical comparison of values provided to account for sample to sample variability.

We performed a simulation study to compare the performance of tests of variance under the presence of within and between individual dependencies. We compare empirical level and power obtained from 10,000 simulations to assess performance. We considered four variance comparison tests: F-test, Levene’s Test, Fligner-Killeen test and permutation F test. We also provided a detailed analysis of a real data set to illustrate our results. Overall, results from our simulation indicate that the performances of the F and the permutation F tests are better than the other methods. However, for all the tests considered, power for detecting small differences in variance is very low when the sample size is small. An interesting finding in our simulation is that the performance of the tests was actually enhanced by the presence of within individual or group dependence, where the power of the tests increased with increased correlation. On the other hand, between dependence and within and between individual dependence have the effect of lowering the power in comparison with the scenarios of independence and within dependence. It is also observed that the higher the correlation the lower the power. It should be noted that in the case of group comparison the simulation scenario of within and between dependence shows opposite results to those observed in the individual comparison. A higher correlation is associated to both a higher level and power.

On another note, the analysis of the Smith-Lemli-Opitz Syndrome (SLOS) dataset has shown that comparison of pattern profile between individuals is a useful tool to identify influential z-scores of craniofacial measurements that affect CVI and the subsequent results of hypothesis testing of equal variances using the classical F test versus Levene-median and Fligner-Killeen tests.

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