Investigating sphericity assumption in repeated measures desings

The term "repeated measurements" refers to data in which the response of each subject is observed on multiple occasions or under multiple conditions. The effect of the condition caused to the repetition can be analyzed with the univariate or multivariate methods. For these methods, the structure of the variance-covariance matrix between the measurements is assumed to be in proper form. Compound symmetry is one of the proper structures in repeated measurements analysis. Sphericity, generalized form of the compound symmetry, states that the variances of all pairwise differences between variables are equal. Repeated measurements analysis is usually assumed the sphericity. However, especially in case of the event which causes to the repetition being time, the equality of variances may not be practical. Several approaches for hypothesis testing were proposed for the situation where the sphericity assumption is violated. In this thesis, it is aimed to examine the effect of the sphericity assumption on the results of methods using for repeated measurements analysis, to state the suitable methods for the analysis of repeated measurements in case of the violation of sphericity assumption and to present the advantages and disadvantages of these methods by comparing them using the data from the field of the medicine. All analyzes were performed by using a real data set obtained from the field of medicine. In the analyzes, it examined whether there was a time-dependent change in systolic arterial pressure throughout the study groups. According to the findings, it can be seen that univariate approach may give incorrect results if the repeated measurement variance analysis assumptions are not met. It is shown that; the choice of the correction may have an effect on the result when the assumption of sphericity is violated, and the appropriate estimation value should be used for the sphericity index in the correction preference. Moreover, it is observed that Type II error may increase if this analysis is used when the normality assumption is violated. Similarly, it is shown that multivariate approach may also give incorrect results if the assumption of normality is violated. As a result of this study, it can be said that although there are proposed corrections for violation of the sphericity assumption in the Repeated Measures Analysis of Variance, this approach is not satisfactory. For this reason, it is recommended to examine the analysis techniques including other variance-covariance structures that can fit the data, for the analysis of repeated measurements. Keywords: Repeated measurements, Sphericity, Greenhouse-Geisser, Huynh - Feldt, Mauchly Sphericity Test