Statistical Analysis of Repeated Measures

Abstract

Repeated measurements are quite common in biological experimentation. Usually, theresponses are taken over time, as in weekly growth measurements to establish growth curves.Furthermore, because of these observations are taken from the same experimental units, theyare not independent. It is important to note in this context that important assumptions are notthe independence of measurements but independence of errors. There are several statisticalmethods used for analysing repeated measures data including separate analyses at each timepoint, univariate analysis of variance, analyses of time contrast variables and multivariatemethod.In this study, plant height of Chrysanthemum (Kapuru) plants was used to compare fourmethods of repeated measures analysis and their respective advantages and shortcomings.The data was from an experiment that investigated effects of eight day lengths on plant heightwith ten replications for each treatment. The statistical analysis methods illustrated in thisstudy focus on treatment comparisons at specific times, treatment comparisons averaged overtimes and on changes over time in specific treatments. Differences between treatments werecomputed at individual times and averaged across times. Standard errors were computedbased on each of the methods of analysis.Firstly the data were analysed in a CRD at each time point examines treatment effectsseparately at individual observation times and makes no statistical comparisons among times.There was no inference is drawn about trends over time, so this method is not truly a repeatedmeasures analysis. Therefore it was not a preferred method for final publication because itdoes not address time effects. In univariate analysis of variance (ANOVA), the data isanalysed as a split-plot design for repeated measurements in a CRD. The treatment wasconsidered the main "plot" and time was considered as the sub-plot. The means of thedependent variable over time was changed violating Huynh-Feldt (H-F) condition. Thereforethe effect of time and time and treatment interaction were invalid. The "Analysis ofContrasts" method transforms the data to remove subject and time variance. According to theresults the interaction effect of time and treatment and their main effects were all significant(P<0.05). As their validity depends on whether or not the covariance structure satisfies thesphericity condition, Mauchlys Criterion was used to check for this condition and thesphericity condition was not met. Therefore the multivariate methods of repeated meaursanalysis were done. In this study, how to choose the correct method depending on the datastructure and underlying statistical assumptions was classified in repeated measurements.