Analysis of repeated measurements using nonparametric smoothers and randomization tests

The mixed-model analysis of variance (ANOVA), which is commonly applied to repeated measurements taken over time, depends on specialized assumptions about the error distribution and fails to exploit information contained in the ordering of the data points over time. This paper describes a procedure that overcomes these disadvantages while preserving familiar features of the mixed-model ANOVA. Group profiles are estimated by nonparametric smoothing of observed mean profiles. Group and time main effects, and the group by time interaction effect, are tested using randomization tests. Results of Zerbe (1979, Journal of the American Statistical Association 74, 215-221) are used to construct F-test approximations for the randomization tests of the group and group by time effects. A new approximate F-test for time effect is proposed. A simulation study demonstrates that the approximations perform well and that smoothing increases the power of the tests for time main effect and group by time interaction. The procedure is applied to data on hormone levels in cows.