PROFANA

Profile Analysis of Multivariate Repeated Measures.

Profile analysis is a special application of multivariate analysis of variance (MANOVA) in which several dependent variables are measured and they are all measured on the same scale. Is also used in research where subjects are measured repeatedly on the same dependent variable. In this case, profile analysis is an alternative to univariate repeated measures analysis of variance. The major question to be answered by profile analysis is whether profiles of groups differ on a set of measures. To apply profile analysis, all measures must have the same range of possible scores, with the same score value having the same meaning on all the measures. The restriction on scaling of the measures is present because in two of the major tests of profile analysis (parallelism and flatness) the numbers that are actually tested are difference scores between dependent variables measured on adjacent occasions. Difference scores are called segments in profile analysis.

There are three main questions to be answered on profile analysis:
--1. Do different groups have parallel profiles?: test of parallelism.
When profile analysis is used as a substitute for univariate repeated measures ANOVA, the parallelism test is the test of interaction.
--2. Whether or not groups produce parallel profiles, does one group, on average, score higher on the collected set of measures than another?: test of difference in levels.
In regular ANOVA, this question is answered by test of the groups hypothesis. In repeated-measures ANOVA, it address as the between-subjects main effects question.
--3. Do the dependent variables all elicit the same average response?: test of flatness. This is relevant only if the profiles are parallel. If not, the at least one of them is necessarily not flat. This test evaluates the within-subjects main effect hypothesis in repeated-measures ANOVA.

Inputs:
X - data matrix (Size of matrix must be n-by-(1+p); sample=column 1, variables=column 2:p).
alpha - significance level (default = 0.05).

Outputs:
- Complete analysis of variance for difference levels test.
- Complete analysis of variance for parallelism test.
- Complete Hotelling's T-squared analysis for flatness test.
- Figure of profiles of dependent variables for the studied groups.