# Analyzing repeated measures ANOVA with two groups

I have a data set that looks like this:

GROUP                    WEEK1 WEIGHT(kg)          WEEK2 WEIGHT(kg)         WEEK3 WEIGHT(kg)
Control
Subject C1             40                        42                       44
Subject C2             52                        57                       57
Subject C3             55                        55                       60
Subject C4             45                        47                       49

Experimental
Subject E1             38                        40                       49
Subject E2             42                        47                       50
Subject E3             55                        60                       68
Subject E4             65                        77                       88


My question is: What tool shall I use to test my hypothesis that the two groups (control and experimental) do not significantly differ with regard to weight?

Please note that the weights are repeated measures. I understand that if I were to examine the data per group (Control first, then Experimental), I'd perform a repeated measures ANOVA for control and another for experimental.

• Despite your last comment ("I understand that if I were to examine the data per group (...)"), I believe this falls under a repeated-measures design. Feel free to update your question if I wrongly interpreted the question. – chl Aug 17 '12 at 21:38

Even for one group only, I don't like the so-called repeated measures ANOVA because it assigns a compound symmetry variance matrix, thereby implying the same correlation between week1 and week2 and between week1 and week3, which is a contestable assumption.

But in fact I'm not sure that all statisticians are in agreement in regards to the meaning of "repeated measures ANOVA". It is more important to understand what we do than only knowing the name of what we do.

The easiest way is to assign an unstructured variance matrix, and this is the so-called MANOVA (by the way, here I was asking about an intermediate between compound symmetry and unstructured).

In the SAS language, your model would be

PROC MIXED DATA=mydata;
MODEL y=group;
REPEATED week / SUBJECT=subject TYPE= *set your type here*;


Setting TYPE=UN is the MANOVA with the group factor. Setting TYPE=CS is the "classical" repeated-measures ANOVA with the group factor.

• The compound symmetry or sphericity assumption is quite common under the RM ANOVA tradition, see e.g., Zar, Biostatistical Analysis (4th ed.), p. 259, and it is not so different from a random-intercept model. The MANOVA approach (and its caveats) has been discussed on this site, Differences between MANOVA and Repeated Measures ANOVA?, or elsewhere on the internet. – chl Nov 4 '12 at 12:27
• @chl This popularity of the sphericity assumption is exactly what I am frightened about. I know some statisticians who use this model whereas it is far to be appropriate (e.g. there are 3 repeated measures at 3 different timepoints and the correlation between measure 3 and measure 1 is clearly lower than the one between measure 2 and mesure 1). Because they do not understand what they are doing. – Stéphane Laurent Nov 4 '12 at 14:22
• Yes I agree with you. You raised a good point (and I may have missed you criticism about RM ANOVA for this particular question). We can model correlated errors with an auto-regressive process, which is often seen when observations are repeated in time. I would say that sometimes time is part of the design, and this is not really a longitudinal study, so maybe that's why we happen to call this DoE repeated-measures. Feel free to retag, though. – chl Nov 4 '12 at 15:26