[p, table] = anova_rm(X, displayopt) performs a repeated measures ANOVA for comparing the means of two or more columns (time) in one or more samples(groups). Unbalanced samples (i.e. different number of subjects per group) is supported though the number of columns (followups) should be the same.
As I had this problem and took me a while to figure it out, I thought it may be useful to someone else.
For anova_rm to be compatible with multcompare function of MATLAB, we need a stat output. I read somewhere (I printed out the webpage about a year ago but I can't find it anymore) that the post-hoc for repeated measures anova is the same as independent measures anova. You just need to replace MS(within) with MS(error) and df(within) with df(error) and then use Tuckey's equation to find the critical value. Thus, as I work with anova_rm as a one-way measure, I added the following lines at the end of anova_rm and added "stat" variable to the output of the function. I can now feed this stat to multcompare and the function sees stat as the output of anova1 and estimates the critical value using Tuckey (if that is your selected ctype) in the same way it does for anova1. As I don't use it for two-way measures, I haven't checked how to define stat for that purpose but I am sure it shouldn't be hard now.
@Dan I cannot help you much with that in MATLAB. These days I mostly use R for anything beyond basic statistics. For your reference, here is a Q/A about something what I believe is exactly similar to your situation:
That's very good but I'd like to run a post-hoc analysis after the rm-anova. I'm currently running a two-way rm anova and I'd like to know the differences between all combinations. Is their a way to do so with multcompare?
@Patrizia your problem with NaN and in general, missing data is beyond the scope of this code. Generally this is handled separately through what we call imputation methods. They range from very basic (and unsatisfactory) approaches like removing incomplete cases to more advanced approaches like multiple imputations. However, the point is that there is no single, universally best approach for the missing data problem.
@J The main difference between repeated measures and the n-way ANOVA is that the former can model within subject variations while the latter can only model between subject variations. Essentially repeated measures ANOVA is a small subset of linear mixed models. In general you cannot model mixed models with simple, n-way ANOVA. In SPSS as well as the newest version of MATLAB linear mixed modeling is supported.
I'm trying to understand something related to a one-way repeated measures ANOVA.
I have one group and two scores over time. In SPSS (and this code) you input every subject's score on one row with each column being the next measurement in time. If I use anovan (built in RM analysis within Matlab) I can do the same thing but have to instead put all data sequentially in a line (row or column does not matter as long as every subject's score follows each other) and create a file the same length as my data file with the condition order.
This doesn't actually change anything a part from the df (which are doubled in anovan since I spread the data in 1 line rather than 2 equal columns) however it also gives different results in the p value (nothing drastic but still different).
Any ideas why anovan and this code producing different results while this code and SPSS produce the same results? THANKS!
@Justin: I'm struggling with the comment editor. A previous comment was magically deleted and the other one does not make much sense now. In short, I verified the code and I think it is fine. Also, I run the same data through R and got identical results. You can see the R output here: http://imgur.com/FHJc4.png
One problem that I noticed is that in your example, you show that time is the within subjects factor, but in your reality you seem to treat the group as the within subjects factor.
the f-value that you get for time seems to come from dividing MStime by MSerror. This should really be MStime / MSsubjects if this is the variable with repeated measures. You also get the f value for group by MSgroup / MSsubjects. The group variable should not have repeated measures, so basically, the two should be reversed. I'm not sure, but I think that the error is consistent with itself int he rest of your code, so In order to get the correct results from this function you need to switch the organize your two factors opposite of the way that the you did it in the example.