What type of ANOVA? Three types of measurement in 2 groups I am working on an assignment where I am expected to use an ANOVA test to analyse a set of data.
The data set consists of two groups, the first group is a healthy group of participants, group 2 have had an operation involving a brain lesion.
Both groups have then been tested with three tests: maths, language, logical reasoning.
I am expected to test whether the brain lesions have led to any significant decrease in cognitive functions. I am not sure what type of ANOVA to use? Maybe a 2x3 mixed ANOVA? would this be the correct choice of statistical analysis? 
Thank you
 A: You need to ask yourself two questions: What is being measured, and why do measurements vary?


*

*You are measuring responses to test scores. 

*Tests vary for 4 reasons: the person is healthy or brain damaged; Bob is different from Paul; a math test is different from a language test; and finally, if Bob does the same test on two separate occasions, he will get a different score.


two of these reasons are fixed effects and two are random. Can you take it from here?
A: You have two independent groups that you are comparing.  If your aim is really testing: You can either (1) do a separate test of shifts in mean (or median) score for each response (math, language, reasoning) using either a t-test or else an equivalent distribution-free test (Wilcoxon-Rank Sum test). (2) If you want to be fancy and bundle all three tests into a single overall test of differences (that will also yield a cognitive 'score' from the three responses), use MANOVA, also called (since there are two groups) Hotelling's T-test. 
However, it is just as likely that you really want to know how much the scores differ between groups and not just that they differ.  I'd recommend a confidence interval for the difference in scores, one interval for each response (these can be obtained from t-test software).  There are also nonparametric versions of these intervals (Hodges-Lehmann) that are fairly robust, but that's probably overkill.  Along with these, a pair of box plots for each response (math, language, reasoning) is a good idea, too.  
