First, I would like to clarify the contrast(s) you seek. As you have four groups, it may be that you seek a contrast among those groups. On the other hand, two comparisons (RHD and Schizophrenia with respective controls) may suit your question more closely. If your question really regards the contrast between each afflicted group and the control, then including all four groups may confound that contrast. This really doesn’t matter statistically, but you must decide this before specific consideration of contrasts and tests of assumptions of those contrasts. On the other hand, if Box’s test was significant for a four-group problem, it may not be for each of the two-group problems.

Now, to the statistical. Homogeneity of covariance matrices is indeed an assumption of MANOVA, and Box’s test is a test of that assumption. However, we find ourselves in the “second-guessing” enterprise here of testing the test of an assumption of a test. Some of us might deem Box’s test a bit “flaky” being heavily dependent on distributions. One might also question why you intend to conduct a MANOVA in the first place. If it is to determine if there is an underlying construct rendered by the relative size of the optimal contrast weightings of the 10 dependent variables, then fine. If, on the other hand, your interest is in whether there are significant differences between groups on each of these 10 variables, I would strongly encourage you to use 10 separate univariate analyses (e.g., ANOVAs with attention to per-hypothesis alpha adjustment), one for each. The problem herein is that the MANOVA is not only unnecessary, but also does not address the question. Carl Huberty and I have given detailed consideration to this here:

Article Multivariate Analysis Versus Multiple Univariate Analyses

Regarding discriminant analysis, what is your goal here as well? My esteemed colleague, Carl Huberty in his 1994 classic book (revised with Steve Olejnik) identifies two goals therein: Descriptive Discriminant Analysis, and Predictive Discriminant Analysis. Respectively, do you wish to entertain constructs identified (possibly) by weightings of the 10 variables (per above)? Or do you wish to ascertain how accurately these 10 variables are able to classify subjects into groups (all four groups, or two two 2-group questions)? A linear discriminant classification rule does require an assumption of equal covariance matrices, but a quadratic rule does not. Indeed, in the later case, the nature of the different covariance matrices becomes part of the quadratic classification function. This too, is not so simple, as there is good evidence (Huberty & Curry, 1978, to start but there is more) that even if the covariance matrices are declared significantly different a linear rule often performs more accurately. This pertains to additional “parameter load” – more parameters to estimate for the function. So, one may be left without theoretical knowledge regarding which mathematical model to use – linear or quadratic. My former student and I posited an empirical method for addressing this question in:

Article A Method for Selecting Between Linear and Quadratic Classifi...

Finally, my guess is that reviewers may want to see that you have considered logistic regression as an alternative. I do say “considered,” as it can be that LR may perform far worse than discriminant analysis, but the obverse is also possible. This too, is an empirical question. More research on that if you are interested.

Thank you, Prof. Morris.

Sir, I seek to:

1) contrast each patient group with their case to case-matched controls.

2) Contrast the two patient groups

3) See if these 10 variables can discriminate Healthily controls, Patients with schizophrenia and patients with right hemisphere damage.

For the discriminant analysis, I had merged the two control groups. Is it wrong to do so? I thought it would illogical to discriminate two control groups as they are not supposed to be very different.

Sir, you are absolutely right the Box M test was not significant (P .001) when I tested it for the two patient groups.

Sir, can I please have your email address? Can I please send the paper to you?

I would expect that if these are truly "control" groups, not matched in some way, combining them is fine. A control group is randomly assigned, so there should be no problem; on the other hand if these are actually "comparison" groups that may have systematic differences either from unknown causes, or by design (e.g., matching with corresponding Patient group), then it may be that more thought needs to go into combining them. This is not a statistical question, but one of logic/homogeneity.

When you say "discriminate," I suspect that the criterion you seek is the degree to which you are able to correctly classify Ss into Patient or control groups and alternatively into the two Patient groups (RHD or Schizophrenia). Is that the case?

Yes, Sir the control groups were matched with the respective patient groups. The average age and education of the control groups HC-I and HC-II matched for SCH and RHD patients were (Av. Age: 41.13, SD=12.0; Av. Education: 13.5, SD=2.8) and (Av. Age: 60.06, SD=9.7; Av. Education: 12.7, SD=3.08) respectively. However, there was no significant difference between the two groups in all the ten tests. Actually, I included age and education as covariates but only education was found to have a significant effect. I think the control groups perhaps did not differ significantly in education.

Yes, Sir, I wanted to assess the degree to which the tests could correctly classify into Patient or control groups and alternatively into the two Patient groups (RHD or Schizophrenia). I also wanted to know the tests which helped to classify the controls from the patients and that which helped distinguish the two patient groups.

A quibble, but then I might elect to call these groups "comparison" rather than "control." But in this case it may not be reasonable to combine these comparison groups, as they are matched to different patient groups. I leave this to you, but I would guess that it is more reasonable to contrast/classify patient group with only the respectively matched comparison group.

In any case, my prior recommendations stand regarding contrast (ANOVA vs MANOVA) and classification (linear vs. quadratic rules, with the addition of logistic regression), regardless of the constitution of the comparison group.

In regard to "the tests which helped to classify" are you seeking to determine the contribution to classification accuracy afforded by DVs or combinations thereof, or are you interested in best performing subsets, or ... There could be more to say here, but I am not sure of the question(s).

Thank you, Sir.