How to perform MANOVA with continuous variables which are not normally distributed (non-parametric)

[#1]

I am performing an analysis of hemoglobin values at 3 different time points between cases and controls. The data is not normally distributed. How should I go about with MANOVA in such a setting? Also is there an alternative test that I can apply in JMP to see the differences in the cases & controls at these 3-time points.

[#2]

How are you assessing normality? Are you assessing the response itself? The predictors?

[#3]

Currently I had analyzed normalcy using the goodness of fit by Shapiro-Wilk test for Y variable at each time point. In my case, the distribution is not normal (p is significant in the Shapiro-Wilk test). In a situation where even at a one-time point (among the 3-time points) the distribution is abnormal, I am presuming to apply a nonparametric test.

Not sure if this is the right way of looking at the normalcy or evaluating the differences in cases and controls over the 3-time points. Please suggest.

[#4]

I suggest that you proceed with your analysis and check the residuals for anomalies before choosing another method of analysis.

[#5]

ANOVA is fairly robust to the underlying distribution of the individual values.  As Mark suggests, go ahead with your analysis and then check residuals for assumptions NID(0, variance).