Repeated measures ANOVA or Friedman test? I have a study with 35 subjects who received hypercoagulability testing at 4 different times (before surgery, after, at 1 week, and at 1 month).  Each subject has 9 different test of hyper coagulability at the 4 time points.  I want to compare each of these 9 tests over time (i.e.: clot time_preop vs. clot time_postop vs. clot time_1wk vs clot time_1mo) to see if they change.  
One issue I am having is how to decide if my data is normal.  How do I assess for normality in the data?  I have explored the data in SPSS and see that although most are normal, some are not.  If one of the measurements in a variable (i.e.: clot time_1wk) is not normal (kurtosis=10 and Shapiro-Wilk <0.01) but the others are, should I use Friedman non-parametric instead?  Or should I be assessing normality another way?
 A: Those tests didn't tell you the data were normal, just that they were generally not significantly deviating from normal.  Those are two different things.  There is no test for normal.  
One way I help my students come to a conclusion about satisfying normality is getting them to calculate the summary statistics of the data in question and then look at quantile-quantile plots of the sample data and simulations of the sample data.  So, you could get the standard deviation you found and the n of the sample and generate several sets of simulated data and look at what typical normal data should look like and compare it what was found.  That helps with the typical advice to really just look at the data and see if it is normal.
Directly addressing what you actually did... I'm guessing you examined each condition across subject?  That's OK but consider the multiple testing issue.  Some of those data were bound to come out looking non-normal, it's inevitable.  Furthermore, the data that you should be testing the normality of is the residuals of the ANOVA.  You should be plotting and examining that in order to see if you met the assumptions... not each condition of the experiment.  Besides getting around the multiple testing issue it's the actual assumption of the ANOVA.
A: I would never ask "Are my data normal?"  Taken literally a safe answwer without looking at the data is to say "no!"  This goes back to the wise and often quoted statement by George Box "All models are wrong, but some are useful.  Real data are complex.  Sometimes a normal iid model is a convenient approximation to describe the data but unless your data is simulated by selection from a normal it will not be a sample from a normal population.  Also random number generation on the computer is not purely random and so are called "pseudo-random".  To get to the specifics of your problem it is clear that you want to assess the data to see if the behavior of the sample is close enough to that from a normal distribution to make that model useful for your inference problem.  Goodness of fit tests have a problem in large sample sizes because you can reject slight departures from normality that are so slight that the normal model might still be very useful.  Since your sample size is small, Shapiro-Wilk is detecting a large difference which is also indicated by th kurtosis estimate = 10 and probably many other univariate tests or exploratory measures would indicate problems with the normal model for that one variable. There are tests for multivariate normality but that is not what I would suggest here.  My feeling is that if all the other variables appear to be close to normal doing the parametric ANOVA would be okay.  What I think is the best approach is to leave this one problem variable out and assess the eqaulity of means just on the others.  After doing that along with contrasts to find which means are different if the F tests rejects equality you could look at comparisons between the "non-normal" variable and comparing it with other variables that you think might be interesting to look at and potentially might have different means.  For this do a Wilcoxon.  My general advice is "when in doubt do both tests to see if the normality assumptions affect your p-values very much."   
A: I know this is an old post...
I don't think anyone mentioned that as long as you have sufficient sample size, your SAMPLING distribution will be close to normal regardless of the SAMPLE distribution that you are all focused on. I've heard several suggestions, but most say that if you have 30 or more data points, the normality assumption is robust in even heavily skewed sample distributions. 
Since you have 35 participants, just go with the regular ANOVA. However, if your sample distribution does not look close to normal, it could be useful to report the median and IQR for descriptive statistics (not inferential stats).
