0
$\begingroup$

I have just conducted an experiment in which I have measured glucose concentration in patients (4 different treatment groups) at 3 different weeks ( pre, 6 weeks and 12 weeks). I want to use Mixed Anova to test if there is any significant difference between treatments in glucose concentration (also possible time and time*treatment interaction).

However, Mixed Anova requires the data to be normally distributed. I am using SPSS. Must I perform for example a Kolmogorov‐Smirnov/Shapiro-Wilks test (glucose data (group1, time1,...,etc.) of every group separately (at each time point)? Or is there another way to look at normality before running Mixed Anova?

$\endgroup$
  • 1
    $\begingroup$ I wouldn't call this "mixed"; it sounds just like two-way analysis of variance. But the assumption is not that the data are normally distributed, rather that the error terms are. Styles differ, but informal graphical examination of the data might indicate e.g. that you should work with logarithm of glucose concentration. Similarly you could look at residuals from the anova and check for normality. Shapiro-Wilk [not Wilks, a different statistician] is a dedicated test for normality and superior to Kolmogorov-Smirnov if you felt a compulsion to include a formal test. $\endgroup$ – Nick Cox Aug 12 '13 at 20:33
  • $\begingroup$ Thanks Nick, Should I run a Shapiro-Wilk test for each group separately at each time point? (thus group 1 time 1, group 1 time...group 2 time 1 ...etc?....Or just test for normality after i obtained the residuals for the ANOVA. $\endgroup$ – Andre Aug 13 '13 at 14:34
  • 1
    $\begingroup$ I personally recommend strongly against that for several reasons, too many to fit into one comment. At most, one Shapiro-Wilk test for all the residuals, but even then a significant result doesn't necessarily undermine an anova. But there are too many possibilities to answer definitively about knowing more about your data. $\endgroup$ – Nick Cox Aug 13 '13 at 14:39
1
$\begingroup$

Sphericity explained here is also assumed and, when violated, increases the Type I error rate substantially. Sphericity is almost always violated so the problem is not to test for it (although that can be done) but rather how to deal with it. Violations of normaility of residuals make less difference unless they are severe. A good argument against testing for normality is that the a priori probability that the distribution is exactly normal is essentially 0, so you know the null hypothesis is false before you do the test.

$\endgroup$
0
$\begingroup$

You can't just test the residuals when it's a mixed-factor ANOVA because the residuals from most stats packages (incl. SPSS) will not have removed the main effect of subjects. You must first transform each piece of data into a deviation (from the subject's mean). Then run the ANOVA, saving the residuals and test those for normality.

Note that this will result in a separate test of normality for each level of the within-subject factor. That is as it should be, because we don't use an estimate of variance that is pooled across levels of a within. We only pool across levels of betweens.

Note, also, that the highly anal might also want to test the subject means for normality, rather than rely on the three tests of normality above. This is done by conducting a one-way univariate analysis of the subject means, saving the residuals.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.