Violation of Normality in Mixed Design ANOVA?

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I conducted a study in which two groups of teachers (pre-service and veteran) all watched four video clips of instances of aggression between students. The clips differed by type of aggression and gender of the students depicted (physical vs. relational aggression; male vs. female). After viewing each clip, the participants answered a series of questions about their perceived severity of the incident, empathy for the victim, empathy for the bully, and likelihood of intervention on a 5-point Likert scale (these constituted the dependent variables). I conducted four separate mixed design ANOVAs in SPSS for each dependent variable, with one between-subject independent variable and two within-subject independent variables:

Teacher status - pre-service vs. veteran (between-subject) Aggression - physical vs. relational (within-subject) Gender - male vs. female (within-subject)

Unfortunately, I have unequal samples sizes for the two groups (28 pre-service teachers, 14 veteran). Also, some of the dependent variables are not normally distributed. I did not violate the assumptions of homogeneity of variance or sphericity.

First of all, I am confused about checking the normality of the data vs. the normality of the residuals in SPSS. When you run the normality tests (K-S and S-W) via "Descriptive Statistics" -> "Explore," do you include the DVs under the "Dependent List"?

Secondly, how robust is a mixed/repeated measures ANOVA to the violation of normality? Can I follow the general rules of thumb regarding the degree of skewness and kurtosis?

I am a graduate student in the social sciences, and statistics is by no means my forte. I have spent several weeks attempting to make sense of all of this, but I find that I am just confusing myself further and further. Any straightforward answers would be much appreciated!

At this point, I am hoping to talk about the violation of normality in the discussion section of my paper, noting it as a limitation for this pilot study. Can anyone point me in the direction of references that basically argue that this violation of normality is not the end of the world?

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关键词：Violation normality Design normal ANOVA Design

       
"some of the dependent variables are not normally distributed" -- good thing that's not an assumption of ANOVA, then. There is a normality assumption, but it's not an assumption about the unconditional distribution of the DV. Specifically, the errors are assumed to be normal. What do residual plots look like?

Looking at the Q-Q plots, the points fall along the diagonal line for some DVs, but not for others. I generated those through Descriptive Stats->Explore. I'm not sure how to obtain other residual plots given the way my data is set up. The within-subject IVs are basically linked with the DVs. For example, I have separate columns for Empathy for Victim - Phys. Aggression Boys, Empathy for Victim - Phys. Aggression Girls, Empathy for Victim - Rel. Aggression Boys, and Empathy for Victim - Rel. Aggression Girls (likewise for Seriousness, Empathy for Bully, and Likelihood of Intervention)

I can't tell whether 'not for others' is an issue or not; that's not enough to tell anything. Even when the assumptions are exactly satisfied, you don't expect that the points will all fall on the line. You expect to see some deviation, more in the tails. The sample sizes are pretty small and not close to equal, so it's possible there's reason to have some concern. –  Glen