First, here's the background to the experiment. It tested participants' judgements of the grammaticality of sentences. There were four different types of sentences tested (variable = "type", levels = 4), each of which appeared in an affirmative and negative form (variable = "polarity", levels = 2). There were two versions of the experiment (to ensure no ordering effects) and participants were assigned to one of four different age groups. So, the ANOVA has 2 within subjects factors: type and polarity; and 2 between subjects factors: age group and version.

My questions are as follows.

First, I know that ANOVA, being a parametric test, assumes a normal distribution. I'm confused about what this means, though: do the data have to be normally distributed? This is problematic for my study, because the expectation was that any participant who behaved like a normal adult should judge 3 out of 4 of the sentence types as grammatical. So, if I draw a histogram with percentage of grammatical responses on the X axis and frequency on the Y axis, then I expect a trend line to be shifted towards the right of the histogram (i.e. towards 100% judgements as grammatical). Does this mean that my data violates the normal distribution assumption, or am I thinking about this in the wrong way?

Second, when I ran the ANOVA, Levene's Test gives significant results, suggesting that the Homogeneity of Variance assumption has been violated. I'm not entirely sure I understand exactly what Levene's Test measures: am I correct in thinking that it's comparing the variance in the way participants respond for each sentence type*polarity? If that's correct, then it seems to me that I'd

*expect*it to be significant, if the participants are more sure in their judgement of some sentence types than others. In any case, the most important questions here are should I worry about the fact that Levene's Test is significant, and, if so, what should I do about it?

Many thanks, if you've taken the time to read this far. I'd be really grateful if anyone can help me out with this.

Gary