In the context of an experiment, I have eight groups (2x2x2 between subjects) and the n per group ranges between 23 and 29. My variable of interest is how many critical details (range from 0 to 5) are provided in a free report. Half of the groups have skew and kurtosis values that are within the range of what I have read is considered to be acceptable (skew: +/- 0.80; kurtosis +/- 2.00). For the other groups, the distribution is skewed negatively with the most common value being the highest value possible. However, this is not a surprise; these groups are actually expected to provide most or all of the details and thus achieve very high values because of one of the experimental factors.
I planned to run an ANOVA and have two questions because of the situation described above:
(1) If the skewed distribution is what would be expected (i.e. considered to be normal), is there still a problem in terms of running an ANOVA? (And, if so, I'd also be interested in understanding why.) Also, it may be relevant to know that the homogeneity of variance assumption is violated too.
(2) If it is a problem, might bootstrapping be an option? I am not aware of a non-parametric alternative to a 2x2x2 between subjects ANOVA.