I am analyzing a data from survey. The data is from a 2X2 between subjects experiment design with 45 subjects in each of the four conditionsThe questions are based on a 5-point or 10-point scale. Since the respondents can only answer the questions with a number between 1 to 5 (or 1 to 10), does it mean that the data are discrete and cannot be normally distributed even if I use transformation? So what should I do before the data analysis? If it is not normal distribution and some are skewed, can I still do the two-way anova analysis or what should I do??
The 2 Way ANOVA assumption I think you're referring to is that the residuals of the dependent variable should be more or less normally distributed for each cell of the design. If this turns out to be the case, you may want to consider using the Kruskal-Wallis H test, which is a non-parametric test. Non-parametrics are often used when data violates the assumptions of parametric tests. I hope that helps.