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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??

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    $\begingroup$ Some survey data might be quite close to normal, depending on what you ask. What you have there are items from ordered categories as might be used in a Likert-scale. These won't be normal and cannot be transformed to be normal. But that may not matter. What are you doing with the individual items (do you add them, for example)? $\endgroup$ – Glen_b -Reinstate Monica Jun 14 '15 at 6:08
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    $\begingroup$ "Analyzing data" is really vague. What are you actually trying to do with the data? $\endgroup$ – shadowtalker Jun 14 '15 at 12:39
  • $\begingroup$ See the posts on our site that mention "Likert". $\endgroup$ – whuber Jun 14 '15 at 18:21
  • $\begingroup$ @ssdecontrol I will do two-way anova to test the main effects and interaction between the two factors. @ Glen_b Because it is a pretest posttest experiment, I take the average of the difference between two tests. $\endgroup$ – Gemini Jun 18 '15 at 2:55
  • $\begingroup$ If you can coerce your scale to numeric (in theory), you can model many distributions using GLM. $\endgroup$ – Roman Luštrik Jun 18 '15 at 5:42
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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.

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  • $\begingroup$ Generally speaking distribution-free procedures like the Kruskal-Wallis only avoid the specific finite-parameter distributional assumption of parametric tests - they still make other assumptions - sometimes including, assumptions about the distribution (e.g. symmetry in some cases) -- and may even be somewhat more sensitive to some of them. $\endgroup$ – Glen_b -Reinstate Monica Jul 3 '16 at 23:47

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