# Solved – Normality test for discrete data / ordinal scale (1-2-3-4)

My test model is:

• 3 factors x -> x1 (3 levels), x2 (2 levels), x3 (2 levels), nominal scale
• 4 dependent var y -> ordinal scale (1-2-3-4)
• 18 participants
• balanced
• –> 12 factor-levels x 18 x 4 = 216 (measurements) x 4 (y) = 864 values

I assume using 4 times a 3-factorial ANOVA in R Studio for each y:

``y1.aov = aov(y1 ~ x1*x2*x3) y2.aov = aov(y2 ~ x1*x2*x3) y3.aov = aov(y3 ~ x1*x2*x3) y4.aov = aov(y4 ~ x1*x2*x3) ``

Before I want to test assumptions normal distribution and equal variance. However I can't test normal distribution successfully because the data is discrete: y_n is element of {1,2,3,4}. Thus normal distribution is rejected:

``shapiro.test(y1) # p-value = 2.21e-13 ad.test(y1) # p-value < 2.2e-16 ``

I searched all over the internet but could not find a proper answer. I just know a lot of researchers performing ANOVA to similar models (ordinal scale). How can I test the assumption properly?

Best regards

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