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What would be the best method to compare to products on a question rated 1-7?

The current technique being utilized in my team is compare mean for the 2 groups using F test.

but doesn't it violates the very assumption of normal distribution of variable being compared?

user2542275
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  • Short answer: *Yes*, in theory, but in practice *no*, as the $F$ test is *extremely* robust to violations against the normality assumptions. As long as you don’t have extremely small sample sizes, the means you’re comparing are approximately normally distributed (by the central limit theorem). – Karl Ove Hufthammer Apr 01 '15 at 08:25

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If your goal is comparing by the median of pairwise differences, you may apply non-parametric tests as the Mann-Whitney-U-Test (unpaired samples) or the Wilcoxon Test (paired samples).

If your sample is large, please check this discussion for options:

When to use the Wilcoxon rank-sum test instead of the unpaired t-test?

Community
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Statos
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  • As have been pointed out numerous times on this site, the Mann–Whitney test or the Wilcoxon test does **not** test for differences in medians (see https://stats.stackexchange.com/questions/11084/why-is-the-mann-whitney-u-test-significant-when-the-medians-are-equal and https://stats.stackexchange.com/questions/136636/reporting-results-of-mann-whitney-u-test-means-vs-medians). – Karl Ove Hufthammer Apr 01 '15 at 09:13
  • changed "comparing means" to "comparing by the median of pairwise differences" – Statos Apr 02 '15 at 10:13