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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