our team initially planned to a sample t-test but the data was non normal even after we applied transformations. wilcoxon would've been a good alternative but it directly looks at the median and not the mean, which is now what we need. any tips or guidance that we can use? all will be gladly appreciated!!!
Parametric tests, such as a T test, involve and refer to parameters of a normal distribution, such as mean value, variance/standard deviation. If a distribution is not normal, the mean value is not assumed to be informative (especially in cases of of assymmetric or multimodal distributions) and therefore not used (let alone in significance tests).
Since your data is non-normal and you’re interested in comparing means, not medians, Wilcoxon isn’t suitable. Instead, try bootstrapping or a permutation test—both are non-parametric methods that let you compare means without assuming normality. You can also consider robust t-tests like Yuen’s test for trimmed means.
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