I am comparing two categories (A and B) of social media posts with the corresponding number of likes for each one. I am taking samples of equal size from each category at random and performing a Mann-Whitney U-test using scipy.stats module in Python.   I have chosen U-test since taking the mean of A or B data does not make a lot of sense in my case and I have been relying on medians so far for the comparisons.  I was performing the test with sample sizes in range of 20-100 which gave the expected results that the two categories were similar. So I decided to try larger samples. With sample sizes >= 200, the p-value of the U-statistic was &lt; .05, which could indicate that the distributions of the two samples might be different (at alpha = 5%). However, the visual analysis of the samples (n = 200) shows otherwise, i.e. the difference in the two distributions is very minuscule (see below). Is there something I'm not getting/doing wrong/misinterpreting? Thanks a bunch in advance.
In a  of Amstat News, the authors (Mark van der Laan and Sherri Rose) stated that "We know that for large enough sample sizes, every study—including ones in which the null hypothesis of no effect is true — will declare a statistically significant effect.".  Well, I for one didn't know that. Is this true? Does it mean that hypothesis testing is worthless for large data sets?
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