So, several people pointed out that this table is very weird, and I agree It's hard to see how these values are ~possible~, given the p-value beneathhttps://twitter.com/GidMK/status/1213944606510866432 …
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And the test that the p-value comes from is actually a Wilcoxon signed-rank test, which compares DISTRIBUTIONS, not mean values In other words, it's VERY unlikely you'd see two samples with the same medians, virtually identical quartiles, but a p of 0.022pic.twitter.com/bTLVXJ6CsF
How unlikely? Well, I thought I'd give it a quick test (using Stata 15) Here's the codepic.twitter.com/rwqwm2qo3H
Basically, I'm generating two variables with the correct quartiles, where all numbers are random between those two I also skewed the numbers slightly up (making before higher and after lower) because...well, you'll see
The code runs for 100,000 iterations, then dumps it all into the file I convert the z-scores into p-values, and voila! 100,000 random simulated distributions and their p-values for a Wilcoxon paired samples test
Straight away it doesn't look good. There are very few tests where we get a significant p-value randomly (129/100000)pic.twitter.com/3kmDbe4glI
Even worse, if I only look at the simulations where the means were congruent I can't find a single simulated example where the p-value is even close to 0.022!pic.twitter.com/TLJMvrI6Z6
If I rejig the code to make the before values higher still, and the after values even lower, I can get a lot more significant results but ~none~ of the means are congruentpic.twitter.com/KAnRBe75pt
I can't find a single example where those mean, median, p-value, and quartiles are all true That's...not ideal Please have a look at my code and tell me if I've made a mistake!
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