aloctavodia
commented
3 years ago Hi @alexander-pv thanks for your comment.
The resported comparison in the book is Thursday - Sunday, the negative value of the Cohen's D means that on Sundays the tip is larger and also that the probability superiority is a 39% chance that a person visit picked at random from the Thursday group will have a higher tip than a person visit picked at random from the Sunday group. If you revert the comparison Sunday - Thursday (which is equivalent to taking the absolute value, as now the differences are positive). You will get the value of 61%. both ways are equivalent as long as you take care of which group (day) is the one used as reference.
alexander-pv
Hi! Thank you for the book! In Chapter2 I made opposite conclusions based on HPD and the Probability of superiority. I believe that this is because Cohen's d may be negative which affects cumulative normal distribution that calculates the Probability of superiority.
For example, based on the HPD I am able to say that the average tip size differs between Thursday and Sunday. But based on the Probability of superiority there is only a 39% chance that a person visit picked at random from the Sunday group will have a higher tip than a person visit picked at random from the Thursday group. However, when I take the absolute value of Cohen's d for cumulative normal distribution then conclusions based on Probability of superiority are consistent with conclusions based on HPD.
So my suggestion:
ps = dist.cdf(np.abs(d_cohen)/(2**0.5))I also attached screenshots in Jypyter:
Before fix:
After fix: