## triste célébration for World Statistics Day

As I was discussing yesterday night with my daughter about a practice stats exam she had just taken in medical school, I came upon the following question:

What is the probability that women have the same risk of cancer as men in the entire population given that the selected sample concluded against equality?

Which just means nothing, since conditioning on the observed event, say |X|>1.96, cancels any probabilistic structure in the problem. Worse, I have no idea what is the expected answer to this question!

### 8 Responses to “triste célébration for World Statistics Day”

1. J-L FOULLEY Says:

Thanks Christian for letting us know about this question in the stat exam of your daughter. It reminds me sth that troubled me when I prepared a lecture in 2013 at Applibugs on the Jeffreys Lindley paradox. Berger and Selke (1987, JASA, 82) wrote on page 120: “Finally we must establish the correspondence between the P value and the posterior probability of H0 when the data x are replaced by the cruder knowledge that x belongs to A={y,T(y)>T(x)}”. It took me some time to rederive this result (page 29 http://www3.jouy.inra.fr/miaj/public/matrisq/Contacts/applibugs.13_12_19.JLF.pdf) but it looks mathematically OK.
Is it not the issue we are faced to here?

• Dear Jean-Louis, thanks for the reminder: I agree that we are conditioning on the fact that the observed p-value is smaller than the 5% bound. And remember this related result of Jim and Tom. But there is nothing left to probabilise, unless we turn Bayesian. Which is certainly not the case in this medical statistics course!

2. Maybe if alpha = 5%, then they think the answer is 5%? I know is not correct, but it seems the only thing that they could be thinking.

• Yes indeed Manoel, my daughter tells me this is the “right” answer and she even thinks it makes sense..!

3. C’est un grand exercice pour pratiquer notre capacité de deviner sur l’universe semantique de cette professeur.

• Ce serait le cas en psychologie, mais en médecine, il n’y a pas encore de cours de lecture de pensées ou d’hypnose!!!

• Vous avez la raison, mais n’oublie pas que Freud a été un médecin neurologue: “ l’inventeur de l’a psychanalyse ´´. er.. ou meilleur, un grand lecteur de Nietzsche.

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