Monthly Archives: October 2020

S. Senn: Testing Times (Guest post)

Posted on October 28, 2020 by Mayo

Stephen Senn
Consultant Statistician
Edinburgh, Scotland

Testing Times

Screening for attention

There has been much comment on Twitter and other social media about testing for coronavirus and the relationship between a test being positive and the person tested having been infected. Some primitive form of Bayesian reasoning is often used to justify concern that an apparent positive may actually be falsely so, with specificity and sensitivity taking the roles of likelihoods and prevalence that of a prior distribution. This way of looking at testing dates back at least to a paper of 1959 by Ledley and Lusted[1]. However, as others[2, 3] have pointed out, there is a trap for the unwary in this, in that it is implicitly assumed that specificity and sensitivity are constant values unaffected by prevalence and it is far from obvious that this should be the case. Continue reading →

Categories: S. Senn, significance tests, Testing Assumptions

Souvenir From the NISS Stat Debate for Users of Bayes Factors (& P-Values)

Posted on October 24, 2020 by Mayo

What would I say is the most important takeaway from last week’s NISS “statistics debate” if you’re using (or contemplating using) Bayes factors (BFs)–of the sort Jim Berger recommends–as replacements for P-values? It is that J. Berger only regards the BFs as appropriate when there’s grounds for a high concentration (or spike) of probability on a sharp null hypothesis, e.g.,H₀: θ = θ₀.

Thus, it is crucial to distinguish between precise hypotheses that are just stated for convenience and have no special prior believability, and precise hypotheses which do correspond to a concentration of prior belief. (J. Berger and Delampady 1987, p. 330).

Continue reading →

Categories: bayes factors, Berger, P-values, S. Senn

My Responses (at the P-value debate)

Posted on October 21, 2020 by Mayo

How did I respond to those 7 burning questions at last week’s (“P-Value”) Statistics Debate? Here’s a fairly close transcript of my (a) general answer, and (b) final remark, for each question–without the in-between responses to Jim and David. The exception is question 5 on Bayes factors, which naturally included Jim in my general answer.

The questions with the most important consequences, I think, are questions 3 and 5. I’ll explain why I say this in the comments. Please share your thoughts. Continue reading →

Categories: bayes factors, P-values, Statistics, statistics debate NISS