2024 Leisurely Cruise

Neyman & Pearson

November Cruise: 3.2

This third of November’s stops in the leisurely cruise of SIST aligns well with my recent BJPS paper Severe Testing: Error Statistics vs Bayes Factor Tests.  In tomorrow’s zoom, 11 am New York time, we’ll have an overview of the topics in SIST so far, as well as a discussion of this paper. (If you don’t have a link, and want one, write to me at error@vt.edu). 

3.2 N-P Tests: An Episode in Anglo-Polish Collaboration*

We proceed by setting up a specific hypothesis to test, H₀ in Neyman’s and my terminology, the null hypothesis in R. A. Fisher’s . . . in choosing the test, we take into account alternatives to H₀ which we believe possible or at any rate consider it most important to be on the look out for . . .Three steps in constructing the test may be defined: Continue reading →

Neyman & Pearson

November Cruise: 3.2

This second of November’s stops in the leisurely cruise of SIST aligns well with my recent Neyman Seminar at Berkeley. Egon Pearson’s description of the three steps in formulating tests is too rarely recognized today. Note especially the order of the steps. Share queries and thoughts in the comments.

3.2 N-P Tests: An Episode in Anglo-Polish Collaboration*

We proceed by setting up a specific hypothesis to test, H₀ in Neyman’s and my terminology, the null hypothesis in R. A. Fisher’s . . . in choosing the test, we take into account alternatives to H₀ which we believe possible or at any rate consider it most important to be on the look out for . . .Three steps in constructing the test may be defined:

Step 1. We must first specify the set of results . . .

Step 2. We then divide this set by a system of ordered boundaries . . .such that as we pass across one boundary and proceed to the next, we come to a class of results which makes us more and more inclined, on the information available, to reject the hypothesis tested in favour of alternatives which differ from it by increasing amounts.

Step 3. We then, if possible, associate with each contour level the chance that, if H₀ is true, a result will occur in random sampling lying beyond that level . . .

In our first papers [in 1928] we suggested that the likelihood ratio criterion, λ, was a very useful one . . . Thus Step 2 proceeded Step 3. In later papers [1933–1938] we started with a fixed value for the chance, ε, of Step 3 . . . However, although the mathematical procedure may put Step 3 before 2, we cannot put this into operation before we have decided, under Step 2, on the guiding principle to be used in choosing the contour system. That is why I have numbered the steps in this order. (Egon Pearson 1947, p. 173)

Continue reading →