Phil 6334: S 14
Reading/Review Questions 2: (March 20)
In a well written ~ 3 page (double-spaced) essay, discuss any 2 of the following questions. Focus on explaining the concepts and issues in the reading. Use quotes from the text. Aside from answering the questions, handle the essay in any way you want, focusing on whatever interests you the most. Less is more: explain just a few things clearly and thoughtfully, rather than trying to cover the ground. (I’ve included specifics just as prompts.)
(1) Among the 3 key phrases Fisher lists (70) in bringing out the “logical” and “ideological” differences he finds between his and Neyman’s view of statistical tests, give the most detailed consideration to the second two: errors of the second kind, and inductive behavior. The objection to “repeated sampling from the same population” is multi-faceted, and more of the facets will be considered later on. But observe how Pearson throws the issue back on Fisher (Pearson, 205).
What are Fisher’s objections to considering errors of the second kind? (73). What should “the worker’s real attitude” be when a null hypothesis is “accepted” (i.e., no statistically significant difference is found)?
(2) When I first met George Barnard, he noted that he is to be credited with “the penetrating observation” one finds in Fisher that “Neyman, thinking that he was correcting and improving” upon Fisher’s work on tests of significance “in fact reinterpreted them in terms of that technological and commercial apparatus which is known as an acceptance procedure.” (Fisher, 69) This suggests, does it not, that the behavioristic or “acceptance sampling” construal of Neyman’s conception of tests was not immediately obvious to Fisher (and perhaps owed more to their growing personality conflicts?)
Barnard further took credit for being careful to leave his friend E.S. Pearson out of this criticism—but consider Pearson’s response to the effect that “there was no sudden descent upon British soil of Russian ideas” (Pearson, 204). Granted Pearson recoils at “inductive behavior” in the last sentence of his contribution.
According to Fisher, when “Neyman denies the existence of inductive reasoning he is merely expressing a verbal preference” for speaking in terms of “inductive behavior”. I have increasingly come to think this is correct. What do you think of this?
(3) What is Neyman’s response to Fisher’s criticism of “errors of the second kind” (more commonly known as Type II errors)? (e.g., Neyman, 289-90). Note the three uses for “power” considerations Neyman lists in the second full paragraph of Neyman page 290 (the third is especially noteworthy!)
Consider Neyman’s remarks (290-1) in light of the charge that in practice, if not in theory, Fisher also considers “errors of the second kind” (and in so doing may even fall into the “fallacy of acceptance” of which he accuses Neyman).
Examine Pearson’s argument (207) that Fisher’s own recommended construals of non-significant results implicitly refer to alternatives that are discrepant from the null hypothesis, and a test’s sensitivity to detecting them.
(4) Consider Neyman’s response to Fisher’s alleged deductive syllogism (in the case of instantiating confidence intervals) in section 4. Objections to the Notion of Fiducial Probability (291). I have always felt this to be a rather unclear response (although in a later work Neyman does a better job, by pointing up the contradictions to which such a “probabilistic instantiation” can lead.) Thoughts?