Just as in the past 6 years since I’ve been blogging, I revisit that spot in the road at 11p.m., just outside the Elbar Room, look to get into a strange-looking taxi, to head to “Midnight With Birnbaum”. (The pic on the left is the only blurry image I have of the club I’m taken to.) I wondered if the car would come for me this year, as I waited out in the cold, given that my Birnbaum article has been out since 2014. The (Strong) Likelihood Principle–whether or not it is named–remains at the heart of many of the criticisms of Neyman-Pearson (N-P) statistics (and cognate methods). 2018 will be the 60th birthday of Cox’s “weighing machine” example, which was the start of Birnbaum’s attempted proof. Yet as Birnbaum insisted, the “confidence concept” is the “one rock in a shifting scene” of statistical foundations, insofar as there’s interest in controlling the frequency of erroneous interpretations of data. (See my rejoinder.) Birnbaum bemoaned the lack of an explicit evidential interpretation of N-P methods. Maybe in 2018? Anyway, the cab is finally here…the rest is live. Happy New Year! Continue reading
Monthly Archives: December 2017
Midnight With Birnbaum (Happy New Year 2017)
60 yrs of Cox’s (1958) weighing machine, & links to binge-read the Likelihood Principle
2018 will mark 60 years since the famous chestnut from Sir David Cox (1958). The example “is now usually called the ‘weighing machine example,’ which draws attention to the need for conditioning, at least in certain types of problems” (Reid 1992, p. 582). When I describe it, you’ll find it hard to believe many regard it as causing an earthquake in statistical foundations, unless you’re already steeped in these matters. A simple version: If half the time I reported my weight from a scale that’s always right, and half the time use a scale that gets it right with probability .5, would you say I’m right with probability ¾? Well, maybe. But suppose you knew that this measurement was made with the scale that’s right with probability .5? The overall error probability is scarcely relevant for giving the warrant of the particular measurement, knowing which scale was used. So what’s the earthquake? First a bit more on the chestnut. Here’s an excerpt from Cox and Mayo (2010, 295-8): Continue reading
Why significance testers should reject the argument to “redefine statistical significance”, even if they want to lower the p-value*
An argument that assumes the very thing that was to have been argued for is guilty of begging the question; signing on to an argument whose conclusion you favor even though you cannot defend its premises is to argue unsoundly, and in bad faith. When a whirlpool of “reforms” subliminally alter the nature and goals of a method, falling into these sins can be quite inadvertent. Start with a simple point on defining the power of a statistical test.
I. Redefine Power?
Given that power is one of the most confused concepts from Neyman-Pearson (N-P) frequentist testing, it’s troubling that in “Redefine Statistical Significance”, power gets redefined too. “Power,” we’re told, is a Bayes Factor BF “obtained by defining H1 as putting ½ probability on μ = ± m for the value of m that gives 75% power for the test of size α = 0.05. This H1 represents an effect size typical of that which is implicitly assumed by researchers during experimental design.” (material under Figure 1). Continue reading
How to avoid making mountains out of molehills (using power and severity)
In preparation for a new post that takes up some of the recent battles on reforming or replacing p-values, I reblog an older post on power, one of the most misunderstood and abused notions in statistics. (I add a few “notes on howlers”.) The power of a test T in relation to a discrepancy from a test hypothesis H0 is the probability T will lead to rejecting H0 when that discrepancy is present. Power is sometimes misappropriated to mean something only distantly related to the probability a test leads to rejection; but I’m getting ahead of myself. This post is on a classic fallacy of rejection. Continue reading