Alternative Statistical Approaches to the Use of Data as Evidence for Hypotheses in Human Behavioral Ecology

Mary Towner sends along this article by herself and Barney Luttbeg that discusses the Trivers-Willard hypothesis and its applications to humans.

I think that Towner and Luttbeg agree with David Weakliem and myself on the substance, but I disagree with them on the question of what models to fit. It’s not so much a Bayesian or non-Bayesian question–we use both approaches in our article–but rather a question of whether to treat parameters as continuous or discrete. In their example on page 100, you consider models in which the probability of boy births is 0.50 and 0.53. I think it would make more sense to consider theta to be a continuous parameter with distribution centered on the historical value of 0.515. Neither of those hypothesized values seem vary plausible to me. On the substance, though, I think we’re all on the same page.

P.S. I was curious.

2 thoughts on “Alternative Statistical Approaches to the Use of Data as Evidence for Hypotheses in Human Behavioral Ecology

  1. This discussion implicitly raises the issue of whether we should be testing just two hypotheses (null value vs. all other values), or more. It's hard to consider more than two hypotheses in the classical approach, but Bayes factors are more flexible. Arnold Zellner (Statistical Science, 1987) suggested considering five: p=0, p positive and small, p negative and small, p positive and large, and p negative and large, where the value separating large and small is set in advance. It's reasonable to represent the hypotheses of small values by a uniform distribution in the range. It's less clear how the hypotheses of large values should be specified, but a point hypothesis specifying the minimum “large” value could be regarded as a way to do that (at least approximately).

    In this case, Towner & Luttberg's test of .53 of vs. .5 could be regarded as “large positive value” vs. null, and your proposed test as “small positive value” vs. null. (I'd agree that the usual observed value of about .515 would make a more reasonable null). I haven't applied Zellner's approach to Kanzawa's data, but I think it would lead to a reasonable conclusion there.

  2. David: I agree that such an approach can work, and that, quite possibly, Towner and Luttbeg's choices give OK answers in this particular example. It still seems like a lot of work and ultimately inferior to the Bayesian approach which uses more continuous prior information.

Comments are closed.