Question for an anthropologist on evolution and statistical testing?
I have a question on Peason/Neyman/Fisherian statistics and evolution. If I were testing for the existence of evolution using regression, such as a time series rate of change, then the most rational null hypothesis is the "no effect," hypothesis, that is, mu=0. In the category where mu=0 is intelligent design, creationism, but also other weird but possible naturalistic explanations. If the null is rejected then by modus tollens, to some degree of confidence, intelligent design is rejected by the data without a need to "assume" naturalism or other materialistic assumptions. Further, as Frequentist methods guarantee an alpha level of coverage, they are a worst case test statistic (assuming a proper statistic was used of course). This would be the distribution that most favored the null, to guarantee coverage. So using the data, with basic assumptions like Kolmogorov's axioms or probability, one would arrive at the rejection of creationism without resorting to naturalistic assumptions. What is the flaw in this argument? Also, sorry to use your professional time on this, but I cannot walk through the flaw. One could extend this, with a Bayesian decision theory framework to modus ponens as well, but only if you include additional assumptions. Criticism very much desired.
Note I am only interested in the strength of the argument on its own merits, I am not concerned with whether or not it is received by the audience as valid. I doubt creationists would "get it," as there would be a strong emotional loss from accepting it. Also, sorry about the typo on Pearson's name.