Statistical approaches

At the Statistics for Experimental Biologists blog, a short article about the four main ways to approach a statistical problem:  Bayesian, frequentist, information-theoretic, and likelihood, entitled "Putting the methods you use into context". The article points out that there are overlaps between the four approaches, and ends with the statement "Knowing the big picture allows you to reflect on the methods you use, and ask whether they are appropriate for the task. It is also a useful antidote to some of the dogmatism associated with statistical analyses (you don't have to do something one way just because that's how you saw others do it)."

The article also includes some references and links to peer-reviewed journal articles in PDF form that are (contrary to my previous post) freely available to the hoi polloi.  One of those is by Gerd Gigerenzer, and appeared in the Journal of Socio-Economics in 2004. In the article, titled "Mindless Statistics", Gigerenzer defines the "null ritual" as having three steps:

1. set up a statistical null hypothesis, but do not specify your own hypothesis nor any alternative hypothesis,
2. use the 5% significance level for rejecting and accepting the null hypothesis, and
3. always perform this procedure.

Gigerenzer then asks "Why do intelligent people engage in statistical rituals rather than in statistical thinking?" His conclusions are rooted in the ritualistic nature of statistical hypothesis testing, in that it has all of the elements of social rituals.  First, there is the repetition of the same action (repeating the test over and over).  Second, there is a focus on special numbers and colours -- 0.05 and 0.01, two standard deviations, etc.  Third, a ritual incorporates fears about serious sanctions for transgressions; in the academy, the adjudicators are professors, academic advisors, journal editors, and textbook publishers.  And finally, the ritual relies on "wishful thinking and delusions that virtually eliminate critical thinking", which in statistical research is the p-value.

I will finish with Gigerenzer's final two paragraphs, quoted here in their entirety:

We know but often forget that the problem of inductive inference has no single solution.
There is no uniformly most powerful test, that is, no method that is best for every problem.
Statistical theory has provided us with a toolbox with effective instruments, which require
judgment about when it is right to use them. When textbooks and curricula begin to teach
the toolbox, students will automatically learn to make judgments. And they will realize that
in many applications, a skilful and transparent descriptive data analysis is sufficient, and
preferable to the application of statistical routines chosen for their complexity and opacity.
Judgment is part of the art of statistics.
To stop the ritual, we also need more guts and nerves.We need some pounds of courage
to cease playing along in this embarrassing game. This may cause friction with editors and
colleagues, but it will in the end help them to enter the dawn of statistical thinking.

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