## Mindless statistics and the null ritual

24 January, 2013 at 09:57 | Posted in Statistics & Econometrics | 2 Comments

Knowing the contents of a toolbox, of course, requires statistical thinking, that is, the art of choosing a proper tool for a given problem. Instead, one single procedure that I call the “null ritual” tends to be featured in texts and practiced by researchers. Its essence can be summarized in a few lines:

The null ritual:
1. Set up a statistical null hypothesis of “no mean difference” or “zero correlation.” Don’t specify the predictions of your research hypothesis or of any alternative substantive hypotheses.
2. Use 5% as a convention for rejecting the null. If signiﬁcant, accept your research hypothesis. Report the result as p < 0.05, p < 0.01, or p < 0.001 (whichever comes next to the obtained p-value).
3. Always perform this procedure …

The routine reliance on the null ritual discourages not only statistical thinking but also theoretical thinking. One does not need to specify one’s hypothesis, nor any challenging alternative hypothesis … The sole requirement is to reject a null that is identiﬁed with “chance.” Statistical theories such as Neyman–Pearson theory and Wald’s theory, in contrast, begin with two or more statistical hypotheses.

In the absence of theory, the temptation is to look ﬁrst at the data and then see what is signiﬁcant. The physicist Richard Feynman … has taken notice of this misuse of hypothesis testing. I summarize his argument:

Feynman’s conjecture:
To report a signiﬁcant result and reject the null in favor of an alternative hypothesis is meaningless unless the alternative hypothesis has been stated before the data was obtained.

Feynman’s conjecture is again and again violated by routine signiﬁcance testing, where one looks at the data to see what is signiﬁcant. Statistical packages allow every difference, interaction, or correlation against chance to be tested. They automatically deliver ratings of “signiﬁcance” in terms of stars, double stars, and triple stars, encouraging the bad afterthe-fact habit. The general problem Feynman addressed is known as overﬁtting … Fitting per se has the same
problems as story telling after the fact, which leads to a “hindsight bias.” The true test of a model is to ﬁx its parameters on one sample, and to test it in a new sample. Then it turns out that predictions based on simple heuristics can be more accurate than routine multiple regressions … Less can be more. The routine use of linear multiple regression exempliﬁes another mindless use of statistics …

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 … 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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## 2 Comments »

1. There is an important word missing from the above quote. (I don’t know what importance the word is given in “The Rationality of Mortals”. The word is “democracy”. What I mean is this.

The fact that people do not maximise utility in an entirely rational way (e.g. they are subject to nudging) is not a good argument for forcibly taking money off them and nudging them in the direction of healthier food or similar.

People devote huge efforts to nudging members of the opposite sex towards the bedroom or towards marriage, but that’s not an argument for arranged or forced marriage. And the latter area is probably subject to even more irrationality than choices to do with consumer goods (just look at the divorce figures).

Forcibly taking money off people and using the money to nudge them is a big step to take. It should never be taken without the consent of the people. I.e. if people vote for X% of GDP to be devoted to what can losely be called “nudge” items (i.e. public spending), that’s OK with me.

But the simple fact that consumer choice does not work anything like perfectly is not of itself an argument for having politicians or bureaucrats make those choices.

• If the bureaucrats do it, they have the accountability, nudging or creating good and bad choices of for instance schools. This remove accountability from politicians and bureaucrats, so instead you pay for it, they sell it and you retain all risk and accountability.

To spin on the bedroom anology, they leave you with the baby afterwards.

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