Friday, February 19, 2010

The Standard Error of Regressions




McClowskey argues that the standard error of regressions is to confuse statistical significance with practical significance. Given a large enough sample, the slightest variation will be considered statistically significant.

McClowskey and confederates read 182 papers in the American Economic Review and, from each paper, asked 19 questions:

1. Does the paper use a small number of observations, such that statistically significant differences are not found at the conventional levels merely by choosing a large number of observations?

2. Are the units and descriptive statistics (means for instance) of all regression variables included?
They should be so the reader can judge importance.

3. Are the coefficients reported in elasticity form, or in some interpretable form?

4. Are the proper null hypothesis specified?
"The only results that leads to a definitive conclusion is a rejection of the null [...] rejecting the null does not imply that the alternative hypothesis is true: there may be other alternatives which would cause rejection of the null."

5. Are coefficients carefully interpreted?
Suppose the dependent variable is weight and the large coefficient is on height, while the smaller coefficient is on exercise. "Neither the physician nor the patient would profit from [...] offering the overweight patient in effect the advice that he's not too fat, merely too short for his weight.

6.Does the paper refrain from reporting meaningless statistics?

7.Does the paper goes in a crescendo culminating at statistical significance?
This should not be the ultimate and crucial test.
...

11. Does the paper avoid sign econometrics?
Te sign is not economically significant unless the magnitude is large enough to matter.

12.Does the paper discuss the size of the coefficients?

The standard error in regressions is confusing statistical significance with importance. Ironically (an fortunately) statistical significance has been valued at its cost: "essentially no one believes a finding of statistical significance [...] My statistical significance is a finding; yours is an ornamented prejudice."
Tu put it another way, no economist has achieved scientific success as a result of a statistically significant coefficient. Massed observations, clever common sense, elegant theorems, new policies, sagacious economic reasoning, historical perspective, relevant accounting: these all have led to scientific success. The quest for statistical significant must be replaced by the attention to the scientific question: How large is large?

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