🚀 go-pugleaf

An anonymous (at least to my mailer) participant asked:

I'm helping a research psychologist who wants to show that a questionnaire
score is predictive of the degree of blood cholesterol lowering.
The questionnaire measures a person's belief in their ability
to adhere to a cholesterol-lowering diet.  The psychologist wants to use
a technique that I am unfamiliar with.  She wants to use the median
questionnaire score to divide the sample into a lower 50% group
and an upper 50% group, then calculate the mean blood cholesterol lowering
for each group and compare them using the t-test.  ...

Reply> This seems to be a variant of a method proposed by Wald (1940) for
an unbiased slope estimate when the explanatory variable is measured with
error.  According to Thiel (1971, p. 610ff.), Wald  "divides the n
observations into two groups, one consisting of the n/2 observations with
the largest values of the explanatory variable and the other containing the
smallest values....  The slope of the straight line which connects the
centers of gravity of the two groups is the estimator of beta."  He then
goes on to discuss properties of this estimator, and to discuss further
research along this line, the most important of which seems to imply that
the data should be divided into 3 groups and the middle one discarded.  I
recommend you look at Thiel's book, which has a much better treatment of
this question than most introductory or mid-level statistics books I am
familiar with.

I don't know what's been done about testing hypotheses on beta.  I think
that bootstrapping would provide a simple nonparametric hypothesis test.

Thiel, H.  1971.  Principles of Econometrics.  John Wiley & Sons.

Wald, A.  1940.  The fitting of straight lines if both variables are
subject to error.  Ann. Math. Stat.  11 284-300.

*====================================================*
*  Michael H. Prager                                 *
*  U.S. National Marine Fisheries Service            *
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