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Re: st: Accounting for measurement error in regression


From   Stas Kolenikov <skolenik@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Accounting for measurement error in regression
Date   Wed, 20 Oct 2010 16:05:57 -0500

On Wed, Oct 20, 2010 at 3:47 PM, Jason Becker <Jason.Becker@ride.ri.gov> wrote:
> Hello,
>
> My data has measurement error which is generally modeled as following a
> Bernoulli distribution.  The data are percentages of students at a
> school who score above a cutoff point on an exam, and the error is
> modeled as sqrt((p)*(q)/N) where p = percentage of students above the
> cutoff, q = percentage of students below the cutoff, and N is the number
> of students).

p*(1-p)/N is the sampling variability: you believe there is a true
probability of something equal to p, and out of N sampled objects, you
will observe variance p*(1-p)*N in the number of positive responses.
You probably want to address the inaccuracy of the instrument, and
that is a far more complex thing to do.

Suppose statalist subscription were only open to people with IQ above
120, and there was an instrument that gives you 3 point margin of
accuracy (standard deviation of the scores in repeated testing, or
between people of identical ability). Then for a person with a given
IQ the probability of getting the highly sought statalist subscription
is p(IQ)=Prob[ N(IQ,3) > 120 ]. To quantify the overall measurement
error for a given university, you would want to sum all
p(IQ)*(1-p(IQ)) over the Stata users in this university; this should
give you something like a variance of the number of people eligible
for subscription. Note that this is conditional on the test score, so
I imagine that for tests with good psychometric properties
(reliability), this variance will be much smaller than p*(1-p)*N where
p = Prob[ N(100,15)>120 ], which is the measure that you think of
using.

-- 
Stas Kolenikov, also found at http://stas.kolenikov.name
Small print: I use this email account for mailing lists only.

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