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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. * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**RE: st: Accounting for measurement error in regression***From:*"Jason Becker" <Jason.Becker@ride.ri.gov>

**References**:**st: Accounting for measurement error in regression***From:*"Jason Becker" <Jason.Becker@ride.ri.gov>

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