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There is some confusion with respect to the measurement error. What is the definition in statistics and definition in psychometry ? The statistics does not seem to recognize the measurement error popularly called construct bias in psychometry.

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    $\begingroup$ Your question title is about measurement error; your final question is about bias. The two are not the same. You also ask simultaneously: what is the difference, and is there a difference? That said, here goes. The central idea of bias is that a procedure is wrong on average, yielding a mean that is higher or lower than the true or correct value, known somehow. That could be true of a measurement procedure, but it can apply where measurement error is not the question. That's what I understand from statistics; psychometrics may have a different notion, but I doubt it. $\endgroup$
    – Nick Cox
    Commented Oct 10, 2013 at 9:02
  • $\begingroup$ @Nick The psychometry presumes that generally there is an error in Scale for measurement of say, fear. And hence, pursues the analysis. For example, error (measurement) variance is deducted from observed variance for arriving at true variance. The statistician presumes inertia of large numbers for mean and variance. There is no need for dealing with measurement error. $\endgroup$
    – user10619
    Commented Oct 13, 2013 at 9:44
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    $\begingroup$ I am at a loss to know what kind of answer you seek. But the implication that statisticians ignore measurement error is contradicted by a substantial literature by statisticians. Go to www.amazon.com and search for "measurement error models" to bring up several major works. $\endgroup$
    – Nick Cox
    Commented Oct 13, 2013 at 10:13

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For measurement error there really isn't a difference in the definitions. Psychometry defines "true score" as "measured score" + "error" and this is the same thing as the statistical definition. The confusion may come from different terminology; that developed because psychometry deals with tests while statistics can deal with almost anything.

"Bias" is a bit more complex. @NickCox gave the definition in statistics. In psychometry, it is used (at least some of the time) in a slightly different way, again due to the specialized nature of the subject. A test is biased for/against a group if its predictions work differently in another setting. So, e.g. if we are using SAT scores to predict college GPA, bias would be that one group gets lower/higher GPA with the same SAT score.

In statistics, a scale could be biased against everyone - e.g. if my scale estimates everyone's weight as 5 pounds less than the actual value, that's bias. In the psychometrics definition, that can't be bias.

BUT psychometricians often use "bias" in the statistical sense as well.

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