What is the difference between the concept and treatment of measurement error in psychometry and in statistics? 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.
 A: 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. 
