True Value

A true value, also called a true score, is a psychometric concept that refers to the measure that would have been observed on a construct were there not any error involved in its measurement. Symbolically, this often is represented by X = T + e, where T is the (error-free) true value, e is the error in measurement, and X is the observed score. For example, a survey respondent's true value (t) on a measure (e.g., a 5-item Likert scale measuring attitudes toward her ancestor's native land) might be 13, but her observed score (X) on a given day may be 15 or 17 or 10. There are many reasons why the observed score may deviate from the true value, but the researcher will rarely know exactly why or exactly by how much. In theory, if the error on the observed score is truly random, then a researcher could take the same measure from the same respondent over and over again, and assuming the true value on that measure for that respondent did not actually change over the time the various measures were being taken, then the mean (average) score of the various observed scores would be the true value. The concept of a true value relates to the concepts of reliability and validity.

For survey researchers, the true value has some very practical applications. First, it reminds researchers that random error is always to be assumed and that any one measurement should never be regarded as error-free. Second, if the researcher has the test-retest reliability on a given variable (x), then the researcher can apply a correction for attenuation to adjust any correlations that are calculated between x and some other variable of interest. The correction of attenuation recognizes that any observed correlation between two variables will be suppressed (i.e. lower than their true correlation) by a function linked to the amount of unreliability in the observed scores for the variables. That is, only when there is no error in the observed variables, and thus the observed scores are in fact the true values, will the observed correlation be the true correlation value.