Interpretation of the Standard Error of Measurement when True Scores and Error Scores on Mental Tests are Not Independent

Abstract

It is shown that for the case of non-independence of true scores and error scores interpretation of the standard error of measurement is modified in two ways. First, the standard deviation of the distribution of error scores is given by a modified equation. Second, the confidence interval for true score varies with the individual's observed score. It is shown that the equation, $s_o=\surd \overline{[(N-O_{/}a]+[{s_o}^2(\stackrel{̄}{r_{oo}}-r_{oo})/\stackrel{̄}{r_{oo}}]}$, where N is the number of items, O is the individual's observed score, a is the number of choices per item, s_o² is observed variance, r_oo is test reliability as empirically determined, and $\overline{r_{oo}}$ is reliability for the case where only non-independent error is present, provides a more accurate interpretation of the test score of an individual.