# Discriminant validity

In psychology, discriminant validity tests whether concepts or measurements that are supposed to be unrelated are, in fact, unrelated.[1]

Campbell and Fiske (1959) introduced the concept of discriminant validity within their discussion on evaluating test validity. They stressed the importance of using both discriminant and convergent validation techniques when assessing new tests. A successful evaluation of discriminant validity shows that a test of a concept is not highly correlated with other tests designed to measure theoretically different concepts.

In showing that two scales do not correlate, it is necessary to correct for attenuation in the correlation due to measurement error. It is possible to calculate the extent to which the two scales overlap by using the following formula where $r_{xy}$ is correlation between x and y, $r_{xx}$ is the reliability of x, and $r_{yy}$ is the reliability of y:

$\cfrac{r_{xy}}{\sqrt{r_{xx} \cdot r_{yy}}}$

Although there is no standard value for discriminant validity, a result less than .85 tells us that discriminant validity likely exists between the two scales. A result greater than .85, however, tells us that the two constructs overlap greatly and they are likely measuring the same thing. Therefore, we cannot claim discriminant validity between them.

Consider researchers developing a new scale designed to measure Narcissism. They may want to show discriminant validity with a scale measuring Self-esteem. Narcissism and Self-esteem are theoretically different concepts, and therefore it is important that the researchers show that their new scale measures Narcissism and not simply Self-esteem.

First, we can calculate the Average Inter-Item Correlations within and between the two scales:

Narcissism — Narcissism: 0.47
Narcissism — Self-esteem: 0.30
Self-esteem — Self-esteem: 0.52

We then use the correction for attenuation formula:

$\cfrac{0.30}{\sqrt{0.47 * 0.52}} = 0.607$

Since 0.607 is less than 0.85, we can conclude that discriminant validity exists between the scale measuring narcissism and the scale measuring self-esteem. The two scales measure theoretically different constructs.