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

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 is correlation between x and y, is the reliability of x, and is the reliability of y:

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
Narcissism is a term with a wide range of meanings, depending on whether it is used to describe a central concept of psychoanalytic theory, a mental illness, a social or cultural problem, or simply a personality trait...

. They may want to show discriminant validity with a scale measuring Self-esteem
Self-esteem is a term in psychology to reflect a person's overall evaluation or appraisal of his or her own worth. Self-esteem encompasses beliefs and emotions such as triumph, despair, pride and shame: some would distinguish how 'the self-concept is what we think about the self; self-esteem, the...

. 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:

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.
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