Validity is whether a test actually measures the thing it claims to measure, rather than something else entirely.
This sounds obvious until you notice how often it's violated. A job interview that's supposed to predict who will perform well often ends up measuring who interviews confidently, which is a related but distinct thing. A personality quiz that claims to reveal your "true self" might really just be measuring how you want to be seen. Both can be reliable — consistent — without being valid.
Validity isn't one property you either have or don't; researchers break it into several related questions. Does the test correlate with other established measures of the same thing (convergent validity)? Does it not correlate with things it shouldn't (discriminant validity)? Does it predict outcomes it should logically predict, like job performance or relationship satisfaction (criterion validity)? A test's overall validity is really the accumulated evidence across many of these checks, not a single score.
This is also why face validity — whether a test looks like it's measuring what it claims — is the weakest form of evidence. Plenty of valid tests don't look impressive on the surface, and plenty of invalid ones, like horoscopes, look compelling anyway.
See also
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Reliability
Reliability is the consistency of a measurement — whether it produces the same result when nothing about what's being measured has actually changed.
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Face Validity
Face validity is whether a test appears, on the surface, to measure what it claims to measure — regardless of whether it actually does.
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Construct Validity
Construct validity is the overarching question of whether a test actually measures the theoretical construct it claims to measure, built from evidence across many separate checks rather than one study.
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Nomological Network
A nomological network is the web of relationships a psychological construct should have with other constructs and observable outcomes if it's real and well-measured.
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Convergent Validity
Convergent validity is whether a test correlates strongly with other established measures of the same or a closely related construct.
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Discriminant Validity
Discriminant validity is whether a test avoids correlating strongly with measures of constructs it shouldn't be related to, showing it measures something distinct.
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Criterion Validity
Criterion validity is whether a test's scores relate to a real-world outcome, or criterion, that the test is supposed to predict or correlate with.
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Content Validity
Content validity is whether a test's items adequately cover the full range of the concept it claims to measure, rather than sampling only part of it.
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Concurrent Validity
Concurrent validity is a form of criterion validity that tests whether a measure correlates with an outcome assessed at roughly the same point in time.
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Predictive Validity
Predictive validity is a form of criterion validity that tests whether a measure's scores forecast an outcome that hasn't happened yet.