Why We Do Not Trust Individual Scores --
and Why We Trust Individual Scores Even Less When They Are Based on a Measure That Has Low Reliability

In the long run, random error tends to balance out toward zero.
So, if you have many scores, a measure's unreliability will usually have little effect on the average score.


However, a measure's unreliability can greatly affect individual scores.
Indeed, even with a fairly reliable measure, random error can make individual scores unreliable.
So, an individual's score on a test is probably not the same as that individual's true score: what that individual's score would have been if there had been no random error.


Although we can't determine an individual's exact true score, we can create a 95% confidence interval for an individual's true score -- a range in which we will be correct about 95% of the time when we say that the individual's true score falls in that range.


Because random error may make the observed score differ from the true score and because a confidence interval can provide a range within which the true score will usually be,
an IQ test administrator may not tell clients their IQ scores, but instead tell them that their IQ score is probably within a certain range.
Use the calculator below to see for yourself how unreliable individual scores may be, how a measure's reliability affects individual test scores, and to decide for yourself whether it is better to
give people their IQ test score or to tell them in what range their IQ falls.


Using the calculator