'Any Test' Estimated True Score Calculator

Estimated 'true scores' (ETS) are used in classical test theory to account for regression to the mean. Extreme scores are considered more likely to be influenced by measurement error and therefore less reliable indicators of a person's 'true' score. ETS calculations are designed to take this into account. This tool can be used for any test where you know the test reliability (usually found in manuals or published validations studies).

How to use this calculator

Choose the (sub)test distribution (standard score, scaled score) to set the mean and standard deviation, or choose custom values.
Enter the client's observed score and the test reliability coefficient (from the manual or other validation studies). We recommend using internal consistency (α) for most neuropsychological tests, although test-retest reliability may be more appropriate in some circumstances.
Click Calculate.

Inputs

Score type

Mean

Observed score

Observed score out of range.

Reliability coefficient (r) We recommend using uncorrected r

Confidence level

Notes on formulas

Estimated true score uses the regression of true score on observed score: T̂ = μ + r × (X − μ).

SEM for observed scores: SEM = SD × √(1 − r).

SEE for the true score given an observed score: SEE_T|X = SD × √(r × (1 − r)).

Confidence interval for the true score: T̂ ± z × SEE_T|X.

Use reliability that best reflects stability for your construct and population.