A person’s true score would be obtained by having them respond to all items in the “universe” of items We only see responses to the sample of items on the test So, reliability is the proportion of variance …

Essentially, true score theory maintains that every measurement is an additive composite of two components: true ability (or the true level) of the respondent on that measure; and random error.

May 24, 2024 · So here, as we do in regression with all variables observed, we're computing the proportion of variance in the dependent variable that's attributed to the independent variable.

Thus, it is possible to find true score variance from the data and to calculate reliability co-efficient that conforms to the theoretical definition even if true scores of individuals taking the test are not known.

The variance of X across different levels of true scores (e.g., the observed values across persons) is the sum of the variance of true scores T and the variance of errors E.

The standard deviation of a person's test scores would indicate how much the test scores vary from the true score. This standard deviation is called the standard error of measurement.

¨ Since a test score (X) consists of true and error components, the total variance (σ x2) of a test administered to a group consists of true score variance (σ t2) and error variance (σ e2):

True variance constitutes the component of the observed score variance that is reliable, systematic, and theoretically stable over repeated measurements.

This is an interesting formula since there’s the notion about how to incorporate uncertainty into the estimation of the true score. The higher the uncertainty (lower the reliability) the less we weight the …

The variance of observed scores across persons is equal to the sum of the variances of true score and measurement error. Measurement errors of different tests are not correlated.