Random Measurement Error

Abstract

A psychological or educational test is an instrument for the measurement of a person’s maximum performance or typical response under standardized conditions, where the performance or response is assumed to reflect one or more latent variables. A test consists of a set of items. Conventional test scoring assigns a priori scores to test takers’ item responses, and a test taker’s observed test score is the sum of his (her) item scores. Test scores are affected by random and systematic errors. Random errors decrease the measurement precision of tests, and systematic errors bias the measurements. A within-person and a between-persons aspect of measurement precision are distinguished. The within-person aspect is the variance of a given test taker’s observed score across hypothetical replications, which assesses the precision of the measurement of the test taker’s true score. The between-persons aspect is the reliability, which is the squared product moment correlation between observed and true test scores in a population of test takers. Measurement precision is increased by applying guidelines for test construction and administration. Classical and modern psychometric methods assess the quality of tests and items. Classical item analysis indices are the item p-value and item-rest correlation, and modern indices are the item difficulty and discrimination parameters of item response models.