Biases Induced by Coarse Measurement Scales

Equations for calculating the biases induced by coarse measurement scales are derived. Equations for the expected value, variance, covariance, correlation coefficient, and reliability coefficient are provided. The equations can be used to study the effects of measurement scale coarseness. Examples are given that illustrate that biases can vary depending on the mean and variance of the quantities being measured, the number of scale points, the rule for assigning quantities to scale points, and the number of items in a scale. Equations for the bias limits are also derived. Under some conditions, the biases disappear as the number of scale points increases. To avoid bias, it is recommended that graphic rating scales be used.