Biases induced by coarse measurement scales

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