An “index of discrepancy” is introduced to measure the deviation of an actual population from the population stated as null-hypothesis. The index is estimated by a statistic proportional to the familiar expression Σ(o–e)2/e, used in chi-square tests, with a subsequent correction for bias. The index can be used for any simple hypothesis and also as a measure of heterogeneity or of association in contingency tables. Asymptotic confidence limits (for large samples) are established on the basis that (under suitable conditions) Σ(o–e)2/eapproaches a non-central chi-square distribution. Nomograms are provided to facilitate the computation of the confidence limits.