On Accuracy and Precision in Statistical Estimates

Abstract

LIn the exact sciences one distinguishes between the exactness of the estimate of a quantity, or the 'accuracy', and the exactness of the symbolic representation of the estimate, its 'precision'. The significant-digits rule, the subject of the most elementary education jn these disciplines, establishes a rough correlation between accuracy and precision. It is shown that many agricultural economists and statisticians are unsure about the proper representation of accuracy in writing. T h e accuracy of one particular statistic, net farm income in Canada, has been estimated using Theil's RMSE statistic. The results suggest that net farm income should be written with two or three digits only according to the significant-digits rule. The author recommends that the significant-digits rule generally be followed. Economy in communication and greater awareness of the nature and limitation of the empirical basis of our knowledge would be gained.Dnns les sciences extictes une distinction precise est fnit entre I'exactitude de In mesure d'une quantite et la prfcision de la reprPsentation synibolique de cette mesure. La rkgle des chiffres signicatifs, le sujet de I'enseignenient le plus Clementaire en les sciences naturelles, Ptablit une correlation approximatif entre l'exactitude de la mesure et la prkcision de In representation. Les tconomistes et les statisticiens rurales seniblent itre incertains sur la representation de I'exactitude de In mesure das la communication ecrite.L'exuctitude d'un devis particulierla revenu net agricole canadiena i t 6 estinii en utilisant la statistique RMEC (la racine de la moyenne de I'erreur cnrre) de THEIL. Les resultnts suggerent que cette statistique devrait i t r e Ccrit avec seulement deux ou trois chiffres, suivant I:i rigle des chiffres signicatifs, au lieu de l'ecrire avec sept chiffres d'apres I'usage courant. L'auteur voudrait conseiller que, i I-avenir, la regle des chiffres signicatifs soit utilise dans toutes les publications de manitre h encourager 1'Cconomie dans lh communication et une conscience professionnelle plus grand de la nature des limitations de la base ernpirique de notre connaissance.Scientific thinking requires a simple and powerful, yet properly diff ercntiated concept of quantities and numbers. Between blind faith in numbersan unscientific numerology, the curse of modern manand complete rejcction of quantitative concepts, there is a wide continuum of degrees of faith in numbers. The face value of a number conveys symbolically a notion of quantity. Yet to some the notion of quantity would not be complete without knowledge of the credibility associated with that number. One component of credibility is 'accuracy'.The purpose of this paper is to 1. demonstrate that confusion is common in our profession about the proper 2. illustrate one method of gauging the accuracy of estimates; and 3. suggest that agricultural economists, and social scientists generally, adopt precision in writing numbers; the significant-digits convention in writing numbers.