A GRAPHICAL PROCEDURE FOR COMPARING GOODNESS-OF-FIT TESTS

A method for comparing tests of normality using their 'isotones', i.e. contours on the surfaces representing P-values, is proposed. Select a family of distributions labelled by two parameters lambda-1 and lambda-2 to represent the null and alternative hypotheses. For each (lambda-1, lambda-2) take an 'ideal sample' from that distribution, calculate the value of the goodness-of-fit statistic and determine the corresponding P-value under the normality assumption. This generates a surface of the P-values of the 'values of the test statistic' in the (lambda-1, lambda-2) plane. In this paper the construction and interpretation of the isotones, the contours on the above surfaces, for competing tests, is illustrated using the Shapiro-Wilk W, Vasicek's entropy test and Lin and Mudholkar's Z(p)-test of the composite hypothesis of normality.