Paper SD05 Using the SAS® System to Construct n-Values Plots

Often a statistical test is performed in which the observed outcome favors the alternative but the evidence in favor of the alternative is not statistically significant. Suppose that, for example, a researcher tests the hypothesis that the mean is 10 versus the alternative is less than 10 using a z-test. Suppose further that based on a sample of size 8, the p-value is 0.078 (hence the null hypothesis is not rejected with level of significance 0.05 ). Given the observed mean (X-bar) how large would the sample have to have been in order for the hypothesis to be rejected? An n-values plot can be used to answer this question. This plot has vertical axis n (sample sizes) and horizontal axis alpha (level of significance). Points forming an n-values line containing combinations of (alpha, n) with the minimum n required to rejected at alpha are plotted. A horizontal line at n =8 in this example would be plotted (the n-values line will intersect the n = 8 line at alpha = 0.078. Using the plot one can “see” that a sample of size 11 would have rejected at level of significance 0.05. SAS macros for generating plots for various commonly used tests will be presented. INTRODUCTION Several macros will be presented that can be used to produce nvalues plots. The following test will be considered: one-sample ztest and t-test for a mean; one sample z-test for a proportion; ANOVA F-test for two or more means; and 2 by 2 table tests. ONE SAMPLE Z-TEST AND PROTOTYPE Consider the standard z-test for the mean. The one sided hypothesis is