Comparison of the Results of Direction Learning and the Simple Alternative Theory

Abstract

In chapter 7 we report the results of the learning direction theory and the alternative theory. In section 7.1 we summarize the results of the first play, in section 7.2 the results of the second play are reported and, finally, section 7.3 reports the simulation results of the third play. For all three plays we first report the distributions of means in the final period. We are interested in what proportion of the simulated means that include 27 values in the first play and 18 values in the second and third play fall below or above the observed mean. Then we compare the results of the scoring rule. For both theories we obtain values from the scoring rule. We use a one-tailed Wilcoxon matched-pairs signed-ranks test to test the null hypothesis that the two theories predict equally well against the alternative hypothesis that the learning direction theory predicts the observed values in period 15 of the three plays better than the simple alternative theory also called naive theory here.