AGENDA Terminating systems Simple two model comparisons Three or more model comparisons SIMPLE TWO MODEL COMPARISONS Can utilize either hypothesis test or a confidence interval approaches Hypotheses tests Limited to either accepting or rejecting the null hypothesis Confidence interval approach Modification of the corresponding hypothesis test Provide more information than hypotheses tests Graphically show the statistical results Easier to use and explain than hypotheses tests TYPES OF CONFIDENCE INTERVAL APPROACHES Welch confidence interval approach Normally used Paired T-Test Confidence Interval Approach Only used for special purposes (variance reduction) WELCH CONFIDENCE INTERVAL APPROACH Based on Smith-Satterwaithe test Automatically accounts for possible differences in variations Must first calculate the degrees of freedom estimator Calculate confidence interval If the confidence interval covers 0, there is no difference between the models If the confidence interval does not cover 0, there is a difference between the models WELCH CONFIDENCE INTERVAL DEGREES OF FREEDOM ARENA Outputs element writes results to a “dat” file Output Processor Analyze Compare Means Two sample t-test THREE OR MORE ALTERNATIVE COMPARISONS ANOVA ONE WAY ANALYSIS OF VARIANCE Determines if one or more alternatives is different than the others Based on a ratio of the variance between and within the different alternatives If the variation between is large and the variance within is small, the ratio is large If the variation between is small and the variance within is large, the ratio is small When the ratio is large then it is more likely there is a difference among alternatives ONE WAY ANOVA PROCEDURE Ho: No difference among means Ha: Difference among means Select level of significance Determine critical value Calculate F statistic Compare F statistic with critical value If the F test statistic is less than the critical F value cannot reject Ho If the F test statistic is greater than the critical F value reject Ho ANOVA CALCULATIONS Calculate the sum of squares total Calculate the sum of squares between Calculate the sum of squares within Calculate the mean squares between Calculate the mean squares within Calculate the F statistic Compare the F statistic to a critical F value SUMS OF SQUARES TOTAL SUMS OF SQUARES BETWEEN SUMS OF SQUARES WITHIN CALCULATE MEANS SQUARES BETWEEN CALCULATE MEANS SQUARES WITHIN CALCULATE F STATISTIC ANOVA RESULTS If the Ho is rejected, one or more means is statistically significantly different To determine which means are different use the Duncan Multiple Range Test ANOVA EXAMPLE ANOVA EXAMPLE CALCULATE MEANS CALCULATE SUMS OF SQUARES CALCULATE MEAN SUMS OF SQUARES CALCULATE F STATISTIC CRITICAL VALUE COMPARE TEST STATISTIC TO CRITICAL VALUE