《2-12Commonassumptions.pptVIP

12/1/2000 LJC DRAFT INTRODUCTION DRAFT Common Assumptions in Statistical Tests Most Common Assumptions Normal distribution Raw data Residuals Equal variances Raw data Residuals Independence Raw data Residuals Predictor variables Normality Issues When Testing for Normality (1) Issues When Testing for Normality (2) Steps for Testing Normality Assumption Graphical Methods for Checking Normality (1) Graphical Methods for Checking Normality (2) Statistical Tests for Checking Normality Equal Variances Issues When Testing for Equal Variances Steps for Testing Equal Variance Assumption Graphical Methods for Testing Equal Variances Assumption (1) Graphical Methods for Testing Equal Variances Assumption (2) Graphical Methods for Testing Equal Variances Assumption (3) Independence Issues Related to Independence Testing Independence Creating a Matrix Plot in MINITAB Matrix Plot and Independent Variables(Variables A through E are all X Variables) Creating an I-Chart in MINITAB (1) Creating an I-Chart in MINITAB (2) I-Chart and Independent Data What is the take-away? We often make way too much of the normality assumption. Since most statistical tests and procedures are quite robust to non-normality, especially as sample sizes increase, we should not be that concerned unless the problem we are working on calls for extreme accuracy, or the data are VERY non-normal. We should also remember that tests for normality have little power for small samples – certainly much less power than almost any standard statistical test we would perform on the data. So, consider the folly of using a very low power test to determine whether the data we have is normal so we can decide what statistical procedure to use, when the chances are that the statistical procedure we had planned on using is probably more robust (and way more powerful) than the test that decided whether it is “appropriate”. Take-Away As with normality, we can make too much of the equal variance assumption, in particular for pro