statstutor community project encouraging academics to share statistics support resources All stcp resources are released under a Creative Commons licence Stcp-marshallowen-7 The Statistics Tutor’s www.statstutor.ac.uk © Ellen Marshall, University of Sheffield Reviewer: Jean Russell University of Sheffield Quick Guide to Commonly Used Statistical Tests Page 2 of 57 Contents CONTENTS .............................................................................................................................................................................................. 2 INTRODUCTION ........................................................................................................................................................................................ 3 TIPS FOR TUTORING ................................................................................................................................................................................... 4 SECTION 1 GENERAL INFORMATION ............................................................................................................................................................... 5 DATA TYPES ............................................................................................................................................................................................ 6 SUMMARY STATISTICS ................................................................................................................................................................................ 6 Summary of descriptive and graphical statistics ............................................................................................................................. 6 DECIDING ON APPROPRIATE STATISTICAL METHODS FOR RESEARCH .......................................................................................................................... 7 ORDINAL DATA ........................................................................................................................................................................................ 7 WHICH TEST SHOULD I USE? ....................................................................................................................................................................... 7 Common Single Comparison Tests ................................................................................................................................................... 7 Tests of association .......................................................................................................................................................................... 7 One scale dependent and several independent variables ............................................................................................................... 9 ASSUMPTION OF NORMALITY ..................................................................................................................................................................... 10 Statistical tests for normality ......................................................................................................................................................... 10 Non-parametric tests ..................................................................................................................................................................... 11 OTHER COMMON ASSUMPTIONS ................................................................................................................................................................. 12 For independent t-tests and ANOVA .............................................................................................................................................. 12 For repeated measures ANOVA ..................................................................................................................................................... 12 Independent observations ............................................................................................................................................................. 12 CONFIDENCE INTERVALS ........................................................................................................................................................................... 13 HYPOTHESIS TESTING ............................................................................................................................................................................... 14 MULTIPLE TESTING .................................................................................................................................................................................. 14 SAMPLE SIZE AND HYPOTHESIS TESTS ............................................................................................................................................................ 15 EFFECT SIZE ........................................................................................................................................................................................... 15 SECTION 2 THE MOST COMMON STATISTICAL TECHNIQUES USED ................................................................................................................. 16 INDEPENDENT T-TEST ............................................................................................................................................................................... 17 MANN-WHITNEY TEST ............................................................................................................................................................................ 18 PAIRED T-TEST ....................................................................................................................................................................................... 19 WILCOXON SIGNED RANK TEST ................................................................................................................................................................. 20 ONE-WAY ANOVA ............................................................................................................................................................................... 21 KRUSKAL-WALLIS TEST ............................................................................................................................................................................ 22 ONE-WAY ANOVA WITH REPEATED MEASURES (WITHIN SUBJECTS) .................................................................................................................... 23 FRIEDMAN TEST ..................................................................................................................................................................................... 24 TWO-WAY ANOVA ............................................................................................................................................................................... 25 CHI-SQUARED TEST ................................................................................................................................................................................ 26 ODDS AND RELATIVE RISK ........................................................................................................................................................................ 27 Odds ............................................................................................................................................................................................... 27 Odds Ratio ...................................................................................................................................................................................... 27 Relative Risk (RR) ........................................................................................................................................................................... 27 CORRELATION ........................................................................................................................................................................................ 28 PEARSON’S CORRELATION COEFFICIENT ......................................................................................................................................................... 28 RANKED CORRELATION COEFFICIENTS ............................................................................................................................................................ 30 Spearman’s Rank Correlation Coefficient ..................................................................................................................................... 30 Kendall’s Tau Rank Correlation Coefficient .................................................................................................................................... 30 PARTIAL CORRELATION ............................................................................................................................................................................. 30 REGRESSION .......................................................................................................................................................................................... 31 LINEAR REGRESSION ................................................................................................................................................................................ 31 LOGISTIC