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 Quick Guide to Commonly Used Statistical Tests © Ellen Marshall, University of Sheffield Reviewer: Jean Russell University of Sheffield www.statstutor.ac.uk Contents CONTENTS ..................................................................................................................................................................................2 INTRODUCTION ............................................................................................................................................................................4 TIPS FOR TUTORING .......................................................................................................................................................................5 SECTION 1 GENERAL INFORMATION ............................................................................................................................................6 DATA TYPES .................................................................................................................................................................................7 SUMMARY STATISTICS ....................................................................................................................................................................7 Summary of descriptive and graphical statistics ..................................................................................................................8 DECIDING ON APPROPRIATE STATISTICAL METHODS FOR RESEARCH ...........................................................................................................9 ORDINAL DATA .............................................................................................................................................................................9 WHICH TEST SHOULD I USE? ..........................................................................................................................................................10 Common Single Comparison Tests ....................................................................................................................................10 Tests of association ...........................................................................................................................................................10 One scale dependent and several independent variables ..................................................................................................11 ASSUMPTION OF NORMALITY .........................................................................................................................................................12 Statistical tests for normality ............................................................................................................................................12 Non-parametric tests ........................................................................................................................................................13 OTHER COMMON ASSUMPTIONS ....................................................................................................................................................14 For independent t-tests and ANOVA .................................................................................................................................14 For repeated measures ANOVA .........................................................................................................................................14 Independent observations .................................................................................................................................................14 CONFIDENCE INTERVALS ...............................................................................................................................................................15 HYPOTHESIS TESTING ...................................................................................................................................................................17 MULTIPLE TESTING ......................................................................................................................................................................18 SAMPLE SIZE AND HYPOTHESIS TESTS ...............................................................................................................................................19 EFFECT SIZE ...............................................................................................................................................................................19 SECTION 2 THE MOST COMMON STATISTICAL TECHNIQUES USED ............................................................................................20 INDEPENDENT T-TEST ...................................................................................................................................................................21 MANN-WHITNEY TEST .................................................................................................................................................................22 PAIRED T-TEST ...........................................................................................................................................................................23 WILCOXON SIGNED RANK TEST ......................................................................................................................................................24 ONE-WAY ANOVA .....................................................................................................................................................................25 KRUSKAL-WALLIS TEST .................................................................................................................................................................26 ONE-WAY ANOVA WITH REPEATED MEASURES (WITHIN SUBJECTS) .......................................................................................................27 FRIEDMAN TEST ..........................................................................................................................................................................28 TWO-WAY ANOVA ....................................................................................................................................................................29 CHI-SQUARED TEST......................................................................................................................................................................30 ODDS AND RELATIVE RISK .............................................................................................................................................................31 Odds .................................................................................................................................................................................31 Odds Ratio ........................................................................................................................................................................31 Relative Risk (RR) ..............................................................................................................................................................31 CORRELATION ............................................................................................................................................................................32 PEARSON’S CORRELATION COEFFICIENT ............................................................................................................................................32 RANKED CORRELATION COEFFICIENTS ...............................................................................................................................................33 Spearman’s Rank Correlation Coefficient ..........................................................................................................................33 Kendall’s Tau Rank Correlation Coefficient ........................................................................................................................33 PARTIAL CORRELATION .................................................................................................................................................................33 REGRESSION ..............................................................................................................................................................................34 LINEAR REGRESSION ....................................................................................................................................................................34 LOGISTIC REGRESSION ..................................................................................................................................................................36 SECTION 3 OTHER STATISTICAL TESTS AND TECHNIQUES ...........................................................................................................37 PROPORTIONS TEST (Z-TEST)..........................................................................................................................................................38 RELIABILITY ...............................................................................................................................................................................39