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An Introduction to Statistics Assessing Ranks

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An Introduction to Statistics Assessing Ranks An Introduction to statistics Assessing ranks Written by: Robin Beaumont e-mail: [email protected] http://www.robin-beaumont.co.uk/virtualclassroom/stats/course1.html Date last updated Wednesday, 19 September 2012 Version: 2 Interval Ranking data data 2 independent samples Paired samples Mann Whitney U Wilcoxon Permutations Exact p value Reporting Calcul ating Interpretation PASW ,r excel , open office of results Assumptions p value Critical Conditional value α ranks H0=0 Decision rule Range= Area u nder curve Relation to CI • Independent Statistical • Ordinal?, interval data validity Effect size Clinical G power Research design importance Accessing ranks How this chapter should be used: This chapter has been designed to be suitable for both web based and face-to-face teaching. The text has been made to be as interactive as possible with exercises, Multiple Choice Questions (MCQs) and web based exercises. If you are using this chapter as part of a web-based course you are urged to use the online discussion board to discuss the issues raised in this chapter and share your solutions with other students. This chapter is part of a series see: http://www.robin-beaumont.co.uk/virtualclassroom/contents.htm Who this chapter is aimed at: This chapter is aimed at those people who want to learn more about statistics in a practical way. It is the eighth in the series. I hope you enjoy working through this chapter. Robin Beaumont Acknowledgment My sincere thanks go to Claire Nickerson for not only proofreading several drafts but also providing additional material and technical advice. Robin Beaumont [email protected] D:\web_sites_mine\HIcourseweb new\stats\basics\part8.docx page 2 of 37 Accessing ranks Contents 1. NON-PARAMETRIC / DISTRIBUTION FREE STATISTICS – WHEN TO USE THEM ..............................................................4 1.1 RANKING DATA ........................................................................................................................................................................5 1.2 MAGNITUDE AND RANKING ......................................................................................................................................................5 2. THE PAIRED SITUATION - WILCOXON MATCHED-PAIRS STATISTIC...................................................................................6 + - 2.1 T AND T .................................................................................................................................................................................6 2.2 INTERPRETATION OF THE ASSOCIATED P-VALUE ..........................................................................................................................8 2.3 THE DECISION RULE ..................................................................................................................................................................9 2.4 ASSUMPTIONS..........................................................................................................................................................................9 2.5 CHECKING THE ASSUMPTIONS ................................................................................................................................................ 10 2.6 HOW IT WORKS - ALTERNATIVE EXPLANATION ....................................................................................................................... 10 2.7 EFFECT SIZE – CLINICAL IMPORTANCE ..................................................................................................................................... 11 2.8 CONFIDENCE INTERVALS......................................................................................................................................................... 11 2.9 CARRYING OUT THE WILCOXON MATCHED PAIRS TEST ............................................................................................................ 12 2.9.1 In R Commander .......................................................................................................................................................... 12 2.9.1.1 Creating a new column in a dataframe ................................................................................................................. 13 2.9.1.2 Wilcoxon matched Pairs in R Commander............................................................................................................ 14 2.9.2 In R directly ................................................................................................................................................................... 14 2.9.2.1 Finding and reporting ties ..................................................................................................................................... 15 2.10 WRITING UP THE RESULTS ...................................................................................................................................................... 15 3. THE 2 INDEPENDENT SAMPL ES SITUATION -MANN WHITN EY U STATISTIC ................................................................ 16 3.1 MANN WHITNEY U NON PARAMETRIC EQUIVALENT TO THE T STATISTIC – I THINK NOT!............................................................ 17 3.2 MEANING OF U ..................................................................................................................................................................... 18 3.2.1 Verbal explanation ...................................................................................................................................................... 18 3.2.2 Formula explanation................................................................................................................................................... 18 3.2.3 Degree of enfoldment/separation............................................................................................................................ 19 3.2.4 Selecting with replacement ....................................................................................................................................... 20 3.3 CONFIDENCE INTERVAL .......................................................................................................................................................... 20 3.4 THE DECISION RULE ............................................................................................................................................................... 20 3.5 INTERPRETATION OF P-VALUE ................................................................................................................................................. 21 3.6 ASSUMPTIONS....................................................................................................................................................................... 22 3.7 CHECKING THE ASSUMPTIONS ................................................................................................................................................ 22 3.8 CARRYING OUT THE MANN WHITNEY U (MVU) TEST ............................................................................................................. 23 3.8.1 In R Commander .......................................................................................................................................................... 23 3.8.1.1 Viewing the distributions ...................................................................................................................................... 24 3.8.1.2 Converting a grouping variable into a factor in R Commander ............................................................................ 25 3.8.1.3 Boxplots ................................................................................................................................................................. 25 3.8.1.4 Mann Whitney U Test in R Commander ............................................................................................................... 26 3.8.2 Doing it in R directly .................................................................................................................................................... 26 3.8.2.1 Effe ct size............................................................................................................................................................... 27 3.8.2.2 Fi nding ties and mean rankings for each group .................................................................................................... 27 3.9 ANOTHER EXAMPLE IN R - ENTERING DATA DIRECTLY ............................................................................................................... 28 3.10 W IN R IS THE SAME AS U IN SPSS ......................................................................................................................................... 28 3.11 WRITING UP THE RESULTS ...................................................................................................................................................... 28 4. PERMUTATION TESTS – RANDOMIZATION AND EXACT PROBABILITIES....................................................................... 29 5. MUL TIPLE CHOICE QUESTIONS............................................................................................................................................... 31 6. SUMMARY .................................................................................................................................................................................
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