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“Victor Babes” UNIVERSITY OF MEDICINE AND PHARMACY TIMISOARA DEPARTMENT OF MEDICAL INFORMATICS AND BIOPHYSICS Medical Informatics Division www.medinfo.umft.ro/dim 2007 / 2008
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STATISTICAL TESTS (II) COURSE 5
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5. USUAL STATISTICAL TESTS PARAMETERS TO BE COMPAREDPARAMETERS TO BE COMPARED RECOMMENDED TESTRECOMMENDED TEST CONDITIONSCONDITIONS OTHER COMMENTSOTHER COMMENTS
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5.1. TWO MEANS - ON TWO SERIES -5.1. TWO MEANS - ON TWO SERIES - DIFFERENT INDIVIDUALS DIFFERENT INDIVIDUALS UNPAIRED (unmatched, pooled) t TESTUNPAIRED (unmatched, pooled) t TEST H 0 : X 1 = X 2, condition: s 1 = s 2H 0 : X 1 = X 2, condition: s 1 = s 2 SIGNIFICANCE TEST, PARAMETRICALSIGNIFICANCE TEST, PARAMETRICAL
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5.2 TWO MEANS - TWO SERIES OBTAINED ON ONE GROUP5.2 TWO MEANS - TWO SERIES OBTAINED ON ONE GROUP (SAME INDIVIDUALS)(SAME INDIVIDUALS) UNDER TWO DIFFERENT CONDITIONSUNDER TWO DIFFERENT CONDITIONS PAIRED (matched) t TESTPAIRED (matched) t TEST H 0 : X 1 = X 2H 0 : X 1 = X 2 SIGNIFICANCE TEST, PARAMETRICALSIGNIFICANCE TEST, PARAMETRICAL
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5.3. TWO MEANS - TWO SERIES WITH UNKNOWN OR NON-GAUSSIAN DISTRIBUTION5.3. TWO MEANS - TWO SERIES WITH UNKNOWN OR NON-GAUSSIAN DISTRIBUTION MANN - WHITNEY TEST (u test)MANN - WHITNEY TEST (u test) H 0 : X 1 = X 2H 0 : X 1 = X 2 SIGNIFICANCE TEST, NONPARAMETRICALSIGNIFICANCE TEST, NONPARAMETRICAL
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5.4. RANKS - TWO SERIES5.4. RANKS - TWO SERIES a) INDEPENDENT SERIESa) INDEPENDENT SERIES WILCOXON TEST - ‘RANK SUM’WILCOXON TEST - ‘RANK SUM’ H 0 : Me 1 = Me 2H 0 : Me 1 = Me 2 SIGNIFICANCE, NONPARAMETRICAL, FOR ORDINAL VARIABLESSIGNIFICANCE, NONPARAMETRICAL, FOR ORDINAL VARIABLES
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5.4. RANKS - TWO SERIES5.4. RANKS - TWO SERIES b) DEPENDENT SERIESb) DEPENDENT SERIES (PAIRED SERIES)(PAIRED SERIES) WILCOXON TEST - ‘SIGN - RANK’WILCOXON TEST - ‘SIGN - RANK’ H 0 : Me 1 = Me 2H 0 : Me 1 = Me 2 SIGNIFICANCE, NONPARAMETRICAL, FOR ORDINAL VARIABLESSIGNIFICANCE, NONPARAMETRICAL, FOR ORDINAL VARIABLES
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5.5. n EXPERIMENTAL SERIES ANALYSIS OF VARIANCEANALYSIS OF VARIANCE ANOVAANOVA
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a) n INDEPENDENT SERIES =a) n INDEPENDENT SERIES = ONE WAY ANALYSIS (unifactorial)ONE WAY ANALYSIS (unifactorial) KRUSKAL - WALLIS TESTKRUSKAL - WALLIS TEST H 0 : X 1 = X 2 =... = X nH 0 : X 1 = X 2 =... = X n NONPARAMETRICALNONPARAMETRICAL Bonferoni refinementBonferoni refinement
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b) n DEPENDENT SERIES =b) n DEPENDENT SERIES = TWO WAYS ANALYSIS (bifactorial)TWO WAYS ANALYSIS (bifactorial) FRIEDMAN TESTFRIEDMAN TEST H 0 : X 1 = X 2 =... = X nH 0 : X 1 = X 2 =... = X n NONPARAMETRICALNONPARAMETRICAL LATIN SQUARE: A B C DLATIN SQUARE: A B C D C A D B C A D B D C B A D C B A B D A C B D A C
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5.6. TESTS FOR DISPERSION INDICATORS5.6. TESTS FOR DISPERSION INDICATORS a) TWO SERIESa) TWO SERIES FISHER TEST (F TEST, F RATIO)FISHER TEST (F TEST, F RATIO) H 0 : s 1 = s 2H 0 : s 1 = s 2 HOMOGENEITY TESTHOMOGENEITY TEST
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b) n INDEPENDENT SERIESb) n INDEPENDENT SERIES BARTLETT TESTBARTLETT TEST c) n SERIES - PAIREDc) n SERIES - PAIRED COCHRAN TESTCOCHRAN TEST H 0 : s 1 = s 2 =... = s nH 0 : s 1 = s 2 =... = s n HOMOGENEITY TESTSHOMOGENEITY TESTS
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3.7. PROPORTIONS - NOMINAL (QUALITATIVE VARIABLES)3.7. PROPORTIONS - NOMINAL (QUALITATIVE VARIABLES) CHI - SQUARE (PEARSON) TESTCHI - SQUARE (PEARSON) TEST (or Z test)(or Z test) H 0 : O i = E i for all classes iH 0 : O i = E i for all classes i (or P 1 = P 2 )(or P 1 = P 2 ) CONCORDANCE TESTSCONCORDANCE TESTS
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3.8. CLASSIFICATION (CONTINGENCY)3.8. CLASSIFICATION (CONTINGENCY) CHI SQUARE TESTCHI SQUARE TEST INDEPENDENCE TESTINDEPENDENCE TEST 3.9. NORMALITY3.9. NORMALITY CHI SQUARE TESTCHI SQUARE TEST CONCORDANCE TESTCONCORDANCE TEST 3.10. CORRELATION COEFFICIENT3.10. CORRELATION COEFFICIENT t TESTt TEST SIGNIFICANCE TESTSIGNIFICANCE TEST
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