“Victor Babes” UNIVERSITY OF MEDICINE AND PHARMACY TIMISOARA DEPARTMENT OF MEDICAL INFORMATICS AND BIOPHYSICS Medical Informatics Division / 2008

STATISTICAL TESTS (II) COURSE 5

5. USUAL STATISTICAL TESTS PARAMETERS TO BE COMPAREDPARAMETERS TO BE COMPARED RECOMMENDED TESTRECOMMENDED TEST CONDITIONSCONDITIONS OTHER COMMENTSOTHER COMMENTS

5.1. TWO MEANS - ON TWO SERIES 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

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

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

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

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

5.5. n EXPERIMENTAL SERIES ANALYSIS OF VARIANCEANALYSIS OF VARIANCE ANOVAANOVA

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

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

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

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

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

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 CORRELATION COEFFICIENT3.10. CORRELATION COEFFICIENT t TESTt TEST SIGNIFICANCE TESTSIGNIFICANCE TEST

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