Stata 11 Stata ROC whitepaper mwp anova/oneway 3 mwp-042 kwallis Kruskal Wallis 28 mwp-045 ranksum/median / 31 mwp-047 roctab/roccomp ROC 34 mwp-050 s

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2 Stata 11 Stata ROC whitepaper mwp anova/oneway 3 mwp-042 kwallis Kruskal Wallis 28 mwp-045 ranksum/median / 31 mwp-047 roctab/roccomp ROC 34 mwp-050 sampsi 47 mwp-044 sdtest 54 mwp-043 signrank/signtest / 61 mwp-046 sktest / 65 mwp-048 swilk/sfrancia 67 mwp-049 ttest 70 mwp-041 StataCorp c 2011 Math c 2011 StataCorp LP Math web: master@math-koubou.jp

3 mwp-042 anova/oneway - anova oneway ANOVA ANOVA oneway 4. ANOVA anova ANOVA 7. ANOVA 8. ANOVA 1. 2 t mwp A, B, C t α 5% (1) A-B = 0.95 (2) A-C = 0.95 (3) B-C = = 0.86 (1), (2), (3) = % c Copyright Math c Copyright StataCorp LP (used with permission) 3

4 3 (ANOVA: analysis of variance) F (multiple comparison) 2. (1) (2) (3) (4) (repeated-measures) ANOVA 3. ANOVA oneway (factor) 1 ANOVA (one-way ANOVA) ANOVA anova, oneway oneway anova1.dta. use clear 24 (blood pressure). list if n <= 3 n >= 22, separator(3) * 1 bp drug drug 1, 2, 3, 4 4 drug *2 *1 Data Describe data List data *2 Stata 4

5 drug bp oneway α 5% Statistics Linear models and related ANOVA/MANOVA One-way ANOVA Main : Response variable: bp Factor variable: drug Multiple-comparison tests: Bonferroni Output: Produce summary table: 1 oneway - Main 5

6 . oneway bp drug, bonferroni tabulate Summary of bp drug Mean Std. Dev. Freq Total Analysis of Variance Source SS df MS F Prob > F Between groups Within groups Total Bartlett's test for equal variances: chi2(3) = Prob>chi2 = Comparison of bp by drug (Bonferroni) Row Mean Col Mean (1) ANOVA tabulate (frequency) 6 oneway anova (unbalanced data) ANOVA Analysis of Variance Source SS df MS F Prob > F Between groups Within groups Total Bartlett's test for equal variances: chi2(3) = Prob>chi2 =

7 SS (sum of squares) regress mwp-037 y (yi ȳ) 2 = (y i ŷ i ) 2 + (ŷ i ȳ) 2 (yi ȳ) 2 TSS (total sum of squares) (ŷi ȳ) 2 MSS (model sum of squares) (yi ŷ i ) 2 RSS (residual sum of squares) MSS (between groups) RSS (within groups) TSS (total) (df: degrees of freedom) MS (mean square) , F /54.16 = 3.92 F F p p < 0.05 ANOVA Bartlett ANOVA p 0.05 (2) ANOVA µ 1 = µ 2 = µ 3 = µ 4 bonferroni Bonferroni ANOVA Comparison of bp by drug (Bonferroni) Row Mean Col Mean M ij M ij µ i µ j 0 Bonferroni p µ 4 µ 2 Bonferroni Scheffe, Šidák 7

8 4. ANOVA anova ANOVA 7. ANOVA 8. ANOVA ANOVA 8

9 mwp-050 roc - ROC roc ROC roc roctab ROC roccomp AUC rocgold AUC 1. ROC AUC 2. roctab 3. roccomp rocgold 1. ROC AUC (ROC: receiver operating characteristic) / 2 roctab ROC (AUC: area under the curve) ROC AUC roc01.dta. use c Copyright Math c Copyright StataCorp LP (used with permission) 9

10 . list in 1/10 * 1 disease rating ROC refvar classvar 2 refvar (observation) / 0/1 0 1 roc01.dta disease refvar classvar roc01.dta rating classvar 1, 2, 3, 4, rating rating 2 rating4. generate rating4 = rating >= 4 * 2 rating >= 4 generate rating4 { rating4 = 0 if rating < 4 rating4 = 1 if rating 4 rating4 disease. tabulate rating4 disease, column * 3 *1 Data Describe data List data *2 Data Create or change data Create new variable *3 Statistics Summaries, tables, and tests Tables Two-way tables with measures of association 10

11 . tabulate rating4 disease, column Key frequency column percentage disease rating4 0 1 Total Total (frequency) (sensitivity) (specificity) 4 { = 78.85% = 91.67% (, ) 2 ROC 11

12 x (1 ) AUC 2. roctab 1 (1) 2 (2) (3) roctab ROC AUC (1) (2) (3) ROC (2) 6 (, ) 2 ROC roctab Statistics Epidemiology and related ROC analysis Nonparametric ROC analysis Main : Reference variable: disease Classification variable: rating Graph the ROC curve: Report the area under the ROC curve:. roctab disease rating, graph summary ROC Asymptotic Normal Obs Area Std. Err. [95% Conf. Interval]

13 AUC summary 95% CI 3. roccomp roccomp AUC (1) ROC (2) ROC 2 (1) wide (2) long wide, long [D] reshape (mwp-036 ) rocgold 13

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