こんにちは由美子です

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みひないなおか
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1 Analysis of Variance 2 two sample t test analysis of variance (ANOVA) CO EFV1 µ 1 µ 2 µ 3 H 0 H 0 : µ 1 = µ 2 = µ 3 H A : Group 1 Group 2.. Group k population mean µ 1 µ µ κ SD σ 1 σ σ κ sample mean x 1 x x k SD s 1 s s k Sample size n 1 n n k S w 2 = (n 1 1)s (n 2 1)s 2 2 +(n 3 1)s 3 2 / n 1 + n 2 + n H 0 95 α = H 0 reject type I error type I error type I error 1 type I error µ One way analysis Source of Variation one way analysis variance dispersion within variation 1

2 between variation, 2 variances k between variability within variability between variability within variability H 0 : µ 1 = µ 2 = µ k S 2 w = (n 1 1)s (n 2 1)s (n 3 1)s 2 k / n 1 + n 2 + n k k n 1 + n 2 + n k = k S 2 w = (n 1 1)s (n 2 1)s (n 3 1)s 2 k / n k k w within-groups variability null hypothesis 2 S 2 B = n 1 (x 1 x) 2 + n 2 (x 2 x) 2 + n k (x k x) 2 / k-1 B between groups x 2

3 x = n 1 x 1 + n 2 x 2 + n k x k / n 2 variance F = S B 2 / S w 2 S 2 B S 2 w F 1 (between groups) (within-group) F 1 t z H 0 1 (between groups) (within-group) H 0 k 1, n k F distribution Fn 1 1, n two sample t test F distribution t 1 n 1 1, n 2 1 F skewed Skewed S 2 w = (n 1 1)s (n 2 1)s (n 3 1)s 2 k / n k = (21 1)(0.496) 2 + (16 1)(0.523) 2 + (23 1)(0.498) 2 / = x = 21 x x x 2.88 / = 2.83 S 2 B = n 1 (x 1 x) 2 + n 2 (x 2 x) 2 + n k (x k x) 2 / k-1 = 21 ( ) ( ) ( ) 2 / 3-1= F = / = k-1 = 2, n-k = < p < 0.10 H 0 acceptable 3 3

4 Multiple Comparisons Procedures One way analysis of variance k null hypothesis H 0 H 0 type I error α α* = 0.05 / ( k 2) modification Bonferroni correction α* = 0.10 / ( k 2) = H 0 = µ 1 = µ 2 t ij = x i x j / S 2 w {1/n 1 1/n 2 } 2.39 t distribution n k = 60 3 = 57 p=0.02 H 0 µ 1 µ 2 2 H 0 Bonferroni multiple comparisons procedure 4

5 STATA ANOVA One way ANOVA analysis list treat wgt anova wgt treat Number of obs = 10 R-squared = Root MSE = Adj R-squared = Source Partial SS df MS F Prob > F Model treat Residual Total

6 10 mean square error (MSE), R2, adjusted R2, sum of squares (partial SS), degree of freedom (df), patial SS/df = mean square F=21.46, p = Model treat model residual total Total MS MSE. anova, regress Source SS df MS Number of obs = F( 3, 6) = Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = wgt Coef. Std. Err. t P>t [95% Conf. Interval] _cons treat (dropped) Coef. 6

7 Two-way ANOVA a*b a b list drug disease systolic

8 summarize Variable Obs Mean Std. Dev. Min Max drug disease systolic tabulate drug disease disease drug Total Total STATA. anova systolic drug disease drug* disease Number of obs = 58 R-squared = Root MSE = Adj R-squared = Source Partial SS df MS F Prob > F -- Model drug disease

9 drug*disease Residual Total ANOVA. table drug disease, c(mean systolic) row col f(%8.2f) disease drug Total Total missing data disease 1 drug 1 missing. anova systolic drug disease drug* disease if ~(drug==1 & disease==1) Number of obs = 52 R-squared = Root MSE = Adj R-squared = Source Partial SS df MS F Prob > F -- Model drug disease

10 drug*disease Residual Total R 2. anova systolic disease drug disease* drug, sequential Number of obs = 58 R-squared = Root MSE = Adj R-squared = Source Seq. SS df MS F Prob > F -- Model disease drug disease*drug Residual Total

11 N-way analysis of variance Variable 11

12 Analysis of covariance Anova command categorical variable continuous(varlist) command. anova systolic drug disease age disease* age, continuous(age) Number of obs = 58 R-squared = Root MSE = Adj R-squared = Source Partial SS df MS F Prob > F - Model drug disease age disease*age Residual Total * categorical variable continuous variable 12

13 Repeated measures analysis of variance ANOVA F test repeated measure repeated measure F test STATA 5 4. list person drug score tabdisp person drug, cellvar(score) drug person anova score person drug, repeated(drug) 13

14 Number of obs = 20 R-squared = Root MSE = Adj R-squared = Source Partial SS df MS F Prob > F Model person drug Residual Total Between-subjects error term: person Levels: 5 (4 df) Lowest b.s.e. variable: person Repeated variable: drug Huynh-Feldt epsilon = *Huynh-Feldt epsilon reset to Greenhouse-Geisser epsilon = Box's conservative epsilon = Prob > F Source df F Regular H-F G-G Box drug Residual 12 Box F test 4 14

15 . table drug, c(mean score) f(%8.2f) drug mean(score) list drug subject response table drug subject, c(mean response) f(%6.2f) row col center 15

16 subject drug Total Total anova response subject drug, repeated(drug) Number of obs = 30 R-squared = Root MSE = Adj R-squared = Source Partial SS df MS F Prob > F Model subject drug Residual Total Between-subjects error term: subject Levels: 10 (9 df) Lowest b.s.e. variable: subject Repeated variable: drug Huynh-Feldt epsilon = Greenhouse-Geisser epsilon = Box's conservative epsilon =

17 Prob > F Source df F Regular H-F G-G Box drug Residual SO 2 Baseline (FEV1/FVC) 3 stratify baseline SO 2. list lung react

18 anova react lung Number of obs = 22 R-squared = Root MSE = Adj R-squared = Source Partial SS df MS F Prob > F Model lung Residual Total F baseline SO 2. anova, regress Source SS df MS Number of obs = F( 2, 19) = 4.99 Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = react Coef. Std. Err. t P>t [95% Conf. Interval] _cons lung

19 (dropped) SO 2 anova. oneway react lung Analysis of Variance Source SS df MS F Prob > F Between groups Within groups Total Bartlett's test for equal variances: chi2(2) = Prob>chi2 = oneway react lung, tabulate Summary of react lung Mean Std. Dev. Freq Total Analysis of Variance Source SS df MS F Prob > F Between groups Within groups

20 Total Bartlett's test for equal variances: chi2(2) = Prob>chi2 = Bonferroni 2. oneway react lung, bonferroni Analysis of Variance Source SS df MS F Prob > F Between groups Within groups Total Bartlett's test for equal variances: chi2(2) = Prob>chi2 = Comparison of react by lung (Bonferroni) Row Mean- Col Mean oneway react lung, noanova scheffe Comparison of react by lung (Scheffe) Row Mean- Col Mean

21 Bonferroni. oneway react lung, noanova sidak Comparison of react by lung (Sidak) Row Mean- Col Mean (mmhg)

22 . list reading day BP summarize Variable Obs Mean Std. Dev. Min Max reading day BP tabulate day reading reading day 1 2 Total 22

23 Total anova BP day reading Number of obs = 20 R-squared = Root MSE = Adj R-squared = Source Partial SS df MS F Prob > F Model day reading Residual Total F test. 23

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

BR003 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