(Analysis of covariance: ANCOV A) .. .. ..
( 2538 :345 ) (Analysis of Covariance : ANCOVA ) 2 ( 2538: 340 ) (Analysis of Covariance : ANCOVA) (2544: 121 ) (Analysis of Covariance: ANCOVA )
( 2549: 218) (Analysis of Covariance : ANCOVA) ( covariate) ( 2544: 352) (Analysis of Covariance : ANCOVA) ( 2548: 186) (Analysis of Covariance : ANCOVA)
2 1 ANCOVA (Valid) ) 1) 2) 3)
(Homogene 4) 5) (Homogeneity of reg Y C ( ) 1) / / 2)
(Covari ate) 1. 2. 3
1. t-test ( 2 ) F-test ( 2 ) () 2.
(rand) om) 3. 2 () 2
(simple linear regression) (ANOVA) (covariate concom 1 X Y Y X
1 X Y (ANOVA) (sum of squares) SPT = SPb + SPw . (1.1) SPT (total sum of prod) ucts) SPb Y = i + iC + e ; i = 1, 2 ,3 , k ( treatment ) Slop treatment k
ANCOVA 3 (ANOVA) 2 ( H0) k H0 : x1 = x2 = = xk
SPSS for Wind) ows 2 2
1 5 5 1 6 7 2 11 15 2 6 5 3
12 20 3 7 8 4 26 28 4 12 11 5
28 27 5 14 15 6 24 29 6 9 10 7 11
15 7 8 9 8 27 28 8 7 6 9 12
11 9 11 14 10 20 23 SPSS for 1. Wind) ows
pre post 5 11 2 6 7 11 15 12 2
6 5 1 12 20 13 2 7 8 4 1 26 28
14 2 12 11 5 1 28 27 15 2 14 15
6 1 24 29 16 2 9 10 7 1 11 15 17
2 8 9 8 1 27 28 18 2 7 6 9
1 12 11 19 2 11 14 10 1 20 23 pre post
1 1 5 2 1 3 2. SPSS Variable View - = group wid) th = 1 d) ecimals = 0 measure = nominal - = pre wid) th =2 d) ecimals = 0 measure = scale
- = post wid) th = 2 d) ecimals = 0 wid) th = 4 measure = scale 3. Data View case 4. Analyze Compare Means Ind) epend) ent-Samples T Test Test Variable 6. group Grouping Variable 7. Define Groups Group 1 = 1 Group 2 = 2 8. OK ( .05 T - Test
Group Statistics PRE POST GROUP 1 2 1 2 N 10 9 10 9 Mean 17.60 8.89 20.10 9.00 Std. Error Std. Deviation
Mean 8.316 2.630 2.848 .949 8.319 2.631 3.000 1.000 Ind) epend) ent Samples Test Levene's Test for Equality of Variances PRE POST F Equal variances assumed 22.776 Equal variances not assumed Equal variances assumed 10.106 Equal variances not assumed
Sig. .000 .005 t-test for Equality of Means t 2.982 Mean Std. Error df Sig. (2-tailed) Difference Difference 17 .008 8.71 2.921 95% Confidence Interval of the Difference Lower Upper
2.547 14.875 3.116 11.283 .010 8.71 2.796 2.576 14.846 3.779 17 .001 11.10
2.938 4.902 17.298 3.944 11.518 .002 11.10 2.814 4.939 17.261 1. (pre) (group=1) 17.60 (group=2) 8.89
() F=22.776 Sig.=.000 ( .05) t = (post) 2.982 Sig. =.008 (group=1) 20.10 ( .05) (group=2 ) 9.00 () F = 10.106(t-ttest)
Sig.=.005 ( .05) t = 3.779 Sig.=.001 ( 2. (ANCOVA) - Analyze Compare Means Ind) epend) ent-Samples T Test - pre post (Test Variables) - group Grouping Variable 1 2 OK - SPSS d) ata - Analyze General Linear Mod) el Univariate - post Depend) ent Variable - group
Fixed) Factor(s) - pre Covariate(s) - Options OVEALL group Display Means for : - check box Parameter estimates Continue OK T - Test Group Statistics PRE POST GROUP 1 2 1 2
N 10 9 10 9 Mean 17.60 8.89 20.10 9.00 Std. Error Std. Deviation Mean 8.316 2.630 2.848 .949 8.319 2.631 3.000 1.000
Between-Subjects Factors N GROUP 1 2 10 9 Tests of Between-Subjects Effects Dependent Variable: POST Type III Sum Source of Squares Corrected Model 1197.226a Intercept 13.454 PRE 613.600 GROUP 25.603 Error 81.300 Total 5464.000
Corrected Total 1278.526 df 2 1 1 1 16 19 18 Mean Square 598.613 13.454 613.600 25.603 5.081 a. R Squared = .936 (Adjusted R Squared = .928) F 117.808 2.648 120.757
5.039 Sig. .000 .123 .000 .039 Estimated Marginal Means GROUP Dependent Variable: POST GROUP 1 2 Mean 16.201a 13.332a 95% Confidence Interval Std. Error Lower Bound Upper Bound .796 14.513 17.889 .849
11.533 15.131 a. Evaluated at covariates appeared in the model: PRE = 13.47. SS d) f MS F Sig Pre 613.60 0
1 613.6 00 120.75 7 .000 25.603 1 25.60 3 5.039 .039
81.300 16 5.081 720.50 3 18 (F=120.757, Sig.=.000 .05) N
30 x S.D 30 x S.D 30 x 10 17.6 0 8.316 20.10
8.31 9 16.20 54.003 1 9 8.89 2.848 3.00 13.33 2 9.00 44.44
ANCOVA ..
1. 80/80 2. 3. 4. 1. 2. 3.
1. ( 1.1 (Analysis) 1.2 (Design) 1.3 (Development) 1.4 / (Implementation) 1.5 (Evaluation 2. 1968 : 110) Thinking) 2.1 (Fluency) 2.2 (Flexibility) 2.3 (Originality) 2.4 (Elaboration)
1. 2. 3.