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第十章 單變量變異數分析. 10-1 變異數分析 10-2 單因子變異數分析的設計 10-3 變異數分析的基本假設條件 10-4 單變量變異數分析 10-5 單變量變異數分析範例 10-6 單變量變異數分析範例: One-Way ANOVA 10-7 重複量數 Repeated Measures. 10-1 變異數分析. - PowerPoint PPT Presentation
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10-1 10-2 10-3 10-4 10-5 10-6 One-Way ANOVA 10-7 Repeated Measures
10-1 (Analysis of Variance)ANOVA ( Analysis of Variance)MANOVA(Multivariate Analysis of Variance) (ANOVA) ()()
Y1 = X1 + X2 + X3++Xn () ()
MANOVA ()()()
Y1+ Y2+..+ Yn = X1 + X2 + X3++Xn () (, )
10-2 , , y1+y2+= x (y (), x 1 )2: 1. 2.
1. , (1): HSD , Newman-Keals (2) (2): Scheffe
2., (1), (k) (2), k
10-3
, (skewness)(kcat osis), , ()
, , + residual
1y, Levene >= 2y, Boxs M
10-4 (ANOVA)(y)(x)(y)t()ANOVAtANOVA
t (Test) t Test 2 t2(y)x
2()2uuu
2ztt2
(n 30) ---- z ---- t
(n< 30) , ---- z ---- t
(n< 30) ,
t t (Null hypothesis)t
t t = u1 () - u2 () / u1 u2
t crit t I (type I) a ( 0.050.01) 12degree of freedm = (N1+N2) 2 , t crit
tt crit tt crit Null hypothesis (u1 = u2) u1 u2 ttcrit () Null hypothesis u1= u2
F tF
10-5 A20 ~29B30 ~39C40~49Bubble51 10
F,05,2,12 = 3.89FF crit, 5%Ho u 30 ~ 39 20 ~ 2940 ~ 49
SPSS 1. ANOVA.SAV 2. Analyze General Linear Model Univariate 3. Univariate, score 4. ,scoreDependent Variable, code 5. codeFixed Factor 6. Model 7. continue, Univariate 8. contrast () 9. continue, Univariate 10. Plots 11. continue, Univariate 12. Post Hoc, code 13. , codePost Hoc Test for, Scheffe, Tukey Duncan 14. Continue, Univerate 15. Options, 16. Continue, Univariate 17. OK,
Univariate Analysis of Variance
Tests the null hypothesis that the error variance of the dependent variable is equal across groups.a Design: Intercept+code
Levenes Test , ,
, F = 0.43, Sig, P= 0.66 > 0.05, , ,
Post Hoc TestscodeMultiple Comparisons
Post Hoc , , TurkeyScheffe, (I) code 2 (J) code 3, (I-J), , code 3 - code 2, code 2 30 ~39code 3 40 ~49, , 30 ~39 40 ~ 49
ANOVA:Levene 30~3940~49 30~3940~49
10-6 One-Way ANOVA 27(Fit)Category 1Category 2Category 3 (Fit)
SPSS
ANOVA1. SAV AnalyzeCompare MeansOne-Way ANOVAOne-Way ANOVA fit Dependent ListCategoryFactorPost HocScheffe TukeyContinueOptionDescriptive Homogeneity of variance testContinueOK
(Between Groups)(Within Groups)(Total)(Between Groups)(Sum of Squares)=20.222=2(Mean Square)=10.111F =3.445 p=0.048(Within Groups) (Sum of Squares)=70.444=24(Mean Square)=2.935 (Total) (Sum of Squares)= 90.667=26fit () F (F=3.445p=.048.05)(1 2 3 )fit ()
Post Hoc Tests
Scheffe 1.
2.
*P
10-7 Repeated Measures(k)Repeated Measures 15
score1score2score3
ANOVA2. SAV Analyze General Linear Model Repeated Measures Repeated MeasuresWithin-Subject Factor NamefactorNumber of Levels Add Define score1score2score3OptionsfactorCompare main effectsDescriptive statistics ContinueRepeated Measures OK
Measure: MEASURE_1
score1score2score3Descriptive Statistics
score1 =5.93=1.831score2 =6.53=1.06score3 =7.33=1.234
Multivariate Tests(b)
a Exact statisticb Design: Intercept Within Subjects Design: factor
Mauchly's Test of Sphericity(b)Measure: MEASURE_1
Mauchlys W 0.75Greenhouse-Geisser 0.75Huynh-Feldt 0.75Mauchly .8222.55df=2p=.279>.05
Tests of Within-Subjects EffectsMeasure: MEASURE_1
(Sphericity Assumed)typeIII SS=14.8df=2MS=7.4F=4.723p=.017
Tests of Between-Subjects EffectsMeasure: MEASURE_1Transformed Variable: Average
(Tests of Between-Subjects Effects ) (Block)=40.133=14=2.867
Estimated Marginal MeansfactorEstimatesMeasure: MEASURE_1
95%
Pairwise ComparisonsMeasure: MEASURE_1
Based on estimated marginal means* The mean difference is significant at the .05 level.a Adjustment for multiple comparisons: Least Significant Difference(equivalent to no adjustments).()(Mean Difference).05 (M=7.333) (M=5.933)
**P