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