變異數分析檢定類型 –One Way ANOVA –Two way ANOVA –Three way ANOVA –..five

變異數分析• 檢定 • 類型

– One Way ANOVA– Two way ANOVA– Three way ANOVA– ..five..

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公式

1

2

2

NS

xx

變異數的不偏估計數

2

2

:

:

:

xxSSupBetweenGro

ixxSSpWithinGrou

SSSSSStionTotalVaria

ib

ijw

bwt

公式

w

b

wb

w

ww

b

bb

MSMSvalueF

dfdfN

dfssMS

dfssMS

1

假定的評估• 常態性檢定• 變異數同質性 Homogeneity of variance

• 當變異數非同質時 , 資料轉換

Tests of Normality

.227 12 .087 .810 12 .012

.224 12 .097 .868 12 .069

組別AB

成績Statistic df Sig. Statistic df Sig.

Kolmogorov-Smirnova Shapiro-Wilk

Lilliefors Significance Correctiona.

Test of Homogeneity of Variance

.024 1 22 .877

.027 1 22 .870

.027 1 21.720 .870

.015 1 22 .903

Based on MeanBased on MedianBased on Median andwith adjusted dfBased on trimmed mean

成績Levene Statistic df1 df2 Sig.

Spread vs. Level Plot of By 成績群組

* Plot of LN of Spread vs LN of Level

Slope = .605 Power for transformation = .395

Level

4.44.24.03.83.63.43.2

Spread

3.8

3.6

3.4

3.2

3.0

2.8

2.6

2.4

One Way ANOVA

• 各組人數相等 / 不相等– Question: 是否不同的香水包裝外觀 , 會影響

消費者購買意願– One way: 香水包裝外觀 (factor)– Hypothesis

• Ho: U1=U2=U3 (U1, U2, U3 是不同包裝香水購買的平均數量 )

Cont.

ANOVA

銷售量

503.467 4 125.867 2.708 .0531162.000 25 46.4801665.467 29

Between GroupsWithin GroupsTotal

Sum of Squares df Mean Square F Sig.

Test of Homogeneity of Variances

銷售量

2.643 4 25 .057Levene Statistic df1 df2 Sig.

Descriptives

銷售量

6 21.33 8.98 3.67 11.91 30.76 10 326 14.67 3.72 1.52 10.76 18.57 11 216 20.00 5.51 2.25 14.21 25.79 13 286 27.33 6.28 2.56 20.74 33.93 19 376 19.00 8.25 3.37 10.35 27.65 10 31

30 20.47 7.58 1.38 17.64 23.30 10 37

12345Total

N Mean Std. Deviation Std. Error Lower Bound Upper Bound

95% Confidence Interval forMean

Minimum Maximum

造型

54321

Mean o

f 銷售量

30

28

26

24

22

20

18

16

14

12

Cont.

• Case (One way ANOVA)– Question: 不同心理疾病的人 , 其說話的中斷

次數是否相同– One way: 心理疾病 (factor)– Ho: U1=U2=U3


中斷次數


ANOVA

中斷次數

258.194 2 129.097 23.708 .000179.695 33 5.445437.889 35



One way ANOVA 相依樣本• Question

– 同一群人試驗不同彈藥裝卸的程序 , 是否不同裝卸的程序會有不同的裝卸速度

• Factor: 不同彈藥裝卸的程序• Hypothesis: Ho: U1=U2=U3=U4=U5

Cont.

Within-Subjects Factors

Measure: MEASURE_1

程序一程序二程序三程序四程序五

PROCE12345

DependentVariable

Tests of Within-Subjects Effects

Measure: MEASURE_1

66.867 4 16.717 7.610 .00166.867 2.721 24.574 7.610 .00466.867 4.000 16.717 7.610 .00166.867 1.000 66.867 7.610 .04043.933 20 2.19743.933 13.605 3.22943.933 20.000 2.19743.933 5.000 8.787

Sphericity AssumedGreenhouse-GeisserHuynh-FeldtLower-boundSphericity AssumedGreenhouse-GeisserHuynh-FeldtLower-bound

SourcePROCE

Error(PROCE)

Type III Sumof Squares df Mean Square F Sig.

Cont.

Tests of Within-Subjects Contrasts

Measure: MEASURE_1

15.042 1 15.042 9.601 .02716.667 1 16.667 5.515 .06613.500 1 13.500 3.293 .12966.667 1 66.667 13.158 .0157.833 5 1.567

15.111 5 3.02220.500 5 4.10025.333 5 5.067

PROCELevel 1 vs. LaterLevel 2 vs. LaterLevel 3 vs. LaterLevel 4 vs. Level 5Level 1 vs. LaterLevel 2 vs. LaterLevel 3 vs. LaterLevel 4 vs. Level 5

SourcePROCE

Error(PROCE)


Two Way ANOVA

• 種類– 自變數都是獨立樣本– 自變數都是相依樣本– 混合設計 : 自變數有的是獨立樣本 , 有的是

相依樣本

Two Way ANOVA- 獨立樣本– Question: 不同的戒菸宣導短片對不同性別

的戒菸者是否有同樣的效果– Factor

• 宣導短片• 性別

– Hypothesis• Ho: U1=U2=U3

• Ho’:Uf=Um

Levene's Test of Equality of Error Variancesa

Dependent Variable: 戒煙傾向

.550 5 54 .738F df1 df2 Sig.

Tests the null hypothesis that the error variance of thedependent variable is equal across groups.

Design: Intercept+ + + * 性別影片性別影片a.

Tests of Between-Subjects Effects

Dependent Variable: 戒煙傾向

2164.733a 5 432.947 23.890 .000 .689390426.667 1 390426.667 21544.083 .000 .997

614.400 1 614.400 33.903 .000 .38643.433 2 21.717 1.198 .310 .042

1506.900 2 753.450 41.576 .000 .606978.600 54 18.122

393570.000 603143.333 59

SourceCorrected ModelIntercept性別影片

* 性別影片ErrorTotalCorrected Total


Partial EtaSquared

R Squared = .689 (Adjusted R Squared = .660)a.

Multiple Comparisons

Dependent Variable: 戒煙傾向Tukey HSD

-.7000 1.3462 .862 -3.9443 2.5443-2.0500 1.3462 .288 -5.2943 1.1943

.7000 1.3462 .862 -2.5443 3.9443-1.3500 1.3462 .578 -4.5943 1.89432.0500 1.3462 .288 -1.1943 5.29431.3500 1.3462 .578 -1.8943 4.5943

(J) 影片2.003.001.003.001.002.00

(I) 影片1.00

2.00

3.00

Mean Difference(I-J) Std. Error Sig. Lower Bound Upper Bound

95% Confidence Interval

Based on observed means.

Two Way ANOVA 相依樣本– Question: 在農業的實驗之中 , 檢驗光線與水

分 , 強中弱狀態 , 對於玉米是否有影響– Factor

• 光線與水分• 強中弱狀態

– Hypothesis• Ho: U1=U2 ( 控制光線與控制水是一樣的效果 )

• Ho’:Ua=Ub=Uc( 強度不論為何者 , 都是一樣的效果 )


Measure: MEASURE_1

4.800 1 4.800 .783 .426 .164

4.800 1.000 4.800 .783 .426 .164

4.800 1.000 4.800 .783 .426 .164

4.800 1.000 4.800 .783 .426 .164

24.533 4 6.133

24.533 4.000 6.133

24.533 4.000 6.133

24.533 4.000 6.133

101.400 2 50.700 14.520 .002 .784

101.400 1.178 86.070 14.520 .013 .784

101.400 1.379 73.547 14.520 .008 .784

101.400 1.000 101.400 14.520 .019 .784

27.933 8 3.492

27.933 4.712 5.928

27.933 5.515 5.065

27.933 4.000 6.983

42.200 2 21.100 5.199 .036 .565

42.200 1.565 26.961 5.199 .052 .565

42.200 2.000 21.100 5.199 .036 .565

42.200 1.000 42.200 5.199 .085 .565

32.467 8 4.058

32.467 6.261 5.186

32.467 8.000 4.058

32.467 4.000 8.117

Sphericity Assumed

Greenhouse-Geisser

Huynh-Feldt

Lower-bound

Sphericity Assumed

Greenhouse-Geisser

Huynh-Feldt

Lower-bound

Sphericity Assumed

Greenhouse-Geisser

Huynh-Feldt

Lower-bound

Sphericity Assumed

Greenhouse-Geisser

Huynh-Feldt

Lower-bound

Sphericity Assumed

Greenhouse-Geisser

Huynh-Feldt

Lower-bound

Sphericity Assumed

Greenhouse-Geisser

Huynh-Feldt

Lower-bound

SourceÀô¹Ò

Error(Àô¹Ò)

±j«×

Error(±j«×)

Àô¹Ò * ±j«×

Error(Àô¹Ò*±j«×)

Type IIISum ofSquares df

MeanSquare F Sig.

EtaSquared

Tests of Within-Subjects Contrasts

Measure: MEASURE_1

3.200 1 3.200 .783 .426 .164

16.356 4 4.089

28.800 1 28.800 4.760 .095 .543

54.450 1 54.450 77.786 .001 .951

24.200 4 6.050

2.800 4 .700

51.200 1 51.200 6.244 .067 .610

88.200 1 88.200 4.846 .093 .548

32.800 4 8.200

72.800 4 18.200

±j«×

Level 2 vs. Level 1

Level 3 vs. Previous

Level 2 vs. Level 1


Level 2 vs. Level 1


Level 2 vs. Level 1


Àô¹ÒLevel 2 vs. Level 1

Level 2 vs. Level 1

Level 2 vs. Level 1

Level 2 vs. Level 1

SourceÀô¹Ò

Error(Àô¹Ò)

±j«×

Error(±j«×)

Àô¹Ò * ±j«×

Error(Àô¹Ò*±j«×)

Type IIISum ofSquares df

MeanSquare F Sig.

EtaSquared

Two Way ANOVA 混合設計– Question: 三部戒菸宣導短片對於不同性別

的戒菸者是否有不同的影響 ( 每個人都對短片說出感想 )

– Factor• 宣導短片• 性別

– Hypothesis• Ho: U1=U2=U3• Ho’: Uf=Um


Measure: MEASURE_1Transformed Variable: Average

390426.667 1 390426.667 25748.705 .000 .999614.400 1 614.400 40.520 .000 .692272.933 18 15.163

SourceIntercept性別Error


Partial EtaSquared


Measure: MEASURE_1

43.433 2 21.717 1.108 .341 .05843.433 1.810 23.997 1.108 .337 .05843.433 2.000 21.717 1.108 .341 .05843.433 1.000 43.433 1.108 .306 .058

1506.900 2 753.450 38.438 .000 .6811506.900 1.810 832.558 38.438 .000 .6811506.900 2.000 753.450 38.438 .000 .6811506.900 1.000 1506.900 38.438 .000 .681705.667 36 19.602705.667 32.579 21.660705.667 36.000 19.602705.667 18.000 39.204

Sphericity AssumedGreenhouse-GeisserHuynh-FeldtLower-boundSphericity AssumedGreenhouse-GeisserHuynh-FeldtLower-boundSphericity AssumedGreenhouse-GeisserHuynh-FeldtLower-bound

SourceFILM

FILM * 性別

Error(FILM)


Partial EtaSquared

多重比較• 事前比較

– 正交 / 非正交• 事後 (Pg 7-16)

– Tukey – Scheffee– Bonferroni– New man- Keul– Ducans

事前比較– 正交 / 非正交

4321 0011 XXXX

4321 0101 XXXX

4321 5.05.05.05.0 XXXX

Cont.• Case

– Question: • 四種不同銷售法中 ,A, B 是否會得到不同銷售結果

• 四種不同銷售法中 ,C, D 是否會得到不同銷售結果

• A, B 是舊的銷售法 ,CD 是新的銷售法 , 新舊是否會得到不同銷售結果

4321 0011 XXXX

4321 1100 XXXX

4321 5.05.05.05.0 XXXX


銷售量


ANOVA

銷售量

2984.150 3 994.717 8.426 .0011888.800 16 118.0504872.950 19



Contrast Coefficients

1 -1 0 0Contrast1

1 2 3 4銷售法

Contrast Tests

-2.00 6.87 -.291 16 .775-2.00 4.35 -.460 6.984 .659

Contrast11

Assume equal variancesDoes not assume equalvariances

銷售量

Value ofContrast Std. Error t df Sig. (2-tailed)

Q1

Q2


銷售量


ANOVA

銷售量

2984.150 3 994.717 8.426 .0011888.800 16 118.0504872.950 19



Contrast Coefficients

.5 .5 -.5 -.5Contrast1

1 2 3 4銷售法

Contrast Tests

16.50 4.86 3.396 16 .00416.50 4.86 3.396 6.622 .013

Contrast11

Assume equal variancesDoes not assume equalvariances

銷售量

Value ofContrast Std. Error t df Sig. (2-tailed)

事後比較• Case

– Question1: 不同裝卸彈藥的程序是否會影響執行時間

– Question2: 哪一類卸彈藥的程序比較費時– Factor: 不同裝卸彈藥的程序


裝卸次數

.034 4 25 .998Levene Statistic df1 df2 Sig.

ANOVA

裝卸次數

66.867 4 16.717 4.338 .00896.333 25 3.853

163.200 29




Dependent Variable: 裝卸次數Scheffe

-.3333 1.1333 .999 -4.0981 3.4315-3.0000 1.1333 .170 -6.7648 .7648

.1667 1.1333 1.000 -3.5981 3.9315-3.1667 1.1333 .133 -6.9315 .5981

.3333 1.1333 .999 -3.4315 4.0981-2.6667 1.1333 .268 -6.4315 1.0981

.5000 1.1333 .995 -3.2648 4.2648-2.8333 1.1333 .215 -6.5981 .93153.0000 1.1333 .170 -.7648 6.76482.6667 1.1333 .268 -1.0981 6.43153.1667 1.1333 .133 -.5981 6.9315-.1667 1.1333 1.000 -3.9315 3.5981-.1667 1.1333 1.000 -3.9315 3.5981-.5000 1.1333 .995 -4.2648 3.2648

-3.1667 1.1333 .133 -6.9315 .5981-3.3333 1.1333 .103 -7.0981 .43153.1667 1.1333 .133 -.5981 6.93152.8333 1.1333 .215 -.9315 6.5981.1667 1.1333 1.000 -3.5981 3.9315

3.3333 1.1333 .103 -.4315 7.0981

(J) 程序23451345124512351234

(I) 程序1

2

3

4

5



裝卸次數

6 18.16676 18.3333 18.33336 18.6667 18.66676 21.3333 21.33336 21.5000

.068 .0686 18.16676 18.33336 18.66676 21.33336 21.5000

.103

程序41235Sig.41235Sig.

Tukey HSDa

Scheffea

N 1 2Subset for alpha = .05

Means for groups in homogeneous subsets are displayed.Uses Harmonic Mean Sample Size = 6.000.a.

Case2


中斷次數


ANOVA

中斷次數

258.194 2 129.097 23.708 .000179.695 33 5.445437.889 35



Case2


Dependent Variable: 中斷次數Scheffe

4.87* 1.00 .000 2.31 7.436.10* .92 .000 3.74 8.45

-4.87* 1.00 .000 -7.43 -2.311.23 .97 .454 -1.25 3.71

-6.10* .92 .000 -8.45 -3.74-1.23 .97 .454 -3.71 1.25

(J) 患者類型231312

(I) 患者類型1

2

3



The mean difference is significant at the .05 level.*.

Case2

中斷次數

Scheffea,b

14 5.5710 6.8012 11.67

.451 1.000

患者類型321Sig.

N 1 2Subset for alpha = .05

Means for groups in homogeneous subsets are displayed.Uses Harmonic Mean Sample Size = 11.776.a. The group sizes are unequal. The harmonic mean of thegroup sizes is used. Type I error levels are not guaranteed.

b.

MANOVABetween-Subjects Factors

146154100100

100

8213583

12

學生性別

123

家庭狀況

1.002.003.00

工作投入組別

N

Multivariate Test Results

.084 8.530a 3.000 280.000 .000

.916 8.530a 3.000 280.000 .000

.091 8.530a 3.000 280.000 .000

.091 8.530a 3.000 280.000 .000

Pillai's traceWilks' lambdaHotelling's traceRoy's largest root

Value F Hypothesis df Error df Sig.

Exact statistica.

Levene's Test of Equality of Error Variancesa

1.282 17 282 .2031.054 17 282 .400.687 17 282 .815

數學成就學習信心探究動機

F df1 df2 Sig.

Tests the null hypothesis that the error variance of the dependentvariable is equal across groups.

Design: Intercept+ + + + * 性別家庭狀況投入組別性別家+ * + * + * 庭狀況性別投入組別家庭狀況投入組別性別

* 家庭狀況投入組別

a.


6085.085a 17 357.946 3.684 .0007227.088b 17 425.123 9.575 .0001784.379c 17 104.963 7.027 .000

170416.108 1 170416.108 1753.729 .000240880.029 1 240880.029 5425.554 .000118914.805 1 118914.805 7960.459 .000

712.926 1 712.926 7.337 .007493.208 1 493.208 11.109 .001

.813 1 .813 .054 .816910.754 2 455.377 4.686 .01067.206 2 33.603 .757 .47010.015 2 5.008 .335 .715

3379.316 2 1689.658 17.388 .0006137.418 2 3068.709 69.119 .0001587.554 2 793.777 53.137 .000107.221 2 53.611 .552 .57754.151 2 27.076 .610 .5443.469 2 1.734 .116 .890

365.195 2 182.598 1.879 .1555.634 2 2.817 .063 .939

10.388 2 5.194 .348 .707452.536 4 113.134 1.164 .327338.959 4 84.740 1.909 .10923.731 4 5.933 .397 .811

437.166 4 109.291 1.125 .34587.303 4 21.826 .492 .74257.724 4 14.431 .966 .426

27402.952 282 97.17412520.042 282 44.3974212.568 282 14.938

216861.000 300276767.000 300132236.000 30033488.037 29919747.130 2995996.947 299

Dependent Variable數學成就學習信心探究動機數學成就學習信心探究動機數學成就學習信心探究動機數學成就學習信心探究動機數學成就學習信心探究動機數學成就學習信心探究動機數學成就學習信心探究動機數學成就學習信心探究動機數學成就學習信心探究動機數學成就學習信心探究動機數學成就學習信心探究動機數學成就學習信心探究動機

SourceCorrected Model

Intercept

性別

家庭狀況

投入組別

* 性別家庭狀況

* 性別投入組別

* 家庭狀況投入組別

* * 性別家庭狀況投入組別

Error

Total

Corrected Total


R Squared = .182 (Adjusted R Squared = .132)a. R Squared = .366 (Adjusted R Squared = .328)b. R Squared = .298 (Adjusted R Squared = .255)c.

Documents

變異數分析 檢定 類型 –One Way ANOVA –Two way ANOVA –Three way ANOVA –..five

變異數分析檢定類型 –One Way ANOVA –Two way ANOVA –Three way ANOVA –..five