ANOVA ANALYSIS

Eighth-Grade Pupils in the Netherlands

494310085 宋汶達494310217 孫偉傑494310425 陳盈志494310463 徐健豪494310504 朱明興

第八組

Eighth-Grade Pupils in the Netherlands

Description Snijders and Bosker (1999) use as a running example a study of 2287 eighth-gr

ade pupils (aged about 11) in 132 classes in 131 schools in the Netherlands. Only the variables used in our examples are supplied.

Usage nlschools Format This data frame contains 2287 rows and the following columns: lang

language test score. IQ

verbal IQ. class

class ID. GS

class size: number of eighth-grade pupils recorded in the class (there may be others: see COMB, and some may have been omitted with missing values).

SES social-economic status of pupil's family.

COMB were the pupils taught in a multi-grade class (0/1)? Classes which contained pup

ils from grades 7 and 8 are coded 1, but only eighth-graders were tested.

Levels

We set IQ for 3 levels Level 1. 4~ 9.5 Level 2. 10~13.5 Level 3. 14~18

We set SES for 3 levels Level 1. 10 ~ 17 Level 2. 18 ~ 38 Level 3. 39 ~ 50

We set COMB for 2 levels Level 1. 0 N Level 2. 1 Y

假設 虛無假設 :IQ 對於 lang 沒有顯著差異 對立假設 :IQ 對於 lang 有顯著差異

IQ 與成績的關係圖

I II III

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20

30

40

50

IQ 的 ANOVA TABLE

Analysis of Variance Table

Response: lang Df Sum Sq Mean Sq F value Pr(>F) IQ 2 49686 24843 418.35 < 2.2e-16 **

* Residuals 2284 135631 59 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

IQ 的迴歸式 Call: lm(formula = lang ~ IQ)

Residuals: Min 1Q Median 3Q Max -27.1115 -5.1115 0.8885 5.6154 21.6154

Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 31.3846 0.4363 71.94 <2e-16 *** IQII 9.7268 0.4761 20.43 <2e-16 *** IQIII 17.4195 0.6033 28.87 <2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 7.706 on 2284 degrees of freedom Multiple R-squared: 0.2681, Adjusted R-squared: 0.2675 F-statistic: 418.3 on 2 and 2284 DF, p-value: < 2.2e-16

假設 虛無假設 :SES 對於 lang 沒有顯著差異 對立假設 :SES 對於 lang 有顯著差異

SES 與成績的關係圖

A B C

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50

SES 的 ANOVA TABLE

Analysis of Variance Table

Response: lang Df Sum Sq Mean Sq F value Pr(>F) SES 2 18946 9473 130.05 < 2.2e-16 *** Residuals 2284 166371 73 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

SES 的迴歸式 Call: lm(formula = lang ~ SES)

Residuals: Min 1Q Median 3Q Max -31.684 -5.684 1.202 6.316 23.202

Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 34.7978 0.5223 66.62 <2e-16 *** SESB 5.8859 0.5655 10.41 <2e-16 *** SESC 10.4715 0.6546 16.00 <2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 8.535 on 2284 degrees of freedom Multiple R-squared: 0.1022, Adjusted R-squared: 0.1015 F-statistic: 130.1 on 2 and 2284 DF, p-value: < 2.2e-16

虛無假設 :COMB 對於 lang 沒有顯著差異 對立假設 :COMB 對於 lang 有顯著差異

假設

COMB 與成績的關係圖

N Y

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50

COMB 的 ANOVA TABLE

Analysis of Variance Table

Response: lang Df Sum Sq Mean Sq F value Pr(>F) COMB 1 2678 2678 33.501 8.1e-09 *** Residuals 2285 182640 80 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

COMB 的迴歸式 Call: lm(formula = lang ~ COMB)

Residuals: Min 1Q Median 3Q Max -30.178 -6.178 0.822 7.399 18.822

Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 41.6013 0.2196 189.472 < 2e-16 *** COMBY -2.4233 0.4187 -5.788 8.1e-09 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 8.94 on 2285 degrees of freedom Multiple R-squared: 0.01445, Adjusted R-squared: 0.01402 F-statistic: 33.5 on 1 and 2285 DF, p-value: 8.1e-09

交互影響

虛無假設 :IQ 與 SES 的交互作用 對於 lang 沒有顯著差異

對立假設 :IQ 與 SES 對於 lang 有顯著差異 虛無假設 :IQ 與 COMB 的交互作用 對於 lang 沒有顯著差

異 對立假設 :IQ 與 COMB 對於 lang 有顯著差異 虛無假設 :SES 與 COMB 的交互作用 對於 lang 沒有顯著

差異 對立假設 :SES 與 COMB 對於 lang 有顯著差異

> anova(lm(lang~IQ*SES*COMB)) Analysis of Variance Table

Response: lang Df Sum Sq Mean Sq F value Pr(>F) IQ 2 49686 24843 452.2850 < 2.2e-16 *** SES 2 7710 3855 70.1861 < 2.2e-16 *** COMB 1 1981 1981 36.0686 2.212e-09 *** IQ:SES 4 107 27 0.4872 0.745171 IQ:COMB 2 790 395 7.1880 0.000773 *** SES:COMB 2 6 3 0.0545 0.946954 IQ:SES:COMB 4 407 102 1.8506 0.116498 Residuals 2269 124631 55 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0--- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0

ANOVA TABLE

IQ與 COMB的交互影響圖3

03

54

04

5

IQ

me

an

of

lan

g

I II III

COMB

NY

進階分析 -1

> TukeyHSD(aov(lm(lang~IQ))) Tukey multiple comparisons of means 95% family-wise confidence level

Fit: aov(formula = lm(lang ~ IQ))

$IQ diff lwr upr p adj II-I 9.726836 8.610211 10.843461 0 III-I 17.419478 16.004608 18.834348 0 III-II 7.692642 6.617922 8.767363 0

進階分析 -2

> TukeyHSD(aov(lm(lang~SES))) Tukey multiple comparisons of means 95% family-wise confidence level

Fit: aov(formula = lm(lang ~ SES))

$SES diff lwr upr p adj B-A 5.885881 4.559735 7.212027 0 C-A 10.471478 8.936361 12.006595 0 C-B 4.585597 3.530036 5.641158 0

進階分析 -3

> TukeyHSD(aov(lm(lang~COMB))) Tukey multiple comparisons of means 95% family-wise confidence level

Fit: aov(formula = lm(lang ~ COMB))

$COMB diff lwr upr p adj Y-N -2.423266 -3.244276 -1.602257 0

Thank for your attention