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ANOVA Analysis of Eighth-Grade Pupils' Language Scores in the Netherlands

This study analyzes the language test scores of 2,287 eighth-grade pupils from 132 classes across 131 schools in the Netherlands. Using ANOVA, we examine the effects of variables such as IQ, socio-economic status (SES), and multi-grade class arrangement (COMB) on student language performance. The results indicate significant differences in language scores influenced by IQ and SES levels, as well as notable interactions between these factors. Key results include F-statistics and p-values, highlighting the statistical significance of the findings.

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ANOVA Analysis of Eighth-Grade Pupils' Language Scores in the Netherlands

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  1. ANOVA ANALYSIS Eighth-Grade Pupils in the Netherlands

  2. 第八組 • 494310085 宋汶達 • 494310217 孫偉傑 • 494310425 陳盈志 • 494310463 徐健豪 • 494310504 朱明興

  3. Eighth-Grade Pupils in the Netherlands • Description • Snijders and Bosker (1999) use as a running example a study of 2287 eighth-grade 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 pupils from grades 7 and 8 are coded 1, but only eighth-graders were tested.

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

  5. 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

  6. IQ與成績的關係圖

  7. 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

  8. 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

  9. 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

  10. SES與成績的關係圖

  11. 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

  12. 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

  13. 假設 • 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

  14. COMB與成績的關係圖

  15. 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

  16. 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

  17. 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

  18. ANOVA TABLE • > 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

  19. IQ與COMB的交互影響圖

  20. 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

  21. 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

  22. 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

  23. Thank for your attention

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