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Data from the Laboratory School of the University of Chicago. They consist of scores from a cohort of pupils in grades 8-11 on the vocabulary section of the Cooperative Reading Test. The scores are scaled to a common, but arbitrary origin and unit of measurement, so as to be comparable over the four grades.

1 |

A data frame with 64 observations on the following 4 variables.

`grade8`

Grade 8 vocabulary score

`grade9`

Grade 9 vocabulary score

`grade10`

Grade 10 vocabulary score

`grade11`

Grade 11 vocabulary score

Since these data cover an age range in which physical growth is beginning to decelerate, it is of interest whether a similar effect occurs in the acquisition of new vocabulary.

R.D. Bock,
*Multivariate statistical methods in behavioral research*, McGraw-Hill, New York,
1975, pp453.

Friendly, Michael (2010). HE Plots for Repeated Measures Designs. *Journal of Statistical Software*,
37(4), 1-40. URL https://www.jstatsoft.org/v37/i04/.

Keesling, J.W., Bock, R.D. et al, "The Laboratory School study of vocabulary growth", University of Chicago, 1975.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 | ```
data(VocabGrowth)
# Standard Multivariate & Univariate repeated measures analysis
Vocab.mod <- lm(cbind(grade8,grade9,grade10,grade11) ~ 1, data=VocabGrowth)
idata <-data.frame(grade=ordered(8:11))
Anova(Vocab.mod, idata=idata, idesign=~grade, type="III")
##Type III Repeated Measures MANOVA Tests: Pillai test statistic
## Df test stat approx F num Df den Df Pr(>F)
##(Intercept) 1 0.653 118.498 1 63 4.115e-16 ***
##grade 1 0.826 96.376 3 61 < 2.2e-16 ***
heplot(Vocab.mod, type="III", idata=idata, idesign=~grade, iterm="grade",
main="HE plot for Grade effect")
### doing this 'manually' by explicitly transforming Y -> Y M
# calculate Y M, using polynomial contrasts
trends <- as.matrix(VocabGrowth) %*% poly(8:11, degree=3)
colnames(trends)<- c("Linear", "Quad", "Cubic")
# test all trend means = 0 == Grade effect
within.mod <- lm(trends ~ 1)
Manova(within.mod)
heplot(within.mod, terms="(Intercept)", col=c("red", "blue"), type="3",
term.labels="Grade",
main="HE plot for Grade effect")
mark.H0()
``` |

```
Loading required package: car
Type III Repeated Measures MANOVA Tests: Pillai test statistic
Df test stat approx F num Df den Df Pr(>F)
(Intercept) 1 0.65289 118.498 1 63 4.115e-16 ***
grade 1 0.82578 96.376 3 61 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Note: model has only an intercept; equivalent type-III tests substituted.
Type III MANOVA Tests: Pillai test statistic
Df test stat approx F num Df den Df Pr(>F)
(Intercept) 1 0.82578 96.376 3 61 < 2.2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
```

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