VocabGrowth {heplots}

Vocabulary growth data

Description

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.

Format

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

Details

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.

Source

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

References

Friendly, Michael (2010). HE Plots for Repeated Measures Designs. Journal of Statistical Software, 37(4), 1-40. doi:10.18637/jss.v037.i04.

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

Examples

library(car)
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))
car::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()