VocabGrowth: Vocabulary growth data

In heplots: Visualizing Hypothesis Tests in Multivariate Linear Models

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.

Usage

data(VocabGrowth)

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. URL http://www.jstatsoft.org/v37/i04/.

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

Examples

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()

Example output

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

heplots documentation built on May 31, 2017, 4:54 a.m.