Rohwer Data Set

Description

Data from an experiment by William D. Rohwer on kindergarten children designed to examine how well performance on a set of paired-associate (PA) tasks can predict performance on some measures of aptitude and achievement.

Format

A data frame with 69 observations on the following 10 variables.

group

a numeric vector, corresponding to SES

SES

Socioeconomic status, a factor with levels Hi Lo

SAT

a numeric vector: score on a Student Achievement Test

PPVT

a numeric vector: score on the Peabody Picture Vocabulary Test

Raven

a numeric vector: score on the Raven Progressive Matrices Test

n

a numeric vector: performance on a 'named' PA task

s

a numeric vector: performance on a 'still' PA task

ns

a numeric vector: performance on a 'named still' PA task

na

a numeric vector: performance on a 'named action' PA task

ss

a numeric vector: performance on a 'sentence still' PA task

Details

The variables SAT, PPVT and Raven are responses to be potentially explained by performance on the paired-associate (PA) learning taskn, s, ns, na, and ss.

Source

Timm, N.H. 1975). Multivariate Analysis with Applications in Education and Psychology. Wadsworth (Brooks/Cole), Examples 4.3 (p. 281), 4.7 (p. 313), 4.13 (p. 344).

References

Friendly, M. (2007). HE plots for Multivariate General Linear Models. Journal of Computational and Graphical Statistics, 16(2) 421–444. http://datavis.ca/papers/jcgs-heplots.pdf

Examples

str(Rohwer)

## ANCOVA, assuming equal slopes
rohwer.mod <- lm(cbind(SAT, PPVT, Raven) ~ SES + n + s + ns + na + ss, data=Rohwer)
car::Anova(rohwer.mod)

# Visualize the ANCOVA model
heplot(rohwer.mod)
# Add ellipse to test all 5 regressors
heplot(rohwer.mod, hypotheses=list("Regr" = c("n", "s", "ns", "na", "ss")))
# View all pairs
pairs(rohwer.mod, hypotheses=list("Regr" = c("n", "s", "ns", "na", "ss")))

# or 3D plot
## Not run: 
col <- c("red", "green3", "blue", "cyan", "magenta", "brown", "gray")
heplot3d(rohwer.mod, hypotheses=list("Regr" = c("n", "s", "ns", "na", "ss")), 
                     col=col, wire=FALSE)

## End(Not run)

## fit separate, independent models for Lo/Hi SES
rohwer.ses1 <- lm(cbind(SAT, PPVT, Raven) ~ n + s + ns + na + ss, data=Rohwer, subset=SES=="Hi")
rohwer.ses2 <- lm(cbind(SAT, PPVT, Raven) ~ n + s + ns + na + ss, data=Rohwer, subset=SES=="Lo")

# overlay the separate HE plots
heplot(rohwer.ses1, ylim=c(40,110),col=c("red", "black"))
heplot(rohwer.ses2, add=TRUE, col=c("blue", "black"), grand.mean=TRUE, error.ellipse=TRUE)