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.

1 |

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

The variables `SAT`

, `PPVT`

and `Raven`

are responses to be
potentially explained by performance on the paired-associate (PA) learning task`n`

, `s`

, `ns`

, `na`

, and `ss`

.

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).

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

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

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