heplots (version 1.7.8)

Rohwer: 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 tasks, n, s, ns, na, and ss, which differed in the syntactic and semantic relationship between the stimulus and response words in each pair.

Timm (1975) does not give a source, but the most relevant studies are Rowher & Ammons (1968) and Rohwer & Levin (1971). The paired-associate tasks are described as:

n

(named): Simple paired-associate task where participants learn pairs of nouns with no additional context

s

(sentence): Participants learn pairs embedded within a sentence

ns

(named sentence): A combination where participants learn noun pairs with sentence context

na

(named action): Pairs are learned with an action relationship between them

ss

(sentence still): Similar to the sentence condition but with static presentation

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

Rohwer, W.D., Jr., & Levin, J.R. (1968). Action, meaning and stimulus selection in paired-associate learning. Journal of Verbal Learning and Verbal Behavior, 7: 137-141.

Rohwer, W. D., Jr., & Ammons, M. S. (1971). Elaboration training and paired-associate learning efficiency in children. Journal of Educational Psychology, 62(5), 376-383.

Examples

str(Rohwer)

# Plot responses against each predictor
library(tidyr)
library(dplyr)
library(ggplot2)

yvars <- c("SAT", "PPVT", "Raven" )
xvars <- c("n", "s", "ns", "na", "ss")
Rohwer_long <- Rohwer %>%
  pivot_longer(cols = all_of(xvars), names_to = "xvar", values_to = "x") |>
  pivot_longer(cols = all_of(yvars), names_to = "yvar", values_to = "y") |>
  mutate(xvar = factor(xvar, xvars), yvar = factor(yvar, yvars))

ggplot(Rohwer_long, aes(x, y, color = SES, shape = SES, fill = SES)) +
  geom_point() +
  geom_smooth(method = "lm", se = FALSE, formula = y ~ x) +
  stat_ellipse(geom = "polygon", level = 0.68, alpha = 0.1) +
  facet_grid(yvar ~ xvar, scales = "free") +
  labs(x = "predictor", y = "response") +
  theme_bw(base_size = 14)


## 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
if (FALSE) {
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)
}

## 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)