case1302 {Sleuth3}

Pygmalion Effect

Description

One company of soldiers in each of 10 platoons was assigned to a Pygmalion treatment group, with remaining companies in the platoon assigned to a control group. Leaders of the Pygmalion platoons were told their soldiers had done particularly well on a battery of tests which were, in fact, non-existent. In this randomised block experiment, platoons are experimental units, companies are blocks, and average Practical Specialty test score for soldiers in a platoon is the response. The researchers wished to see if the platoon response was affected by the artificially-induced expectations of the platoon leader.

Usage

case1302

Format

A data frame with 29 observations on the following 3 variables.

Company

a factor indicating company identification, with levels "C1", "C2", ..., "C10"

Treat

a factor indicating treatment with two levels, "Pygmalion" and "Control"

Score

average score on practical specialty test of all soldiers in the platoon

Source

Ramsey, F.L. and Schafer, D.W. (2013). The Statistical Sleuth: A Course in Methods of Data Analysis (3rd ed), Cengage Learning.

References

Eden, D. (1990). Pygmalion Without Interpersonal Contrast Effects: Whole Groups Gain from Raising Manager Expectations, Journal of Applied Psychology 75(4): 395–398.

Examples

str(case1302)
attach(case1302)

## EXPLORATION AND MODEL DEVELOPMENT
plot(Score ~ as.numeric(Company),cex=1.5, pch=21, 
  bg=ifelse(Treat=="Pygmalion","blue","light gray"))
myLm1   <- lm(Score ~ Company + Treat + Company:Treat) # Fit with interaction.
plot(myLm1,which=1)  # Plot residuals.
myLm2   <- update(myLm1, ~ . - Company:Treat) # Refit, without interaction.
anova(myLm2, myLm1)  # Show extra-ss-F-test p-value (for interaction effect).
if(require(car)){   # Use the car library                               
  crPlots(myLm2)
}

## INFERENCE
myLm3 <- update(myLm2, ~ . - Company)  # Fit reduced model without Company.
anova(myLm3, myLm2)   # Test for Company effect.
summary(myLm2)   # Show estimate and p-value for Pygmalion effect.  
confint(myLm2,11)  # Show 95% CI for Pygmalion effect.

## DISPLAY FOR PRESENTATION
beta        <- myLm2$coef
partialRes  <- myLm2$res + beta[11]*ifelse(Treat=="Pygmalion",1,0) # partial res
boxplot(partialRes ~ Treat,  # Boxplots of partial residuals for each treatment
  ylab="Average Test Score, Adjusted for Company Effect (Deviation from Company Average)",
  names=c("19 Control Platoons","10 Pygmalion Treated Platoons"),
  col="green", boxlwd=2, medlwd=2,whisklty=1, whisklwd=2, staplewex=.2, 
  staplelwd=2, outlwd=2, outpch=21, outbg="green", outcex=1.5	)	   

detach(case1302)