Rubin1981 {bayesmeta}

8-schools example data

Description

SAT coaching experiments in 8 schools.

Usage

data("Rubin1981")

Format

The data frame contains the following columns:

school	character	school identifier
n	integer	number of students
effect	numeric	effect estimate
stderr	numeric	associated standard error

Details

Quoting from Gelman et al. (1997), Sec. 5.5: “A study was performed for the Educational Testing Service to analyze the effects of special coaching programs for SAT-V (Scholastic Aptitude Test-Verbal) in each of eight high schools. The outcome variable in each study was the score on a special administration of the SAT-V, a standardized multiple choice test administered by the Educational Testing Service and used to help colleges make admissions decisions; the scores can vary between 200 and 800, with mean about 500 and standard deviation about 100. The SAT examinations are designed to be resistant to short-term efforts directed specifically toward improving performance on the test; instead they are designed to reflect knowledge acquired and abilities developed over many years of education. Nevertheless, each of the eight schools in this study considered its short-term coaching program to be very successful at increasing SAT scores. Also, there was no prior reason to believe that any of the eight programs was more effective than any other or that some were more similar in effect to each other than to any other.”

Source

A. Gelman, J.B. Carlin, H. Stern, and D.B. Rubin. Bayesian data analysis. Chapman & Hall / CRC, Boca Raton, 1997.

References

D.B. Rubin. Estimation in parallel randomized experiments. Journal of Educational Statistics, 6(4):377-401, 1981. doi:10.3102/10769986006004377.

A. Gelman. Prior distributions for variance parameters in hierarchical models. Bayesian Analysis, 1(3):515-534, 2006. doi:10.1214/06-BA117A.

See Also

traceplot.

Examples

data("Rubin1981")

## Not run: 
# analysis using a weakly informative half-Cauchy prior:
schools <- bayesmeta(y=Rubin1981[,"effect"], sigma=Rubin1981[,"stderr"],
                     labels=Rubin1981[,"school"],
                     tau.prior=function(x){return(dhalfcauchy(x, scale=25))})

# show summary:
summary(schools)

# show shrinkage effect for 8 individual estimates:
schools$theta
traceplot(schools)

## End(Not run)