bootstrap (version 2015.2)

scor: Open/Closed Book Examination Data

Description

This is data form mardia, Kent and Bibby on 88 students who took examinations in 5 subjects. Some where with open book and other with closed book.

Usage

data(scor)

Format

A data frame with 88 observations on the following 5 variables.

mec

mechanics, closed book note

vec

vectors, closed book note

alg

algebra, open book note

ana

analysis, open book note

sta

statistics, open book note

Source

Efron, B. and Tibshirani, R. (1993) An Introduction to the Bootstrap. Chapman and Hall, New York, London.

Details

The book uses this for bootstrap in principal component analysis.

Examples

str(scor) 
if(interactive())par(ask=TRUE)
plot(scor) 
# The parameter of interest (theta) is the fraction of variance explained 
# by the first principal component.
# For principal components analysis svd is better numerically than 
# eigen-decomposistion, but for bootstrapping the latter is _much_ faster.
theta <- function(ind) {
   vals <- eigen(var(scor[ind,]), symmetric=TRUE, only.values=TRUE)$values
   vals[1] / sum(vals) }
scor.boot <- bootstrap(1:88, 500, theta)
sd(scor.boot$thetastar) # bootstrap standard error
hist(scor.boot$thetastar)
abline(v=theta(1:88), col="red2")
abline(v=mean(scor.boot$thetastar), col="blue")