scor: Open/Closed Book Examination Data

In bootstrap: Functions for the Book "An Introduction to the Bootstrap"

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

Details

The book uses this for bootstrap in principal component analysis.

Source

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

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")

Example output

'data.frame':	88 obs. of  5 variables:
 $ mec: num  77 63 75 55 63 53 51 59 62 64 ...
 $ vec: num  82 78 73 72 63 61 67 70 60 72 ...
 $ alg: num  67 80 71 63 65 72 65 68 58 60 ...
 $ ana: num  67 70 66 70 70 64 65 62 62 62 ...
 $ sta: num  81 81 81 68 63 73 68 56 70 45 ...
[1] 0.04881289

bootstrap documentation built on June 17, 2019, 5:04 p.m.