cheat: Method to detect excessive similarity in student test...
In wasabi1989/MiscPsycho: Miscellaneous Psychometric Analyses

Description Usage Arguments Details Value Author(s) References Examples

Examines all pairwise comparisons within a group to assess the degree to which response patterns between individuals are too similar to have occured from random chance alone.

cheat(...)
## Default S3 method:
cheat(dat, key, wrongChoice, alpha = .01, rfa = c('nr', 'uni', 'bsct'), bonf = c('yes','no'), con = 1e-12, lower = 0, upper = 50, ...)
## S3 method for class 'formula'
cheat(formula, data, na.action, subset, key, wrongChoice, ...)

`formula`	an object of class `"formula"` (or one that can be coerced to that class): a symbolic description of the model to be fitted. The details of model specification are given under `Details`.
`data`	an optional data frame, list or environment (or object coercible by `as.data.frame` to a data frame) containing the variables in the model. If not found in `data`, the variables are taken from `environment(formula)`, typically the environment from which `cheat` is called.
`dat`	A data frame or matrix with item responses. Implemented only for the default method.
`na.action`	a function which indicates what should happen when the data contain `NA`s. Defaults to `getOption("na.action")`.
`subset`	an optional vector specifying a subset of observations to be used.
`key`	a numeric vector containing the correct resposnes to each test item
`rfa`	the Root Finding Algorithm used. Options include `nr` for newton-raphson, `uni` to use R's internal uniroot function, or `bsct` for the bisection method.
`alpha`	Level of significance
`bonf`	Option to choose bonferonni adjustment to the `alpha`
`con`	Tolerance for root finding algorithms
`lower`	the lower end points of the interval to be searched for the bisection and uniroot functions
`upper`	the upper end points of the interval to be searched for the bisection and uniroot functions
`wrongChoice`	a list containing the probability of choosing each incorrect response option. See `wrongProb` for details
`...`	Not implemented

The dataframe must be organized with examinees as rows and their responses in columns

A list with class "cheat" containing the following components:

`Number of Possible Cheatering Pairs`	the number of individuals with similar response patterns)
`Possible Cheating Pairs`	the identified individuals. S28:32 denotes that individuals in rows 28 and 32 have similar response patterns
`Number of Exact Matches`	Number of observed exact matches between the two individuals compared
`Observed Z Values`	the statistical result comparing number of observed exact matches to the expected
`Critical Z`	the z value used as the threshold
`Expected Number of Matches`	the expected number of matches between the two individuals compared

Harold C. Doran

Wesolowsky, G.E (2000). Detecting excessive similarity in answers on multiple choice exams. Journal of Applied Statistics (27)7

## Simulate data
NumStu   <- 30
NumItems <- 50
dat <- matrix(0, nrow=NumStu, ncol=NumItems) 
set.seed(1234)
for(i in 1:NumStu){
   dat[i,] <- sample(1:4, NumItems, replace=TRUE)
}
dat <- data.frame(dat)

## Add in explicit answer copying 
dat[(NumStu+1),] <- dat[NumStu,]
dat[(NumStu+2),] <- c(dat[(NumStu-1), 1:25], dat[(NumStu-2), 26:50 ])

## Answer Key
set.seed(1234)
key <- sample(1:4, NumItems, replace=TRUE)

## Formula interface
ff <- as.formula(paste('~', paste( names(dat), collapse= "+")))
## See wrongProb help page
mm <- wrongProb(ff, data = dat, key = key)
(result <- cheat(ff, data = dat, key = key, wrongChoice = mm))
summary(result)

## Default interface
(result <- cheat(dat, key = key, wrongChoice = mm))