| Type: | Package |
| Title: | Classical Test Theory (CTT) Analysis |
| Version: | 0.7.5 |
| Maintainer: | Andrés Christiansen <andres.christiansen@iea-hamburg.de> |
| Description: | Functions for classical test theory analysis, following methods presented by Wu et al. (2006) <doi:10.1007/978-981-10-3302-5>. |
| Depends: | R (≥ 3.5.0) |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2.0)] |
| Encoding: | UTF-8 |
| LazyData: | true |
| RoxygenNote: | 7.3.2 |
| NeedsCompilation: | no |
| Packaged: | 2025-06-19 21:00:49 UTC; andreschristiansen |
| Author: | Andrés Christiansen [aut, cre] |
| Repository: | CRAN |
| Date/Publication: | 2025-06-19 21:20:07 UTC |
Reliability measures
Description
Estimates the Cronbach's alpha coefficients and the split-halves coefficient for a scored matrix.
Usage
alphatest(x, wt = NULL)
splithalf(
x,
wt = NULL,
tries = 100,
seed = NA,
administered = NULL,
maxscore = NULL
)
Arguments
x |
a data frame or matrix of scored data. |
wt |
a vector with total weights. Default is |
tries |
a numeric value indicating the number of samples for the
split-halves coefficient. Default is |
seed |
a single value, interpreted as an integer, or |
administered |
a logical matrix indicating which items were administered.
The dimensions should be the same as |
maxscore |
a numeric value indicating which is the maximum score possible
per item. The minimum score is assumed to be 0. If |
Value
a list or a numeric vector.
Examples
# No weights
ex <- correct(x = dichodata, key = dichokey, navalue = NA)
alphatest(ex)
splithalf(ex, tries = 5)
# With weights
set.seed(1919)
wt <- sample(x = 1:4, size = nrow(dichodata), replace = TRUE)
alphatest(ex,wt = wt)
splithalf(ex,wt = wt, tries = 5)
Classical test theory item and person statistics
Description
Calculates several item and person statistics following
ctitem(), and ctperson().
Usage
classicaltest(
x,
key,
navalue = NA,
wt = NULL,
itemcategories = NULL,
administered = NULL,
itemscores = NULL,
maxscore = NULL
)
Arguments
x |
a data frame or matrix. |
key |
a vector or a list indicating the keys to score the data. If answers can only be right or wrong use a vector. If partial credits are allowed, use a list where the first element contains the keys for full credits, and next elements contain progressively the partial credit information. If a test has a combination of full credit and partial credit items, leave the full credit items as NAs in the keys for partial credit. |
navalue |
a single value indicating the score of NAs. |
wt |
a vector with total weights. Default is |
itemcategories |
a vector indicating all the possible categories for all items. If NULL, possible categories will be derived from data. |
administered |
a logical matrix indicating which items were administered.
The dimensions should be the same as |
itemscores |
a numeric vector indicating all the possible scores for all items.
If |
maxscore |
a numeric value indicating which is the maximum score possible
per item. The minimum score is assumed to be 0. If |
Value
A list with item and person statistics.
Examples
# Data preparation
## Random weights creation
set.seed(1919)
wt <- sample(x = 1:4, size = nrow(dichodata), replace = TRUE)
# Item and person analysis for multiple choice items
classicaltest(x = dichodata, key = dichokey, wt = wt)
Scoring correct/incorrect answers
Description
Transforms a data frame or matrix from raw answers to scores given a key.
Usage
correct(x, key, navalue = NA)
Arguments
x |
a data frame or matrix. |
key |
a vector or a list indicating the keys to score the data. If answers can only be right or wrong use a vector. If partial credits are allowed, use a list where the first element contains the keys for full credits, and next elements contain progressively the partial credit information. If a test has a combination of full credit and partial credit items, leave the full credit items as NAs in the keys for partial credit. |
navalue |
a single value indicating the score of NAs. |
Value
A data frame with scored answers.
Examples
# Full credit
dichokey
## NAs as NAs
head(dichodata)
ex1 <- correct(x = dichodata, key = dichokey, navalue = NA)
head(ex1)
## NAs as 0s
head(dichodata)
ex2 <- correct(x = dichodata, key = dichokey, navalue = 0)
head(ex2)
# Partial credit
partialkey
## NAs as NAs
head(partialdata)
ex3 <- correct(x = partialdata, key = partialkey, navalue = NA)
head(ex3)
## NAs as 0s
head(partialdata)
ex4 <- correct(x = partialdata, key = partialkey, navalue = 0)
head(ex4)
Classical test theory item statistics
Description
Calculates several item statistics, including: item means, frequencies, proportions, and correlations between item responses and the total score.
Usage
ctitem(
x,
key,
navalue = NA,
wt = NULL,
itemcategories = NULL,
administered = NULL,
itemscores = NULL
)
Arguments
x |
a data frame or matrix. |
key |
a vector or a list indicating the keys to score the data. If answers can only be right or wrong use a vector. If partial credits are allowed, use a list where the first element contains the keys for full credits, and next elements contain progressively the partial credit information. If a test has a combination of full credit and partial credit items, leave the full credit items as NAs in the keys for partial credit. |
navalue |
a single value indicating the score of NAs. |
wt |
a vector with total weights. Default is |
itemcategories |
a vector indicating all the possible categories for all items. If NULL, possible categories will be derived from data. |
administered |
a logical matrix indicating which items were administered.
The dimensions should be the same as |
itemscores |
a numeric vector indicating all the possible scores for all items.
If |
Value
A list.
Examples
# Data preparation
## Random weights creation
set.seed(1919)
wt <- sample(x = 1:4, size = nrow(dichodata), replace = TRUE)
# Item analysis for multiple choice items
ctitem(x = dichodata, key = dichokey, itemcategories = c('A','B','C','D'), wt = wt)
Classical test theory person statistics
Description
Calculates persons statistics given a data frame (or matrix) of corrected data. Including sum scores, number of administered items, number of answered items, proportion of correct items, and mean score by item.
Usage
ctperson(x, administered = NULL, maxscore = NULL)
Arguments
x |
a data frame or matrix of scored data. |
administered |
a logical matrix indicating which items were administered.
The dimensions should be the same as |
maxscore |
a numeric value indicating which is the maximum score possible
per item. The minimum score is assumed to be 0. If |
Value
A data frame with person statistics.
Examples
# Data preparation
## Scored data
corr <- correct(x = dichodata, key = dichokey, navalue = NA)
## Random administered matrix
set.seed(1919)
admin <- sample(x = 0:1, size = nrow(corr)*ncol(corr), replace = TRUE, prob = c(.05,.95))
admin <- matrix(data = as.logical(admin),nrow = nrow(corr))
head(admin)
# Person statistics with all items administered
ex1 <- ctperson(x = corr)
head(ex1)
# Person statistics with NOT all items administered
ex2 <- ctperson(x = corr, administered = admin)
head(ex2)
Standard error of measurement (SEM)
Description
Estimates the standard error of measurement (SEM) of a scored matrix or data frame using Cronbach's alpha or the split-halves coefficient.
Usage
ctsem.alpha(x, wt = NULL, administered = NULL, maxscore = NULL)
ctsem.split(
x,
wt = NULL,
tries = 100,
seed = NA,
administered = NULL,
maxscore = NULL
)
Arguments
x |
a data frame or matrix of scored data. |
wt |
a vector with total weights. Default is |
administered |
a logical matrix indicating which items were administered.
The dimensions should be the same as |
maxscore |
a numeric value indicating which is the maximum score possible
per item. The minimum score is assumed to be 0. If |
tries |
a numeric value indicating the number of samples for the
split-halves coefficient. Default is |
seed |
a single value, interpreted as an integer, or |
Value
a list.
Examples
# No weights
ex <- correct(x = dichodata, key = dichokey, navalue = NA)
ctsem.alpha(ex)
ctsem.split(ex,tries = 5)
# With weights
set.seed(1919)
wt <- sample(x = 1:4, size = nrow(dichodata), replace = TRUE)
ctsem.alpha(ex,wt = wt)
ctsem.split(ex,wt = wt,tries = 5)
Simulated multiple choice data with 1000 cases, and 20 items
Description
Simulated multiple choice data with 1000 cases, and 20 items
Keys for dichodata
Description
Keys for dichodata
Dichotomize data
Description
Converts a matrix or data frame into a dichotomized data frame. Where each possible category is assigned a 1 or a 0.
Usage
dichotomize(x, id = NULL, categories = NULL, NAasNA = TRUE, sortbyItem = FALSE)
Arguments
x |
a data frame or matrix. |
id |
a vector of unique values indicating the ids of the cases.
If |
categories |
a vector indicating all possible categories.
If |
NAasNA |
a logical value indicating if NAs should be kept
as NAs. If |
sortbyItem |
a logical value indicating if the resulting data frame
should be order by item names, on the contrary, by ids.
Default is |
Value
A data frame with columns for the ids, the item names and all the possible item categories, where 1s mean the person answered that category for that item, and 0s mean the contrary.
Examples
data(dichodata)
# Dichotomize with all present categories
ex1 <- dichotomize(dichodata, categories = NULL)
head(ex1)
# Dichotomize with fixed set of categories
ex2 <- dichotomize(dichodata, categories = c('A','B','C','D'))
head(ex2)
# Dichotomize with NAs as 0s
ex3 <- dichotomize(dichodata, NAasNA = FALSE)
head(ex3)
Item discrimination
Description
Estimates item discrimination of a corrected matrix or data frame.
Usage
discrimination(x, wt = NULL, itemscores = NULL, administered = NULL)
Arguments
x |
a data frame or matrix of scored data. |
wt |
a vector with total weights. Default is |
itemscores |
a numeric vector indicating all the possible scores for all items.
If |
administered |
a logical matrix indicating which items were administered.
The dimensions should be the same as |
Value
a list.
Examples
# No weights
ex <- correct(x = dichodata, key = dichokey, navalue = NA)
discrimination(ex)
# With weights
set.seed(1919)
wt <- sample(x = 1:4, size = nrow(dichodata), replace = TRUE)
discrimination(ex,wt = wt)
Distractor statistics
Description
Summarize the statistics for each category of each item.
Usage
distractors(
x,
key,
wt = NULL,
navalue = NA,
itemcategories = NULL,
administered = NULL
)
Arguments
x |
a data frame or matrix. |
key |
a vector or a list indicating the keys to score the data. If answers can only be right or wrong use a vector. If partial credits are allowed, use a list where the first element contains the keys for full credits, and next elements contain progressively the partial credit information. If a test has a combination of full credit and partial credit items, leave the full credit items as NAs in the keys for partial credit. |
wt |
a vector with total weights. Default is |
navalue |
a single value indicating the score of NAs. |
itemcategories |
a vector indicating all the possible categories for all items. If NULL, possible categories will be derived from data. |
administered |
a logical matrix indicating which items were administered.
The dimensions should be the same as |
Value
a list.
Examples
# Full credit items
distractors(x = dichodata, key = dichokey)
# Partial credit items
distractors(x = partialdata, key = partialkey)
Item mean scores
Description
Calculates the item mean scores.
Usage
itemmean(x, wt = NULL)
Arguments
x |
a data frame or matrix of scored data. |
wt |
a vector with total weights. Default is |
Value
a data frame.
Examples
# No weights
ex <- correct(x = dichodata, key = dichokey, navalue = NA)
itemmean(ex)
# With weights
set.seed(1919)
wt <- sample(x = 1:4, size = nrow(dichodata), replace = TRUE)
itemmean(ex,wt = wt)
Simulated multiple choice data with 1000 cases, and 20 items and partial credits
Description
Simulated multiple choice data with 1000 cases, and 20 items and partial credits
Keys for partialdata
Description
Keys for partialdata
Point-biserial correlation
Description
Estimates the point-biserial correlation coefficient between dichotomous items and the person's score.
Usage
pointbiserial(x, wt = NULL, exclude = FALSE, listwise = FALSE, recScore = TRUE)
Arguments
x |
a numeric data frame or matrix containing only two categories. |
wt |
a numeric vector of total weights. Default is |
exclude |
a logical value indicating if the point-biserial correlation
should be calculated excluding the item from the total score.
Defaulft is |
listwise |
only consider complete data (remove rows with NAs).
Defaulft is |
recScore |
a logical value indicating if the total score for
should be calculated based only on valid values. Thus,
if |
Value
A numeric vector with the point-biserial correlation coefficients by item.
Examples
data(dichodata)
data(dichokey)
# Data preparation
## Corrected data
corr <- correct(x = dichodata, key = dichokey, navalue = NA)
## Random weights creation
set.seed(1919)
wt <- sample(x = 1:4, size = nrow(corr), replace = TRUE)
# Correlations without weights
pointbiserial(x = corr, wt = NULL)
# Correlations with weights
pointbiserial(x = corr, wt = wt)
# Correlations if item is excluded
pointbiserial(x = corr, exclude = TRUE)
# Correlations if NAs are considered 0s (recScore)
pointbiserial(x = corr, recScore = FALSE)
# Correlations with listwise
pointbiserial(x = corr, listwise = TRUE)
Simulated polytomous items data with 1000 cases, and 20 items
Description
Simulated polytomous items data with 1000 cases, and 20 items
Population and sample (co)variance
Description
Estimates the weighted and unweighted population and sample covariance for a vector, a matrix or a data frame. Missing values are omitted.
Usage
stcov(x, wt = NULL, sample = TRUE)
Arguments
x |
a numeric vector, matrix or data frame. |
wt |
a vector with total weights. Default is |
sample |
a logical value indicating if the sample variance should be used.
Default is |
Value
a numeric value or a numeric matrix.
Examples
# Variance ----
## Sample variance with no weights
stcov(x = iris$Sepal.Length, sample = TRUE)
## Population variance with no weights
stcov(x = iris$Sepal.Length, sample = TRUE)
## Sample variance with no weights
wt = c(100, rep(1,nrow(iris)-1)) # Unbalanced weights
stcov(x = iris$Sepal.Length, sample = FALSE, wt = wt)
## Population variance with no weights
wt = c(100, rep(1,nrow(iris)-1)) # Unbalanced weights
stcov(x = iris$Sepal.Length, sample = FALSE)
# Covariance ----
## Sample covariance with no weights
stcov(x = iris[,1:4], sample = TRUE)
## Population covariance with no weights
stcov(x = iris[,1:4], sample = TRUE)
## Sample covariance with no weights
wt = c(100, rep(1,nrow(iris)-1)) # Unbalanced weights
stcov(x = iris[,1:4], sample = FALSE, wt = wt)
## Population covariance with no weights
wt = c(100, rep(1,nrow(iris)-1)) # Unbalanced weights
stcov(x = iris[,1:4], sample = FALSE)