gen_test_score_CTT {lazy.tools}

R Documentation

Generating Test Score Distribution according to Classical Test Theory

Description

This function generates a frequency distribution table of n discrete test scores in [minscore,maxscore].

Usage

gen_test_score_CTT(
  n,
  minscore = NULL,
  maxscore = NULL,
  rho0 = 0.9,
  meanX0 = NULL,
  varX0 = 15^2,
  beta = NULL,
  orth = 0,
  discrete = 1,
  seed = NULL,
  print = 0,
  plot = 0,
  title = NULL
)

Arguments

n	# of observations.
minscore	The minimum score.
maxscore	The maximum score.
meanX0	The mean of observed test score
varX0	The variance of observed test score
beta	Vector of alpha and beta parameters for beta distribution in [minscore,maxscore].
orth	= 1 to orthogonalize T and E. (not yet available.)
discrete	= 0 to use continuous random variables
seed	The random number seed or NULL
print	= 1 to print the result.
plot	= 1 to plot the result.
title	Title string to be used in plot.
rho	The reliability coefficient

Details

This function generates a set of
(observed score X, true score T, error score E)
of size n in [minscore <= X <= maxscore] according to the Classical Test Theory.

Continuous random numbers, either normal or generalized beta, are first generated and then they are discretized by cut function. Those values outside of [minscore,maxscore] will be set to minscore or maxscore, resp.

beta parameter has priority over nomal parameter.

Value

A list of:
rho The actual reliability
meanX The actual mean of X
stdX The actual standard deviation of X
meanT The actual mean of T
stdT The actual standard deviation of T
meanE The actual mean of E
stdE The actual standard deviation of E
cor The correlation matrix of (X,T,E)
XTE A matrix consisting of X,T,E. (n times 3 matrix)
scoredist Score distribution of X

Examples

res=gen_test_score_CTT(n=10000, varX0=17^2, rho=0.60, seed=1701
                  , plot=1, print=1, minscore=0, maxscore=100)
seed=1701; set.seed(seed)
res=gen_test_score_CTT(n=10000, varX0=17^2, rho=0.60
                  , plot=1, print=1, minscore=0, maxscore=100)

res=gen_test_score_CTT(n=10000, varX=18^2, rho=0.80, beta=c(5,2)
                  , plot=1, print=1, minscore=0, maxscore=100, seed=1701)
res=gen_test_score_CTT(n=10000, meanX0=60, varX=18^2, rho=0.80, beta=c(5,2)
                  , plot=1, print=1, minscore=0, maxscore=100, seed=1701)

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