Load the required packages
library(CTT)
library(psych)##
## Attaching package: 'psych'## The following object is masked from 'package:CTT':
##
## polyserialsetwd("/Users/munira/Desktop/Education/Masters/Illinois Institute of Technology/Coursework/511-Psychometrics/Homework/HW3")
remove(list=ls())
data <- read.csv("Ex 13.1 data.csv")
key <- read.csv("Ex 13.1 key.csv")items <- data[,2:14]scores <- data.frame(score(items, key, output.scored = TRUE)$scored)
names(scores) <- names(items)
View(scores)results <- itemAnalysis(scores, itemReport = TRUE)## Warning in cor(items[, i], Xd): the standard deviation is zeroView(results$itemReport)distractorAnalysis(items = items, key = key, csvReport = "Ex 13.1 distractor analysis.csv")## $Q1
## correct key n rspP pBis discrim lower mid50 mid75 upper
## 1 1 0 0.0000000 NA 0.00 0.00 0 0.0 0
## 2 * 2 8 0.6666667 0.3952847 0.75 0.25 1 0.5 1
## 3 3 0 0.0000000 NA 0.00 0.00 0 0.0 0
## 4 4 4 0.3333333 -0.6645570 -0.75 0.75 0 0.5 0
##
## $Q2
## correct key n rspP pBis discrim lower mid50 mid75 upper
## 1 1 1 0.08333333 -0.6404230 -0.25 0.25 0.0000000 0.0 0
## 2 2 4 0.33333333 -0.4265626 -0.50 0.50 0.3333333 0.5 0
## 3 3 1 0.08333333 -0.1910634 0.00 0.00 0.3333333 0.0 0
## 4 * 4 6 0.50000000 0.4561716 0.75 0.25 0.3333333 0.5 1
##
## $Q3
## correct key n rspP pBis discrim lower mid50 mid75 upper
## 1 1 2 0.16666667 -0.4303315 -0.5 0.5 0.0000000 0 0
## 2 2 1 0.08333333 -0.1910634 0.0 0.0 0.3333333 0 0
## 3 3 0 0.00000000 NA 0.0 0.0 0.0000000 0 0
## 4 * 4 9 0.75000000 0.1426197 0.5 0.5 0.6666667 1 1
##
## $Q4
## correct key n rspP pBis discrim lower mid50 mid75 upper
## 1 1 0 0 NA 0 0 0 0 0
## 2 2 0 0 NA 0 0 0 0 0
## 3 * 3 12 1 NA 0 1 1 1 1
## 4 4 0 0 NA 0 0 0 0 0
##
## $Q5
## correct key n rspP pBis discrim lower mid50 mid75
## 1 1 1 0.08333333 -0.30765537 -0.25000000 0.25 0.0000000 0.0
## 2 * 2 4 0.33333333 0.04926646 0.33333333 0.00 0.6666667 0.5
## 3 3 7 0.58333333 -0.30210205 -0.08333333 0.75 0.3333333 0.5
## 4 4 0 0.00000000 NA 0.00000000 0.00 0.0000000 0.0
## upper
## 1 0.0000000
## 2 0.3333333
## 3 0.6666667
## 4 0.0000000
##
## $Q6
## correct key n rspP pBis discrim lower mid50 mid75 upper
## 1 1 1 0.08333333 -0.07135061 0.00 0.00 0 0.5 0
## 2 2 1 0.08333333 -0.07135061 0.00 0.00 0 0.5 0
## 3 * 3 9 0.75000000 0.14261974 0.25 0.75 1 0.0 1
## 4 4 1 0.08333333 -0.64042300 -0.25 0.25 0 0.0 0
##
## $Q7
## correct key n rspP pBis discrim lower mid50 mid75
## 1 1 1 0.08333333 0.30856302 0.33333333 0.00 0.0000000 0
## 2 * 2 4 0.33333333 -0.02428215 0.08333333 0.25 0.0000000 1
## 3 3 2 0.16666667 -0.34859574 -0.25000000 0.25 0.3333333 0
## 4 4 5 0.41666667 -0.40352334 -0.16666667 0.50 0.6666667 0
## upper
## 1 0.3333333
## 2 0.3333333
## 3 0.0000000
## 4 0.3333333
##
## $Q8
## correct key n rspP pBis discrim lower mid50 mid75 upper
## 1 1 0 0.00000000 NA 0.0 0.0 0.0000000 0 0
## 2 2 1 0.08333333 -0.1910634 0.0 0.0 0.3333333 0 0
## 3 3 5 0.41666667 -0.5765553 -0.5 0.5 0.3333333 1 0
## 4 * 4 6 0.50000000 0.2940858 0.5 0.5 0.3333333 0 1
##
## $Q9
## correct key n rspP pBis discrim lower mid50 mid75 upper
## 1 * 1 10 0.8333333 -0.1203314 0 1 0.6666667 0.5 1
## 2 2 0 0.0000000 NA 0 0 0.0000000 0.0 0
## 3 3 2 0.1666667 -0.1788854 0 0 0.3333333 0.5 0
## 4 4 0 0.0000000 NA 0 0 0.0000000 0.0 0
##
## $Q10
## correct key n rspP pBis discrim lower mid50 mid75 upper
## 1 1 3 0.25000000 -0.3890891 -0.25 0.25 0.6666667 0 0
## 2 2 0 0.00000000 NA 0.00 0.00 0.0000000 0 0
## 3 * 3 8 0.66666667 0.3952847 0.50 0.50 0.3333333 1 1
## 4 4 1 0.08333333 -0.6404230 -0.25 0.25 0.0000000 0 0
##
## $Q11
## correct key n rspP pBis discrim lower mid50 mid75 upper
## 1 1 6 0.5 -0.7673657 -0.75 0.75 1 0 0
## 2 2 0 0.0 NA 0.00 0.00 0 0 0
## 3 3 0 0.0 NA 0.00 0.00 0 0 0
## 4 * 4 6 0.5 0.5416763 0.75 0.25 0 1 1
##
## $Q12
## correct key n rspP pBis discrim lower mid50 mid75 upper
## 1 1 1 0.08333333 -0.07135061 0.00 0.00 0.0000000 0.5 0
## 2 2 3 0.25000000 -0.71665619 -0.75 0.75 0.0000000 0.0 0
## 3 * 3 6 0.50000000 0.54167626 1.00 0.00 0.6666667 0.5 1
## 4 4 2 0.16666667 -0.34859574 -0.25 0.25 0.3333333 0.0 0
##
## $Q13
## correct key n rspP pBis discrim lower mid50 mid75
## 1 * 1 4 0.3333333 0.3668997 0.6666667 0.00 0.3333333 0.5
## 2 2 4 0.3333333 -0.1653595 -0.1666667 0.50 0.0000000 0.5
## 3 3 2 0.1666667 -0.5881176 -0.2500000 0.25 0.3333333 0.0
## 4 4 2 0.1666667 -0.3485957 -0.2500000 0.25 0.3333333 0.0
## upper
## 1 0.6666667
## 2 0.3333333
## 3 0.0000000
## 4 0.0000000summary(scores)## Q1 Q2 Q3 Q4
## Min. :0.0000 Min. :0.0 Min. :0.00 Min. :1
## 1st Qu.:0.0000 1st Qu.:0.0 1st Qu.:0.75 1st Qu.:1
## Median :1.0000 Median :0.5 Median :1.00 Median :1
## Mean :0.6667 Mean :0.5 Mean :0.75 Mean :1
## 3rd Qu.:1.0000 3rd Qu.:1.0 3rd Qu.:1.00 3rd Qu.:1
## Max. :1.0000 Max. :1.0 Max. :1.00 Max. :1
## Q5 Q6 Q7 Q8
## Min. :0.0000 Min. :0.00 Min. :0.0000 Min. :0.0
## 1st Qu.:0.0000 1st Qu.:0.75 1st Qu.:0.0000 1st Qu.:0.0
## Median :0.0000 Median :1.00 Median :0.0000 Median :0.5
## Mean :0.3333 Mean :0.75 Mean :0.3333 Mean :0.5
## 3rd Qu.:1.0000 3rd Qu.:1.00 3rd Qu.:1.0000 3rd Qu.:1.0
## Max. :1.0000 Max. :1.00 Max. :1.0000 Max. :1.0
## Q9 Q10 Q11 Q12
## Min. :0.0000 Min. :0.0000 Min. :0.0 Min. :0.0
## 1st Qu.:1.0000 1st Qu.:0.0000 1st Qu.:0.0 1st Qu.:0.0
## Median :1.0000 Median :1.0000 Median :0.5 Median :0.5
## Mean :0.8333 Mean :0.6667 Mean :0.5 Mean :0.5
## 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0 3rd Qu.:1.0
## Max. :1.0000 Max. :1.0000 Max. :1.0 Max. :1.0
## Q13
## Min. :0.0000
## 1st Qu.:0.0000
## Median :0.0000
## Mean :0.3333
## 3rd Qu.:1.0000
## Max. :1.0000describe(scores)## vars n mean sd median trimmed mad min max range skew kurtosis
## Q1 1 12 0.67 0.49 1.0 0.7 0.00 0 1 1 -0.62 -1.74
## Q2 2 12 0.50 0.52 0.5 0.5 0.74 0 1 1 0.00 -2.16
## Q3 3 12 0.75 0.45 1.0 0.8 0.00 0 1 1 -1.01 -1.04
## Q4 4 12 1.00 0.00 1.0 1.0 0.00 1 1 0 NaN NaN
## Q5 5 12 0.33 0.49 0.0 0.3 0.00 0 1 1 0.62 -1.74
## Q6 6 12 0.75 0.45 1.0 0.8 0.00 0 1 1 -1.01 -1.04
## Q7 7 12 0.33 0.49 0.0 0.3 0.00 0 1 1 0.62 -1.74
## Q8 8 12 0.50 0.52 0.5 0.5 0.74 0 1 1 0.00 -2.16
## Q9 9 12 0.83 0.39 1.0 0.9 0.00 0 1 1 -1.57 0.53
## Q10 10 12 0.67 0.49 1.0 0.7 0.00 0 1 1 -0.62 -1.74
## Q11 11 12 0.50 0.52 0.5 0.5 0.74 0 1 1 0.00 -2.16
## Q12 12 12 0.50 0.52 0.5 0.5 0.74 0 1 1 0.00 -2.16
## Q13 13 12 0.33 0.49 0.0 0.3 0.00 0 1 1 0.62 -1.74
## se
## Q1 0.14
## Q2 0.15
## Q3 0.13
## Q4 0.00
## Q5 0.14
## Q6 0.13
## Q7 0.14
## Q8 0.15
## Q9 0.11
## Q10 0.14
## Q11 0.15
## Q12 0.15
## Q13 0.14alpha(scores, check.keys = TRUE)## Warning in alpha(scores, check.keys = TRUE): Item = Q4 had no variance and
## was deleted## Warning in cor.smooth(r): Matrix was not positive definite, smoothing was
## done## Warning in alpha(scores, check.keys = TRUE): Some items were negatively correlated with total scale and were automatically reversed.
## This is indicated by a negative sign for the variable name.## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was
## done
## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was
## done
## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was
## done
## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was
## done
## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was
## done
## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was
## done
## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was
## done## In smc, the correlation matrix was not invertible, smc's returned as 1s## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was
## done
## Warning in cor.smooth(R): Matrix was not positive definite, smoothing was
## done##
## Reliability analysis
## Call: alpha(x = scores, check.keys = TRUE)
##
## raw_alpha std.alpha G6(smc) average_r S/N ase mean sd median_r
## 0.64 0.63 0.96 0.12 1.7 0.15 0.53 0.22 9.6e-21
##
## lower alpha upper 95% confidence boundaries
## 0.35 0.64 0.94
##
## Reliability if an item is dropped:
## raw_alpha std.alpha G6(smc) average_r S/N var.r med.r
## Q1 0.59 0.58 0.92 0.110 1.4 0.075 0.0e+00
## Q2 0.59 0.57 0.95 0.109 1.3 0.076 9.6e-21
## Q3 0.68 0.67 0.96 0.158 2.1 0.071 1.2e-01
## Q5 0.62 0.60 0.95 0.118 1.5 0.073 9.6e-21
## Q6 0.63 0.62 0.94 0.129 1.6 0.071 9.6e-21
## Q7- 0.68 0.66 0.95 0.150 1.9 0.072 1.2e-20
## Q8 0.62 0.60 0.93 0.122 1.5 0.077 1.2e-20
## Q9- 0.65 0.65 1.00 0.142 1.8 0.066 1.2e-01
## Q10 0.62 0.61 0.94 0.124 1.6 0.068 1.2e-20
## Q11 0.61 0.59 0.93 0.116 1.4 0.070 0.0e+00
## Q12 0.57 0.56 0.92 0.102 1.3 0.076 0.0e+00
## Q13 0.55 0.53 0.93 0.092 1.1 0.072 0.0e+00
##
## Item statistics
## n raw.r std.r r.cor r.drop mean sd
## Q1 12 0.583 0.576 0.589 0.438 0.67 0.49
## Q2 12 0.593 0.590 0.573 0.441 0.50 0.52
## Q3 12 0.076 0.073 0.031 -0.095 0.75 0.45
## Q5 12 0.466 0.492 0.466 0.302 0.33 0.49
## Q6 12 0.381 0.376 0.366 0.221 0.75 0.45
## Q7- 12 0.163 0.163 0.118 -0.024 0.67 0.49
## Q8 12 0.462 0.453 0.449 0.285 0.50 0.52
## Q9- 12 0.206 0.240 0.220 0.060 0.17 0.39
## Q10 12 0.443 0.425 0.434 0.275 0.67 0.49
## Q11 12 0.528 0.510 0.521 0.362 0.50 0.52
## Q12 12 0.659 0.653 0.667 0.523 0.50 0.52
## Q13 12 0.746 0.762 0.760 0.643 0.33 0.49
##
## Non missing response frequency for each item
## 0 1 miss
## Q1 0.33 0.67 0
## Q2 0.50 0.50 0
## Q3 0.25 0.75 0
## Q5 0.67 0.33 0
## Q6 0.25 0.75 0
## Q7 0.67 0.33 0
## Q8 0.50 0.50 0
## Q9 0.17 0.83 0
## Q10 0.33 0.67 0
## Q11 0.50 0.50 0
## Q12 0.50 0.50 0
## Q13 0.67 0.33 0