Function to compute generic item summary statistics that do not require
prior fitting of IRT models. Contains information about sample sizes (N),
number of observed categories (K), (standardized) coefficient alpha
(and alpha if an item is removed; (alpha_if_rm)),
mean/SD and frequency of total scores,
reduced item-total correlations (cor_if_rm),
average/sd of the correlation between items,
squared multiple correlation (smc), response frequencies,
and conditional mean/sd information given the
unweighted sum scores. Summary information involving the total scores
only included for responses with no missing data to ensure the metric is
meaningful, however standardized statistics (e.g., correlations) utilize
all possible response information.
Usage
itemstats(
data,
group = NULL,
ts_fun = rowSums,
use_ts = TRUE,
itemfreq = "proportions",
ts.tables = FALSE
)Arguments
- data
An object of class
data.frameormatrixwith the response patterns- group
optional grouping variable to condition on when computing summary information
- ts_fun
function to use to build the linear composite score? Recommend inputs are
rowSums(default) androwMeans, and must include an argumentna.rm, though users may define their own as well- use_ts
logical; include information that is conditional on a meaningful total score?
- itemfreq
character vector indicting whether to include item response
"proportions"or"counts"for each item. If set to'none'then this will be omitted- ts.tables
logical; include mean/sd summary information pertaining to the unweighted total score?
References
Chalmers, R. P. (2012). mirt: A Multidimensional Item Response Theory Package for the R Environment. Journal of Statistical Software, 48(6), 1-29. doi:10.18637/jss.v048.i06
Author
Phil Chalmers rphilip.chalmers@gmail.com
Examples
# dichotomous data example
LSAT7full <- expand.table(LSAT7)
head(LSAT7full)
#> Item.1 Item.2 Item.3 Item.4 Item.5
#> 1 0 0 0 0 0
#> 2 0 0 0 0 0
#> 3 0 0 0 0 0
#> 4 0 0 0 0 0
#> 5 0 0 0 0 0
#> 6 0 0 0 0 0
itemstats(LSAT7full)
#> $overall
#> N mean.total sd.total std.alpha alpha SEM.alpha mean.r sd.r
#> 1000 3.707 1.199 0.456 0.453 0.886 0.143 0.052
#>
#> $itemstats
#> N K mean sd cor_if_rm smc alpha_if_rm
#> Item.1 1000 2 0.828 0.378 0.246 0.063 0.396
#> Item.2 1000 2 0.658 0.475 0.247 0.081 0.394
#> Item.3 1000 2 0.772 0.420 0.313 0.106 0.345
#> Item.4 1000 2 0.606 0.489 0.223 0.053 0.415
#> Item.5 1000 2 0.843 0.364 0.175 0.038 0.438
#>
#> $proportions
#> 0 1
#> Item.1 0.172 0.828
#> Item.2 0.342 0.658
#> Item.3 0.228 0.772
#> Item.4 0.394 0.606
#> Item.5 0.157 0.843
#>
itemstats(LSAT7full, itemfreq='counts')
#> $overall
#> N mean.total sd.total std.alpha alpha SEM.alpha mean.r sd.r
#> 1000 3.707 1.199 0.456 0.453 0.886 0.143 0.052
#>
#> $itemstats
#> N K mean sd cor_if_rm smc alpha_if_rm
#> Item.1 1000 2 0.828 0.378 0.246 0.063 0.396
#> Item.2 1000 2 0.658 0.475 0.247 0.081 0.394
#> Item.3 1000 2 0.772 0.420 0.313 0.106 0.345
#> Item.4 1000 2 0.606 0.489 0.223 0.053 0.415
#> Item.5 1000 2 0.843 0.364 0.175 0.038 0.438
#>
#> $counts
#> 0 1
#> Item.1 172 828
#> Item.2 342 658
#> Item.3 228 772
#> Item.4 394 606
#> Item.5 157 843
#>
# composite score expressed as a mean
itemstats(LSAT7full)$overall
#> N mean.total sd.total std.alpha alpha SEM.alpha mean.r sd.r
#> 1000 3.707 1.199 0.456 0.453 0.886 0.143 0.052
itemstats(LSAT7full, ts_fun=rowMeans)$overall
#> N mean.total sd.total std.alpha alpha SEM.alpha mean.r sd.r
#> 1000 0.741 0.24 0.456 0.453 0.177 0.143 0.052
# behaviour with missing data
LSAT7full[1:5,1] <- NA
itemstats(LSAT7full)
#> $overall
#> N.complete N mean.total sd.total std.alpha alpha SEM.alpha mean.r sd.r
#> 995 1000 3.726 1.172 0.427 0.426 0.888 0.137 0.052
#>
#> $itemstats
#> N K mean sd cor_if_rm smc alpha_if_rm
#> Item.1 995 2 0.832 0.374 0.222 0.051 0.396
#> Item.2 1000 2 0.658 0.475 0.247 0.075 0.364
#> Item.3 1000 2 0.772 0.420 0.313 0.096 0.316
#> Item.4 1000 2 0.606 0.489 0.223 0.048 0.384
#> Item.5 1000 2 0.843 0.364 0.175 0.028 0.418
#>
#> $proportions
#> 0 1 <NA>
#> Item.1 0.167 0.828 0.005
#> Item.2 0.342 0.658 NA
#> Item.3 0.228 0.772 NA
#> Item.4 0.394 0.606 NA
#> Item.5 0.157 0.843 NA
#>
# data with no meaningful total score
head(SAT12)
#> Item.1 Item.2 Item.3 Item.4 Item.5 Item.6 Item.7 Item.8 Item.9 Item.10
#> 1 1 4 5 2 3 1 2 1 3 1
#> 2 3 4 2 8 3 3 2 8 3 1
#> 3 1 4 5 4 3 2 2 3 3 2
#> 4 2 4 4 2 3 3 2 4 3 2
#> 5 2 4 5 2 3 2 2 1 1 2
#> 6 1 4 3 1 3 2 2 3 3 1
#> Item.11 Item.12 Item.13 Item.14 Item.15 Item.16 Item.17 Item.18 Item.19
#> 1 2 4 2 1 5 3 4 4 1
#> 2 2 8 2 1 5 2 4 1 1
#> 3 2 1 3 1 5 5 4 1 3
#> 4 2 4 2 1 5 2 4 1 3
#> 5 2 4 2 1 5 4 4 5 1
#> 6 2 3 2 1 5 5 4 4 1
#> Item.20 Item.21 Item.22 Item.23 Item.24 Item.25 Item.26 Item.27 Item.28
#> 1 4 3 3 4 1 3 5 1 3
#> 2 4 3 3 8 1 8 4 1 4
#> 3 4 3 3 1 1 3 4 1 3
#> 4 4 3 1 5 2 5 4 1 3
#> 5 4 3 3 3 1 1 5 1 3
#> 6 4 3 3 4 1 1 4 1 4
#> Item.29 Item.30 Item.31 Item.32
#> 1 1 5 4 5
#> 2 5 8 4 8
#> 3 4 4 4 1
#> 4 4 2 4 2
#> 5 1 2 4 1
#> 6 2 3 4 3
itemstats(SAT12, use_ts=FALSE)
#> $overall
#> N
#> 1 600
#>
#> $itemstats
#> N K mean sd
#> Item.1 600 6 2.497 1.188
#> Item.2 600 6 3.385 1.356
#> Item.3 600 6 3.212 1.534
#> Item.4 600 6 2.762 1.370
#> Item.5 600 6 2.868 0.911
#> Item.6 600 5 2.358 1.135
#> Item.7 600 6 2.422 0.908
#> Item.8 600 6 2.925 1.370
#> Item.9 600 5 2.907 0.567
#> Item.10 600 6 2.320 1.490
#> Item.11 600 5 2.017 0.199
#> Item.12 600 6 3.642 1.184
#> Item.13 600 5 2.317 0.956
#> Item.14 600 6 1.798 1.432
#> Item.15 600 6 4.535 1.087
#> Item.16 600 6 3.368 1.135
#> Item.17 600 5 3.968 0.343
#> Item.18 600 6 3.020 1.514
#> Item.19 600 5 1.900 1.053
#> Item.20 600 6 3.870 0.483
#> Item.21 600 6 2.937 0.554
#> Item.22 600 5 2.985 0.442
#> Item.23 600 6 2.755 1.437
#> Item.24 600 6 1.502 1.037
#> Item.25 600 6 2.740 1.380
#> Item.26 600 6 3.923 1.265
#> Item.27 600 6 1.240 0.766
#> Item.28 600 6 3.262 0.937
#> Item.29 600 6 2.285 1.306
#> Item.30 600 6 3.703 1.553
#> Item.31 600 6 3.788 0.899
#> Item.32 600 6 3.023 1.303
#>
#> $proportions
#> 1 2 3 4 5 8
#> Item.1 0.283 0.203 0.267 0.232 0.013 0.002
#> Item.2 0.212 0.022 0.070 0.568 0.127 0.002
#> Item.3 0.165 0.183 0.260 0.098 0.280 0.013
#> Item.4 0.165 0.378 0.148 0.172 0.128 0.008
#> Item.5 0.093 0.143 0.620 0.093 0.048 0.002
#> Item.6 0.160 0.582 0.107 0.043 0.108 NA
#> Item.7 0.025 0.760 0.007 0.190 0.017 0.002
#> Item.8 0.202 0.205 0.207 0.250 0.133 0.003
#> Item.9 0.065 0.010 0.885 0.033 0.007 NA
#> Item.10 0.422 0.215 0.165 0.028 0.167 0.003
#> Item.11 0.003 0.983 0.008 0.003 0.002 NA
#> Item.12 0.072 0.082 0.218 0.415 0.205 0.008
#> Item.13 0.110 0.662 0.070 0.118 0.040 NA
#> Item.14 0.723 0.027 0.108 0.022 0.117 0.003
#> Item.15 0.035 0.062 0.060 0.025 0.817 0.002
#> Item.16 0.070 0.105 0.413 0.215 0.195 0.002
#> Item.17 0.008 0.005 0.010 0.963 0.013 NA
#> Item.18 0.303 0.033 0.165 0.352 0.142 0.005
#> Item.19 0.548 0.053 0.358 0.030 0.010 NA
#> Item.20 0.012 0.002 0.105 0.873 0.007 0.002
#> Item.21 0.050 0.008 0.915 0.013 0.012 0.002
#> Item.22 0.028 0.005 0.935 0.017 0.015 NA
#> Item.23 0.290 0.177 0.128 0.313 0.087 0.005
#> Item.24 0.728 0.162 0.042 0.022 0.045 0.002
#> Item.25 0.240 0.170 0.375 0.065 0.142 0.008
#> Item.26 0.020 0.227 0.030 0.262 0.460 0.002
#> Item.27 0.862 0.093 0.012 0.020 0.010 0.003
#> Item.28 0.082 0.010 0.530 0.337 0.037 0.005
#> Item.29 0.340 0.295 0.205 0.085 0.067 0.008
#> Item.30 0.150 0.110 0.107 0.183 0.440 0.010
#> Item.31 0.075 0.020 0.012 0.833 0.058 0.002
#> Item.32 0.125 0.183 0.443 0.075 0.162 0.012
#>
# extra total scores tables
dat <- key2binary(SAT12,
key = c(1,4,5,2,3,1,2,1,3,1,2,4,2,1,
5,3,4,4,1,4,3,3,4,1,3,5,1,3,1,5,4,5))
itemstats(dat, ts.tables=TRUE)
#> $overall
#> N mean.total sd.total std.alpha alpha SEM.alpha mean.r sd.r
#> 600 18.202 5.054 0.795 0.798 2.272 0.108 0.075
#>
#> $itemstats
#> N K mean sd cor_if_rm smc alpha_if_rm
#> Item.1 600 2 0.283 0.451 0.300 0.158 0.793
#> Item.2 600 2 0.568 0.496 0.464 0.270 0.785
#> Item.3 600 2 0.280 0.449 0.371 0.184 0.789
#> Item.4 600 2 0.378 0.485 0.235 0.145 0.796
#> Item.5 600 2 0.620 0.486 0.340 0.197 0.791
#> Item.6 600 2 0.160 0.367 0.351 0.185 0.791
#> Item.7 600 2 0.760 0.427 0.289 0.200 0.793
#> Item.8 600 2 0.202 0.402 0.233 0.116 0.795
#> Item.9 600 2 0.885 0.319 0.127 0.095 0.798
#> Item.10 600 2 0.422 0.494 0.383 0.205 0.789
#> Item.11 600 2 0.983 0.128 0.156 0.085 0.797
#> Item.12 600 2 0.415 0.493 0.076 0.054 0.803
#> Item.13 600 2 0.662 0.474 0.358 0.220 0.790
#> Item.14 600 2 0.723 0.448 0.333 0.211 0.791
#> Item.15 600 2 0.817 0.387 0.325 0.201 0.792
#> Item.16 600 2 0.413 0.493 0.278 0.154 0.794
#> Item.17 600 2 0.963 0.188 0.202 0.133 0.796
#> Item.18 600 2 0.352 0.478 0.508 0.290 0.783
#> Item.19 600 2 0.548 0.498 0.314 0.164 0.792
#> Item.20 600 2 0.873 0.333 0.318 0.187 0.792
#> Item.21 600 2 0.915 0.279 0.136 0.088 0.798
#> Item.22 600 2 0.935 0.247 0.238 0.147 0.795
#> Item.23 600 2 0.313 0.464 0.253 0.145 0.795
#> Item.24 600 2 0.728 0.445 0.346 0.198 0.791
#> Item.25 600 2 0.375 0.485 0.297 0.163 0.793
#> Item.26 600 2 0.460 0.499 0.489 0.288 0.783
#> Item.27 600 2 0.862 0.346 0.367 0.209 0.791
#> Item.28 600 2 0.530 0.500 0.383 0.192 0.789
#> Item.29 600 2 0.340 0.474 0.324 0.202 0.791
#> Item.30 600 2 0.440 0.497 0.159 0.092 0.799
#> Item.31 600 2 0.833 0.373 0.419 0.271 0.788
#> Item.32 600 2 0.162 0.368 0.037 0.053 0.802
#>
#> $proportions
#> 0 1
#> Item.1 0.717 0.283
#> Item.2 0.432 0.568
#> Item.3 0.720 0.280
#> Item.4 0.622 0.378
#> Item.5 0.380 0.620
#> Item.6 0.840 0.160
#> Item.7 0.240 0.760
#> Item.8 0.798 0.202
#> Item.9 0.115 0.885
#> Item.10 0.578 0.422
#> Item.11 0.017 0.983
#> Item.12 0.585 0.415
#> Item.13 0.338 0.662
#> Item.14 0.277 0.723
#> Item.15 0.183 0.817
#> Item.16 0.587 0.413
#> Item.17 0.037 0.963
#> Item.18 0.648 0.352
#> Item.19 0.452 0.548
#> Item.20 0.127 0.873
#> Item.21 0.085 0.915
#> Item.22 0.065 0.935
#> Item.23 0.687 0.313
#> Item.24 0.272 0.728
#> Item.25 0.625 0.375
#> Item.26 0.540 0.460
#> Item.27 0.138 0.862
#> Item.28 0.470 0.530
#> Item.29 0.660 0.340
#> Item.30 0.560 0.440
#> Item.31 0.167 0.833
#> Item.32 0.838 0.162
#>
#> $total.score_frequency
#> 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
#> Freq 1 2 2 2 5 7 14 14 17 35 51 45 41 46 50 44 44 20 35 31 18 18 18 19 7 7 3
#> 31 32
#> Freq 1 3
#>
#> $total.score_means
#> 0 1
#> Item.1 16.99535 21.25294
#> Item.2 15.07722 20.57478
#> Item.3 16.79630 21.81548
#> Item.4 16.92225 20.30396
#> Item.5 15.46930 19.87634
#> Item.6 17.28968 22.98958
#> Item.7 14.91667 19.23904
#> Item.8 17.42171 21.28926
#> Item.9 15.55072 18.54614
#> Item.10 16.19597 20.95257
#> Item.11 11.20000 18.32034
#> Item.12 17.46724 19.23695
#> Item.13 15.10837 19.78338
#> Item.14 14.84940 19.48387
#> Item.15 14.01818 19.14082
#> Item.16 16.64773 20.40726
#> Item.17 12.04545 18.43599
#> Item.18 16.05913 22.15166
#> Item.19 15.97048 20.03951
#> Item.20 13.21053 18.92557
#> Item.21 15.05882 18.49362
#> Item.22 12.76923 18.57932
#> Item.23 17.04854 20.72872
#> Item.24 14.71166 19.50343
#> Item.25 16.70400 20.69778
#> Item.26 15.58025 21.27899
#> Item.27 12.84337 19.06190
#> Item.28 15.70567 20.41509
#> Item.29 16.72727 21.06373
#> Item.30 17.06250 19.65152
#> Item.31 12.79000 19.28400
#> Item.32 17.95825 19.46392
#>
#> $total.score_sds
#> 0 1
#> Item.1 4.495009 5.115311
#> Item.2 3.791287 4.583007
#> Item.3 4.322840 5.013323
#> Item.4 4.333771 5.444014
#> Item.5 4.280262 4.756698
#> Item.6 4.448894 5.353788
#> Item.7 4.313744 4.825059
#> Item.8 4.575452 5.661917
#> Item.9 5.007454 4.961288
#> Item.10 4.278821 4.736481
#> Item.11 4.184628 4.985966
#> Item.12 4.861326 5.147431
#> Item.13 4.274965 4.679466
#> Item.14 4.008502 4.822098
#> Item.15 4.212219 4.744448
#> Item.16 4.361290 5.155818
#> Item.17 4.613410 4.923352
#> Item.18 3.955174 4.446051
#> Item.19 4.349442 4.854746
#> Item.20 3.714174 4.809188
#> Item.21 5.092786 4.954396
#> Item.22 3.923355 4.906759
#> Item.23 4.505479 5.276912
#> Item.24 3.896380 4.816172
#> Item.25 4.379749 5.124107
#> Item.26 3.761839 4.627003
#> Item.27 3.775666 4.692898
#> Item.28 4.340725 4.593648
#> Item.29 4.241013 5.281332
#> Item.30 4.817161 4.984363
#> Item.31 3.364386 4.622779
#> Item.32 4.901850 5.638524
#>
# grouping information
group <- gl(2, 300, labels=c('G1', 'G2'))
itemstats(dat, group=group)
#> $G1
#> $G1$overall
#> N mean.total sd.total std.alpha alpha SEM.alpha mean.r sd.r
#> 300 17.987 5.051 0.793 0.796 2.282 0.107 0.09
#>
#> $G1$itemstats
#> N K mean sd cor_if_rm smc alpha_if_rm
#> Item.1 300 2 0.290 0.455 0.331 0.211 0.789
#> Item.2 300 2 0.573 0.495 0.458 0.312 0.783
#> Item.3 300 2 0.290 0.455 0.382 0.240 0.787
#> Item.4 300 2 0.353 0.479 0.255 0.236 0.793
#> Item.5 300 2 0.630 0.484 0.401 0.295 0.786
#> Item.6 300 2 0.130 0.337 0.340 0.224 0.789
#> Item.7 300 2 0.727 0.446 0.303 0.270 0.790
#> Item.8 300 2 0.213 0.410 0.277 0.145 0.791
#> Item.9 300 2 0.897 0.305 0.144 0.174 0.796
#> Item.10 300 2 0.403 0.491 0.349 0.220 0.788
#> Item.11 300 2 0.993 0.082 0.138 0.226 0.796
#> Item.12 300 2 0.413 0.493 0.026 0.115 0.803
#> Item.13 300 2 0.647 0.479 0.359 0.301 0.788
#> Item.14 300 2 0.727 0.446 0.316 0.269 0.790
#> Item.15 300 2 0.793 0.406 0.337 0.244 0.789
#> Item.16 300 2 0.377 0.485 0.249 0.219 0.793
#> Item.17 300 2 0.957 0.204 0.181 0.169 0.795
#> Item.18 300 2 0.360 0.481 0.497 0.306 0.781
#> Item.19 300 2 0.537 0.499 0.347 0.211 0.788
#> Item.20 300 2 0.863 0.344 0.293 0.220 0.791
#> Item.21 300 2 0.910 0.287 0.147 0.162 0.795
#> Item.22 300 2 0.927 0.261 0.211 0.152 0.794
#> Item.23 300 2 0.260 0.439 0.242 0.198 0.793
#> Item.24 300 2 0.707 0.456 0.342 0.260 0.789
#> Item.25 300 2 0.370 0.484 0.321 0.252 0.790
#> Item.26 300 2 0.473 0.500 0.463 0.310 0.783
#> Item.27 300 2 0.857 0.351 0.418 0.304 0.787
#> Item.28 300 2 0.537 0.499 0.350 0.188 0.788
#> Item.29 300 2 0.343 0.476 0.293 0.278 0.791
#> Item.30 300 2 0.440 0.497 0.149 0.138 0.798
#> Item.31 300 2 0.810 0.393 0.457 0.346 0.784
#> Item.32 300 2 0.180 0.385 -0.041 0.095 0.803
#>
#> $G1$proportions
#> 0 1
#> Item.1 0.710 0.290
#> Item.2 0.427 0.573
#> Item.3 0.710 0.290
#> Item.4 0.647 0.353
#> Item.5 0.370 0.630
#> Item.6 0.870 0.130
#> Item.7 0.273 0.727
#> Item.8 0.787 0.213
#> Item.9 0.103 0.897
#> Item.10 0.597 0.403
#> Item.11 0.007 0.993
#> Item.12 0.587 0.413
#> Item.13 0.353 0.647
#> Item.14 0.273 0.727
#> Item.15 0.207 0.793
#> Item.16 0.623 0.377
#> Item.17 0.043 0.957
#> Item.18 0.640 0.360
#> Item.19 0.463 0.537
#> Item.20 0.137 0.863
#> Item.21 0.090 0.910
#> Item.22 0.073 0.927
#> Item.23 0.740 0.260
#> Item.24 0.293 0.707
#> Item.25 0.630 0.370
#> Item.26 0.527 0.473
#> Item.27 0.143 0.857
#> Item.28 0.463 0.537
#> Item.29 0.657 0.343
#> Item.30 0.560 0.440
#> Item.31 0.190 0.810
#> Item.32 0.820 0.180
#>
#>
#> $G2
#> $G2$overall
#> N mean.total sd.total std.alpha alpha SEM.alpha mean.r sd.r
#> 300 18.417 5.056 0.799 0.8 2.262 0.11 0.08
#>
#> $G2$itemstats
#> N K mean sd cor_if_rm smc alpha_if_rm
#> Item.1 300 2 0.277 0.448 0.271 0.227 0.796
#> Item.2 300 2 0.563 0.497 0.472 0.272 0.787
#> Item.3 300 2 0.270 0.445 0.363 0.291 0.792
#> Item.4 300 2 0.403 0.491 0.213 0.161 0.799
#> Item.5 300 2 0.610 0.489 0.283 0.206 0.796
#> Item.6 300 2 0.190 0.393 0.360 0.241 0.792
#> Item.7 300 2 0.793 0.406 0.270 0.211 0.796
#> Item.8 300 2 0.190 0.393 0.190 0.163 0.799
#> Item.9 300 2 0.873 0.333 0.116 0.142 0.801
#> Item.10 300 2 0.440 0.497 0.415 0.270 0.789
#> Item.11 300 2 0.973 0.161 0.184 0.121 0.799
#> Item.12 300 2 0.417 0.494 0.127 0.091 0.803
#> Item.13 300 2 0.677 0.469 0.354 0.227 0.792
#> Item.14 300 2 0.720 0.450 0.351 0.237 0.792
#> Item.15 300 2 0.840 0.367 0.310 0.208 0.794
#> Item.16 300 2 0.450 0.498 0.303 0.180 0.795
#> Item.17 300 2 0.970 0.171 0.226 0.163 0.798
#> Item.18 300 2 0.343 0.476 0.522 0.327 0.784
#> Item.19 300 2 0.560 0.497 0.279 0.196 0.796
#> Item.20 300 2 0.883 0.322 0.343 0.224 0.794
#> Item.21 300 2 0.920 0.272 0.123 0.107 0.800
#> Item.22 300 2 0.943 0.232 0.266 0.231 0.797
#> Item.23 300 2 0.367 0.483 0.260 0.176 0.797
#> Item.24 300 2 0.750 0.434 0.347 0.244 0.793
#> Item.25 300 2 0.380 0.486 0.272 0.202 0.796
#> Item.26 300 2 0.447 0.498 0.520 0.327 0.784
#> Item.27 300 2 0.867 0.341 0.314 0.201 0.794
#> Item.28 300 2 0.523 0.500 0.418 0.270 0.789
#> Item.29 300 2 0.337 0.473 0.357 0.211 0.792
#> Item.30 300 2 0.440 0.497 0.170 0.143 0.801
#> Item.31 300 2 0.857 0.351 0.376 0.267 0.792
#> Item.32 300 2 0.143 0.351 0.128 0.090 0.800
#>
#> $G2$proportions
#> 0 1
#> Item.1 0.723 0.277
#> Item.2 0.437 0.563
#> Item.3 0.730 0.270
#> Item.4 0.597 0.403
#> Item.5 0.390 0.610
#> Item.6 0.810 0.190
#> Item.7 0.207 0.793
#> Item.8 0.810 0.190
#> Item.9 0.127 0.873
#> Item.10 0.560 0.440
#> Item.11 0.027 0.973
#> Item.12 0.583 0.417
#> Item.13 0.323 0.677
#> Item.14 0.280 0.720
#> Item.15 0.160 0.840
#> Item.16 0.550 0.450
#> Item.17 0.030 0.970
#> Item.18 0.657 0.343
#> Item.19 0.440 0.560
#> Item.20 0.117 0.883
#> Item.21 0.080 0.920
#> Item.22 0.057 0.943
#> Item.23 0.633 0.367
#> Item.24 0.250 0.750
#> Item.25 0.620 0.380
#> Item.26 0.553 0.447
#> Item.27 0.133 0.867
#> Item.28 0.477 0.523
#> Item.29 0.663 0.337
#> Item.30 0.560 0.440
#> Item.31 0.143 0.857
#> Item.32 0.857 0.143
#>
#>
#####
# polytomous data example
itemstats(Science)
#> $overall
#> N mean.total sd.total std.alpha alpha SEM.alpha mean.r sd.r
#> 392 11.668 2.003 0.603 0.598 1.27 0.275 0.098
#>
#> $itemstats
#> N K mean sd cor_if_rm smc alpha_if_rm
#> Comfort 392 4 3.120 0.588 0.352 0.148 0.552
#> Work 392 4 2.722 0.807 0.332 0.164 0.567
#> Future 392 4 2.990 0.757 0.488 0.248 0.437
#> Benefit 392 4 2.837 0.802 0.363 0.165 0.541
#>
#> $proportions
#> 1 2 3 4
#> Comfort 0.013 0.082 0.679 0.227
#> Work 0.084 0.250 0.526 0.140
#> Future 0.036 0.184 0.536 0.245
#> Benefit 0.054 0.255 0.492 0.199
#>
# polytomous data with missing
newScience <- Science
newScience[1:5,1] <- NA
itemstats(newScience)
#> $overall
#> N.complete N mean.total sd.total std.alpha alpha SEM.alpha mean.r sd.r
#> 387 392 11.672 2.011 0.609 0.605 1.264 0.276 0.1
#>
#> $itemstats
#> N K mean sd cor_if_rm smc alpha_if_rm
#> Comfort 387 4 3.119 0.590 0.352 0.151 0.552
#> Work 392 4 2.722 0.807 0.311 0.161 0.576
#> Future 392 4 2.990 0.757 0.481 0.248 0.449
#> Benefit 392 4 2.837 0.802 0.370 0.176 0.538
#>
#> $proportions
#> 1 2 3 4 <NA>
#> Comfort 0.013 0.082 0.668 0.224 0.013
#> Work 0.084 0.250 0.526 0.140 NA
#> Future 0.036 0.184 0.536 0.245 NA
#> Benefit 0.054 0.255 0.492 0.199 NA
#>
# unequal categories
newScience[,1] <- ifelse(Science[,1] == 1, NA, Science[,1])
itemstats(newScience)
#> $overall
#> N.complete N mean.total sd.total std.alpha alpha SEM.alpha mean.r sd.r
#> 387 392 11.731 1.917 0.577 0.572 1.254 0.26 0.092
#>
#> $itemstats
#> N K mean sd cor_if_rm smc alpha_if_rm
#> Comfort 387 3 3.147 0.540 0.314 0.110 0.552
#> Work 392 4 2.722 0.807 0.325 0.162 0.517
#> Future 392 4 2.990 0.757 0.490 0.223 0.409
#> Benefit 392 4 2.837 0.802 0.370 0.133 0.525
#>
#> $proportions
#> 1 2 3 4 <NA>
#> Comfort NA 0.082 0.679 0.227 0.013
#> Work 0.084 0.250 0.526 0.140 NA
#> Future 0.036 0.184 0.536 0.245 NA
#> Benefit 0.054 0.255 0.492 0.199 NA
#>
merged <- data.frame(LSAT7full[1:392,], Science)
itemstats(merged)
#> $overall
#> N.complete N mean.total sd.total std.alpha alpha SEM.alpha mean.r sd.r
#> 387 392 14.331 2.231 0.245 0.379 1.759 0.037 0.167
#>
#> $itemstats
#> N K mean sd cor_if_rm smc alpha_if_rm
#> Item.1 387 2 0.568 0.496 -0.030 0.419 0.417
#> Item.2 392 2 0.232 0.423 -0.146 0.425 0.443
#> Item.3 392 2 0.605 0.490 0.014 0.044 0.405
#> Item.4 392 2 0.467 0.500 0.051 0.037 0.392
#> Item.5 392 2 0.760 0.428 0.011 0.032 0.402
#> Comfort 392 4 3.120 0.588 0.288 0.163 0.286
#> Work 392 4 2.722 0.807 0.299 0.168 0.251
#> Future 392 4 2.990 0.757 0.418 0.260 0.185
#> Benefit 392 4 2.837 0.802 0.291 0.190 0.261
#>
#> $proportions
#> 0 1 2 3 4 <NA>
#> Item.1 0.426 0.561 NA NA NA 0.013
#> Item.2 0.768 0.232 NA NA NA NA
#> Item.3 0.395 0.605 NA NA NA NA
#> Item.4 0.533 0.467 NA NA NA NA
#> Item.5 0.240 0.760 NA NA NA NA
#> Comfort NA 0.013 0.082 0.679 0.227 NA
#> Work NA 0.084 0.250 0.526 0.140 NA
#> Future NA 0.036 0.184 0.536 0.245 NA
#> Benefit NA 0.054 0.255 0.492 0.199 NA
#>