# Item analysis tables in conquestr

#### Nathan Zoanetti, Dan Cloney

#### 2025-05-18

# Introduction

This vignette demonstrates how to use conquestr to integrate ‘ACER ConQuest’ item analysis output into a markdown-based analysis and reporting workflow. In the examples provided we also illustrate how conquestr can support the analyst to visualise and communicate ‘ACER ConQuest’ test and item analysis in a user-friendly way through various functions for producing conditioanlly formatted tables of statistics that are germane to psychometric analysis.

The basic approach involves using conquestr to read in and process the `itanal` objects stored in an ‘ACER ConQuest’ system file. This workflow can be used when an ‘ACER ConQuest’ analysis is performed outside of the R environment to produce a system file. It is also easy to extend this workflow to perform end-to-end analysis and reporting by calling ‘ACER ConQuest’ from with conquestr to produce the relevant system file (see the function `ConQuestCall`).

To keep this illustration relatively simple, a short test consisting of 12 multiple-choice items is analysed with a unidimensional Rasch model using Marginal Maximum Likelihood estimation.

# Get itanal from a system file

conquestr has a built in system file that we will use for this example.

The function `getCqItanal` will return a list of list of lists, each list relating to one generalised item from an ‘ACER ConQuest’ `itanal` output. The list for each item contains the following information:

1. the item name according to the item label,
2. a table of item category statistics for the item, and
3. the item-total and item-rest correlations for the item.

Note that you must use `matrixout` in your ‘ACER ConQuest’ call to `itanal` to ensure that these objects are available in the system file from your analysis.

    # get default sys file
    myEx1Sys <- ConQuestSys()
    #> no system file provided, loading the example system file instead
    #> System file is compressed. Decompressing ...
    #> complete

    # get itanal lists
    myEx1Sys_itanal <- getCqItanal(myEx1Sys)

    # show unformatted list objects for first item
    print(myEx1Sys_itanal[[1]][[1]])
    #> $name
    #> [1] "item:1 (item one) group:All Cases"
    #>
    #> $table
    #>   Category Score Count    Percent      Pt Bis Pt Bis t stat.  Pt Bis sig.
    #> 1        M     0     6  0.6006006 -0.10716121      -3.403245 6.923947e-04
    #> 2        a     1   644 64.4644645  0.45520912      16.142876 2.961496e-52
    #> 3        b     0    23  2.3023023 -0.08463114      -2.681876 7.442067e-03
    #> 4        c     0    47  4.7047047 -0.19873699      -6.402901 2.344019e-10
    #> 5        d     0   104 10.4104104 -0.23879800      -7.764760 2.023005e-14
    #> 6        e     0   175 17.5175175 -0.21543829      -6.966112 5.910417e-12
    #>   Ability mean (D1) Ability SD (D1)
    #> 1        -0.9823725       1.0094503
    #> 2         0.3334871       0.8216688
    #> 3        -0.5375707       0.9964098
    #> 4        -0.7459999       0.7851521
    #> 5        -0.6836101       0.6972879
    #> 6        -0.4694728       0.7085121
    #>
    #> $item_rest_total
    #> item-total  item-rest   obs_mean   exp_mean   adj_mean  delta_dot
    #>  0.6059588  0.4552091  0.6446446  0.6468243  0.6467947 -0.7040703

Following the item-specific list objects, the last element of the list returned by `getCqItanal` contains summary statistics for the full set of items. The summary statistics include raw and latent score distribution statistics and Cronbach’s coefficient \(\alpha\).

# Create formatted itanal tables for a report

So far, we have shown how to access the test and item analysis statistics that are available through the itanal command in ‘ACER ConQuest’ and we have shown these without any formatting. One of the many benefits of integrating ‘ACER ConQuest’ output into a markdown document is to permit automated conditional formatting of item analysis output. In this section we show how this conditional formatting can be set up.

## Set up criteria for conditional formatting

Pre-specifying criteria for conditionally formatting item analysis output is a key step in an automated workflow. Any number of metrics from the item analysis can be specified for conditional formatting. Several of these can be passed to conquestr functions as will be illustrated in the following sections.

    # set statistical criteria for conditional formatting

    easyFlag <- 85 # highlight if facility is GREATER than this value
    hardFlag <- 15 # highlight if facility is LESS than this value
    irestFlag <- 0.2 # highlight if item-rest r is LESS than this value
    underfitFlag <- 1.2 # highlight if weighted MNSQ is GREATER than this value
    overfitFlag <- 0.8 # highlight if weighted MNSQ is LESS than this value
    ptBisFlag <- 0.0 # highlight if non-key ptBis r is MORE than this value

## An example of an html itanal table for item categories

The function `fmtCqItanal` will return a formated version of the itanal object that we read in earlier. Presently this function will apply coloured text to any distractor point biserial correlation that is larger than 0. The following example shows the output for the fourth item in the current item analysis.

    # return a conditionally formatted item category statistics table for the fourth item
    myEx1Sys_itanal_f <- fmtCqItanal(myEx1Sys_itanal, ptBisFlag = ptBisFlag, textColHighlight = "red")

    # print table
    myEx1Sys_itanal_f[[1]][[4]]$table

Item category statistics for: item:4 (item four) group:All Cases
Category | Score | Count | Percent | Pt Bis | Pt Bis t stat. | Pt Bis sig. | Ability mean (D1) | Ability SD (D1)
--- | --- | --- | --- | --- | --- | --- | --- | ---
M | 0 | 3 | 0.30 | <span style=” color: black !important;” >-0.07</span> | -2.29 | 0.02 | -1.09 | 1.42
a | 0 | 151 | 15.12 | <span style=” color: red !important;” >0.06</span> | 1.77 | 0.08 | -0.07 | 0.76
b | 0 | 73 | 7.31 | <span style=” color: black !important;” >-0.2</span> | -6.39 | 0.00 | -0.64 | 0.76
c | 0 | 224 | 22.42 | <span style=” color: black !important;” >-0.32</span> | -10.59 | 0.00 | -0.51 | 0.79
d | 1 | 548 | 54.85 | <span style=” color: black !important;” >0.34</span> | 11.33 | 0.00 | 0.33 | 0.85

    # print summary
    myEx1Sys_itanal_f[[1]][[length(myEx1Sys_itanal_f[[1]])]] # the last object is always the summary

Item Analysis Summary Statistics
Statistic | Value
--- | ---
Percent Missing | 0.00
N | 999.00
Mean | 8.44
SD | 2.40
Variance | 5.78
Skew | -0.60
Kurtosis | -0.20
Standard error of mean | 0.08
Standard error of measurement | 1.43
Alpha | 0.64

# Conclusion

This short vignette has illustrated how to access and display itanal output from an ‘ACER ConQuest’ analysis using conquestr. Future vignettes will demonstrate basic and advanced plotting and the production of publication quality item analysis technical reports.