Multiple-choice tests are straightforward to answer, straightforward to optically scan, and deceptively straightforward to analyze. As an analyst, it is easy to delude oneself that all is well, when, in fact, things have gone awry.
A frequent source of self-deception is the answer key or code book. All multiple-choice answer keys tend to look the same, just a string of letters or numbers: "ACDEBCDA". A garbled or misaligned key looks just as valid as a correct key. Even a key from a different test appears as good as the genuine key. It's extremely easy to perform an entire analysis and report the results without noticing there's been a major flaw in the process.
How can we avoid this kind of embarrassing misadventure? What must we watch for? Let's compare some results using correct and incorrect keys. The figures show the variable maps for two analyses of the same data. The first analysis uses the correct key. In the second analysis, every other item has the wrong key. What has happened?
MEASURE PERSONS ITEMS 4.0 . + 3.0 .#### + P Q 2.0 .########### + R 1.0 .############ + S T .0 .######################## + U -1.0 .########### + V W -2.0 .########## + X -3.0 .#### + Y Z -4.0 ## +
Analysis with correct key. Person and items spread out. Persons and items aligned.
MEASURE PERSONS + ITEMS 4.0 + 3.0 + Y 2.0 + 1.0 .## + P Q R U W .0 .##### + S T -1.0 .########################### + -2.0 + V -3.0 .###### + X -4.0 .## + Z
Analysis with incorrect key. Persons and items bunched up. Persons below items.
Impact on Items:
The intended item order was "P" to "Z". With the correct key, the
items are ordered in that intended descending order of difficulty.
With an incorrect key, the construct validity of the items collapses.
The incorrect key still has half the items keyed correctly. Even so
the item hierarchy is lost in a confusing jumble. Of course, to
detect this problem, the analyst must be familiar enough with the
items on the test to predict their order of difficulty. Statistics
alone can not reveal item-content disorder. Statistics, however, do
give warning signs: observe how the items in the figure bunch up.
Impact on Persons:
With a wrong key, getting an item correct becomes random. This causes
examinees to bunch up in ability. In addition, their performance is
somewhat below the mean apparent item difficulty because examinee
responses are unlikely to match the incorrect key even 50% of the
time.
The moral: Without construct validity, you have nothing. Don't leave home without it!
Miskey cues. Garcia HI. … Rasch Measurement Transactions, 1992, 5:4 p.185
| Rasch Publications | ||
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| Rasch Measurement Transactions (free, online) | Rasch Measurement research papers (free, online) | Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch |
| Applying the Rasch Model 2nd. Ed., Bond & Fox | Best Test Design, Wright & Stone | Rating Scale Analysis, Wright & Masters |
| Introduction to Rasch Measurement, E. Smith & R. Smith | Introduction to Many-Facet Rasch Measurement, Thomas Eckes | Invariant Measurement: Using Rasch Models in the Social, Behavioral, and Health Sciences, George Engelhard, Jr. |
| Statistical Analyses for Language Testers, Rita Green | Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar | Journal of Applied Measurement |
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