Is Aberrant Response Behavior a Stable Characteristic of Students in Classroom Math Tests?

Various psychological and demographic characteristics of individuals have been reported to have an association with aberrant response behavior. If indeed they have (or at least some of them do) then one would expect, as suggested by Smith (1986) and Lamprianou (2005), that an individual with an aberrant response pattern may exhibit such behavior in other testing situations too. The research reported here aimed to see if aberrant response behavior is a stable characteristic of high-school students in classroom math tests as expected. That is, whether essentially the same students will misfit in administrations of two different classroom math tests.

In the classroom setting math tests are more relevant, low-stakes, administered by the students' own comfortable-to-be-with teacher and one would perhaps expect less aberrance. This is a completely different context from the high-stakes tests administered in a much stricter and possibly a more stressful environment. At the same time, one would expect some type of aberrance to occur due to carelessness, sleepy behavior, copying, cheating, plodding or guessing.

Table 1. Chi-square tests for association between misfit in Test 1 and misfit in Test 2
Cut-off 
Test 1
Test 2Chi-squarep-value
FittingMisfitting
1.3Fitting 196
(68.1%)
92
(31.9%)
0.514
(0.371)
0.474
(0.542)
Misfitting 112
(71.3%)
45
(28.7%)
1.4Fitting 233
(72.6%)
88
(27.4%)
0.000
(0.000)
0.999
(1.000)
Misfitting 90
(72.6%)
34
(27.4%)
1.5Fitting 261
(76.8%)
79
(23.2%)
0.104
(0.036)
0.747
(0.849)
Misfitting 79
(75.2%)
26
(24.8%)
1.6Fitting 276
(78.0%)
78
(22.0%)
0.000
(0.000)
0.991
(1.000)
Misfitting 71
(78.0%)
20
(22.0%)
1.8Fitting 323
(82.8%)
67
(17.2%)
0.034
(0.000)
0.854
(1.000)
Misfitting 45
(81.8%)
10
(18.2%)
2.0Fitting 345
(86.0%)
56
(14.0%)
0.573
(0.281)
0.449
(0.596)
Misfitting 36
(81.8%)
8
(18.2%)

For the purposes of the study two classroom math tests were used with a sample of 15-16 year old high school students in three different schools in Cyprus. The first test was administered to 635 students and the second to 445 of them. The Rasch Partial Credit Model (PCM) was used for the analyses of the data collected. Misfitting students in both tests were identified with the use of the infit and outfit mean square statistics for six different cut-off values (1.3, 1.4, 1.5, 1.6, 1.8 and 2.0). The hypothesis of no association between misfit in the one test and misfit in the other was investigated with Chi square tests and it was very clearly accepted with p-values much closer to 1.00 than to 0.05. Table 1 shows the observed frequencies and row percentages in brackets for each cut-off value. The last two columns show the chi-square statistics and p-values without the continuity correction and with it in brackets.

The findings of this study do not support Smith's and Lamprianou's suggestion that aberrance is a stable characteristic of individuals. It is concluded that misfit in the one test is not associated with misfit in the other among high school students taking classroom math tests.

A couple of cautions should be made about this study. First, the test items used were mainly multistep mathematical problems with partial credit awarding for partial success instead of the usual dichotomous items found in the majority of studies on student aberrance. Perhaps it is easier to respond unexpectedly in dichotomous items, especially for high ability students, as reported by Petridou and Williams (2007). Where the answer is marked either right or wrong if a high ability student follows the correct method (as expected) but gives the wrong answer (because of a careless mistake such as a miscalculation, or a miscopy of the right answer) he or she scores 0 and that signals his or her response as unexpected and probably the whole response string as aberrant (especially if the test is short). This is much less likely to happen with multistep problems. If such a mistake occurs, on the last stages of the solution process, the student will get most of the marks on that item and the answer will not be considered unexpected. Second the low stakes status of the tests linked to the administration procedure, with the familiar classroom setting may make the test takers feel more relaxed and perform more as expected than in a stricter and less familiar environment.

The finding of this study, explored further in Panayides' (2009), lead to the following intuitive conclusion: In classroom math tests, although misfits do occur, they do not predict misfits in other tests and are not dependent on psychological or demographic characteristics of the test-takers.

Panayiotis Panayides - Lyceum of Polemidia (Cyprus)
Peter Tymms - Durham University (UK)

References

Lamprianou, I. (2005). Aberrant response patterns: Issues of internal consistency and concurrent validity. Paper presented at the annual meeting of the American Educational Research Association, April 11-15, in Montreal, Canada.

Panayides, P. (2009). Exploring the reasons for aberrant response patterns in classroom math tests. PhD thesis. Durham University, UK.

Smith, R. M. (1986). Person Fit in the Rasch model. Educational and Psychological Measurement 46, 359-372.

Petridou, A. and J. Williams. (2007). Accounting for Aberrant test Response Patterns using multilevel models. Journal of Educational Measurement 44(3), 227-247.

*Note* Full article available at: Panayiotis, P., & Tymms, P. (2012). Investigating whether aberrant response behavior in classroom math tests is a stable characteristic of students. Assessment in Education, Principles, Policy & Practice, DOI:10.1080/0969594X.2012.723610


Is Aberrant Response Behavior a Stable Characteristic of Students in Classroom Math Tests? Panayiotis Panayides & Peter Tymms … Rasch Measurement Transactions, 2012, 26:3 p. 1382-3


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