Abstract
For every IRT model, a mathematical function is used to specify the probability of item responses as a function of the ability (latent trait). The degree to which the observed data fit the mathematical function needs to be examined since valid results can only be drawn if the data fit the model.
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Appendices
Hands on Practise
-
(1)
The following table shows the percentages correct of PISA 2009 mathematics items for Shanghai and Australia (Table 11.4).
Table 11.4 Percentages correct for Shanghai and Australia PISA Mathematics items
The following shows a plot of these percentages correct.
Given the information provided in the table and the graph, discuss the relative performances of Shanghai and Australian students, and give your impressions of the presence/absence of DIF.
Discussion Points
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(1)
Why is it that the existence of DIF items would violate the assumptions of the IRT model applied to the test?
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(2)
Do you agree that the ability estimates will not change a great deal when DIF items are retained? Why or why not?
Exercises
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Q1.
Indicate whether you agree or disagree with each of the following statements
A statistical DIF analysis did not detect any DIF item in a test. We can be assured then the test is a fair test for the groups of respondents for which the DIF analysis was performed | Agree/disagree |
To determine if a test is a fair test, count the number of DIF items in a test using a statistical DIF detection procedure. If there are considerably more items favouring one group than the other group, then the test is biased | Agree/disagree |
A test is biased if the average performance of one group of respondents is considerably higher than for other groups | Agree/disagree |
When sample size increases, the magnitudes of DIF (difference in item difficulties for two groups of respondents) will tend to increase | Agree/disagree |
When sample size increases, more items will tend to show statistically significant DIF estimates | Agree/disagree |
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Wu, M., Tam, H.P., Jen, TH. (2016). Differential Item Function. In: Educational Measurement for Applied Researchers. Springer, Singapore. https://doi.org/10.1007/978-981-10-3302-5_11
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DOI: https://doi.org/10.1007/978-981-10-3302-5_11
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