Objective 1B: To investigate the reliability of different test items (Bachman, 2004, pp. 129–131; Fulcher & Davidson, 2007, pp. 87–88, pp. 103–104).


Item difficulty statistics


Statistics such as the Item difficulty index, Item discrimination index and Item- total test score correlations can be used to:


• give feedback to test takers, teachers and test developers. • help identify problems with items which can help with control characteristics of score distribution.


• identify weaknesses for correction, to increase the internal consistency and reliability of a test.


• ascertain why items are not operating satisfactorily.


As an example, in order to calculate how difficult a particular set of EAP test questions is, the difficulty index can be determined. In the case of multiple- choice questions, this procedure requires EAP assessors to work out the number of test takers who provided the correct response. It is also possible to identify faulty items by looking at the number of instances of selection of the range of alternatives provided. The data below show the responses to an EAP cloze vocabulary activity with five options (A, B, C, D and E), where 42 took the test.


Item 1 2


A 5 11 * correct answer


In the case of the first item, it is clear that option B did not function well as a distractor, as no test takers chose this option. The difficulty index is calculated by dividing the number of test takers who chose the correct answer – in this case, option C, with 29 responses – by the total number of people who took the test, 42. Using this approach, the difficulty of Item 1 is 29/42, which equals 69. In general, if the difficulty is calculated as 75 or more, then it can be considered to be an easy item, and if a value of 25 or less is returned, it may be considered hard. In this situation, whilst 69 is not yet in the easy band, it is quite close, so it may be suitable to consider modifying the distractors used in A, B, D and E, so that the question challenges a wider spread of test takers. On the other hand, for Item 2, correct responses to B total 20, which results in a difficulty of 47. This item could be considered to be more difficult.


0 20* B


29* 5


C


3 4


D


5 2


E


Chapter 10: Inferential statistics and applications in EAP assessment


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