Page 148 - DEDU504_EDUCATIONAL_MEASUREMENT_AND_EVALUATION_ENGLISH

Educational Measurement and Evaluation

Notes Item No. 27% Top Right Responses 27% Bottom Right Responses

1. 74 50
2. 62 38
3. 42 10

Now, validity index and difficulty index of each item has to be calculated.
We shall use the table for validity index. For item 1, when we move our finger along 27%
column below 74 and 27% row along 50, we come to the point where both these cross each other.
The number written there is 26, that is the validity index of the item. Therefore, the reliability of
this item is .26. All numbers is the intervening numbers in the table have point (fraction). In the
same way, the validity index for item 2 and 3 is .25 and .41.
In order to calculate difficulty index, these two percentages are added and average is calculated.
74 + 50 124
Therefore, the difficulty index of items 1 = = = .62
2 2
In the same way, the difficulty index for items 2 and 3 is .50 and .26.
Thus, we make a table, like the one given below, for all 300 items of the test :

Item No. 27% Top Right 27% Bottom Validity Index. Difficulty Index
Responses Right Responses
1. 74 50 .26 .62
2. 62 38 .25 .50
3. 42 10 .41 .16
. . . . .

. . . . .
300 . . . .

The items with .20 or more validity index are considered satisfactory. The items with validity
index less than this are deleted. If a very good test is needed, then only those items are selected
which have a validity index over .50.

10.9 Relationship Between Difficulty Index and Discrimination Index

Theoretically, the more difficult a question (or item) or easier the question (or item), the lower
will be the discrimination index. Stanley and Hopkins (1972) provide a theoretical model to
explain the relationship between the difficulty index and discrimination index of a particular
question or item. According to the model, a difficulty index of 0.2 can result in a discrimination
index of about 0.3 for a particular item (which may be described as an item of ‘moderate
discrimination’). Note that, as the difficulty index increase from 0.1 to 0.5, the discrimination
index increases even more. When the difficulty index reaches 0.5 (described as an item of ‘moderate
difficulty’), the discrimination index is positive 1.00 (very high discrimination). Interestingly, a
difficulty index of > 0.5 leads to the discrimination index decreasing.

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