Using the data set for 20 students on a 10-item test, calculate item difficulty and index of discrimination for each item. Use the top five students to make up the upper group; and the bottom five for the lower group. Present your results in the table provided below (include the computations). Item # Item Difficulty Item Discrimination Index
1
2
3
4
5
6
7
8
9
10

b. From your analysis of the test results (i) which items should be retained (ii) which items should be excluded from the test?

Test scores for 20 students on a 10-item test

Student Item 1 Item 2 Item 3 Item 4 Item 5 Item 6 Item 7 Item 8 Item 9 Item 10 Total score
1 1 0 1 1 1 1 1 1 1 1 9
2 1 0 1 0 1 1 1 1 0 0 6
3 1 0 1 1 0 1 0 1 1 0 6
4 0 1 1 1 0 1 1 1 1 1 8
5 0 0 1 1 0 1 1 1 1 0 6
6 0 0 0 1 1 1 0 1 1 1 6
7 0 1 0 0 0 1 0 0 0 0 2
8 1 0 0 1 0 1 0 0 0 0 3
9 1 1 1 1 1 1 1 1 1 1 10
10 0 0 1 1 0 1 1 1 1 1 7
11 0 0 1 1 0 1 1 1 0 0 5
12 0 0 1 1 1 1 0 1 1 0 6
13 0 0 1 1 1 1 1 1 1 1 8
14 0 0 0 1 0 1 0 0 0 0 2
15 0 0 0 1 1 1 0 1 1 1 6
16 1 0 0 1 0 1 0 0 1 0 4
17 1 0 0 0 0 1 0 1 0 0 3
18 0 0 1 0 1 1 1 1 1 0 6
19 0 0 1 1 1 1 1 1 0 0 6
20 1 0 1 1 1 1 0 1 1 1 8
Total 8 3 13 16 10 20 10 16 13 8

The range of the index of discrimination is from -1 to +1. The desirable pattern for the discrimination index is negative for incorrect answers and positive for the correct answers. The generally accepted standards are:

● .40 & up Very good (top students choose and bottom students avoid)
● .30 - .39 Reasonably good, possibly subject to improvement.
● .20 - .29 Marginal items, need revision.
● Below .19 Poor items, reject or revise (top students avoid and bottom students choose).