Calculating Discrimination Index

Calculating the Discrimination Index (DI) may seem complicated but actually, it's fairly straightforward. It only seems complex because it involves numbers in tables and because there are a several steps invovled. But if you keep your cool and follow them one by one, you'll have a DI in no time and be able to judge which sentences are the best ones for determining second langauge proficiency.

Prepartion for Calculating the DI

Figure 1: In preparation for calculating the DI, subjects and sentences are arranged to the initial SRT scores.

The first step involves using the test scores from your 50 or so participants that you pilot tested the 40-50 sentences with.

1. Order the participants by their scores ⇒ In Figure 1, the scores of 15 participants (labelled A to O along the top) are shown on the scale at the bottom. Note that no one scored the maximum 21 points for the 7 sentences shown in this example so the scale only needs to go up to the highest score of 20. You can see that for 50 participants doing 50 sentences, this table would be much, much larger. But in a spreadsheet program, even such a large table is very manageable.

The participants are arranged in the table according to their total score. In this example, A and E scored 1 and so are on the far left hand side. L, on the other hand, scored 20 and is on the right.

1. Order the sentences by points scored ⇒ The next step is to arrange the sentences from top to bottom according to the score that all the participants achieved for each sentence. In this example, sentence 2 was the hardest. If 3 represents a perfect repetition of the sentence, then theoretically with 15 participants all repeating it perfectly, each sentence could score 45 points. But the participants only achived 14 out of a possible 45 points for this sentence making it harder than all the others. Sentence 6, by contrast, was the easiest with participants scoring 32 out of the possible 45 points.

1. Fill in each participant's individual sentence scores ⇒ Finally, you fill in the centre of the table by writing what each participant scored for each sentence. In Figure 1, participant J scored 2 for sentence 6, 1 for sentences 3, 7, 4, 5 and 2 and a 0 for sentence 1.

Once these three steps have been carried out, preparation is complete and you can go on to actually calculate the DI.

Calculating the DI

The rows containing what each participant actually scored are labelled "actual" in the image on the right (which you can click to enlarge).

Figure 2: To calculate the DI, sentence scores are rearranged and subtracted from actual scores.