Ratna Komala Dewi

Nuke Sari Nastiti

Item analysis is a method that is used in education to evaluate test item. This can ensure that questions are in appropriate standard and measure the effectiveness of individual test item. Item analysis is purposed to improve test items and identify unfair or biased item. Item analysis is conducted to avoid the chance of tests that are too difficult (and have an insufficient floor) tend to lead to frustration and lead to deflated scores, and tests that are too easy (and have an insufficient ceiling) facilitate a decline in motivation and lead to inflated scores.

Item analysis can be analyzed by computing: Difficulty Index, Discrimination Index, Validity Coefficient, and Effectiveness of Distraction.

A. Difficulty Index

According to Wilson (2005),  item difficulty is the most essential component of item analysis.  Item difficulty is determined by the number of people who answer a particular test item correctly.  It is important for a test to contain items of various difficulty levels in order to distinguish between students who are not prepared at all, students who are fairly prepared, and students who are well prepared.

To compute level of difficulty we use the formula:

Difficulty Index (p) = C/T

p = Difficulty Index

C = the number of students who answer item X correctly

T = the number of total students who answer item X

For example:

There are 50 students who answer an item X, 30 of whom can answer the item correctly. So that, the level of difficulty is:

Level of difficulty (p) = 30 / 50

= 0.6

  • The highest score for p is 1.0 and the lowest score is 0
  • p always has positive value
  • The higher score for p the easier item
  • The lower score for p the harder item

According to Allen & Yen (1986) to avoid a test is too difficult or too easy,  each items in a test should have a difficulty range from 0.3 to 0.7. It is used to differentiate between individuals’ level of knowledge, ability, and preparedness.


B. Discrimination Index

Discrimination goes beyond determining the proportion of people who answer correctly and looks more specifically at who answers correctly. In other words, item discrimination determines whether those who did well on the entire test did well on a particular item. An item should in fact be able to discriminate between upper and lower scoring groups.

To compute discrimination index, the first thing we have to do is dividing test-takers into two groups, upper group and lower group. Then using this formula:

Discrimination index (D) = Pu – Pl

D = Discrimination index

Pu = Level difficulty of item X from the upper group

Pl = Level difficulty of item X from lower group

For Example:

30 students are divided into two group, 15 students in the lower group and 15 others in the upper group.  In the upper group, there are 12 students who answer item X correctly whereas in the lower group only 6 students who answer item X correctly. Discrimination index is:


Pu = 12/15 = 0.8;

Pl = 6/15 = 0.4;

D = Pu – Pl

D = 0.8 – 0.4

D = 0.4

C. Coefficient Validity

Coefficient validity can be computed by using correlation. There are two technique of corellation which is popular to be used. They are Point-biserial technique and Biserial technique.

D. The Effectiveness of Distraction

Multiple choice tests have one question and several options of answer. Among the options, there is only one answer which is correct, and the other options are wrong answers. Those wrong answers in multiple choice tests are called distraction. A distraction is called effective when there are a lot of students choosing it.  According to Fernandez (1984) a distraction can be called as a good distraction when there are 2% of test takers choosing it.


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