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Item Analysis

Item analysis yields information about the relationships between questions or items on a test or questionnaire and the total score on a survey or a test battery. Typically, three indices are obtained, item difficulty and item discrimination, and internal consistency reliability.

 

Item difficulty

Item difficulty is nothing else but an arithmetic mean of an item. Paradoxically, it this index is high, the item on a test is easy. If the item difficulty is low, the item is difficult. For this reasons some psychometricians tried to change the name of this index to the neutral item popularity, but this never quite caught on.

 

(1)

 

 

 

Item discrimination

Item discrimination, for the binary items of a true-false, agree-disagree questionnaires is the point-biserial correlation of an item with the total test score. If this correlation is high, it means that the item is internally consistent with the total score on the test. Subjects who answered this item correctly are also getting a high score on the test. If the item discrimination is negative, it means that subjects who failed this item are getting high scores on the test, i.e., that something is wrong with the item. In this case sometimes the scoring key is wrong, or the item itself is wrong and should be deleted.

 

 

(2)

 

 

In the above table, item 4 shows a negative correlation with the total test score X and can be deleted.

 

Internal consistency reliability

 

(3)

 

 

 

(4)

 

For data in Table 3, the internal consistency reliability  equals (5 / 4) (1.44 - .64) / 1.44 which is .694.