**12. Discrimination index (Power)**

Item discrimination (DI) is the ability of an item to discriminate between higher achiever (good) students and low ones. It was defined as "stated that item discrimination is a statistic that indicates the degree to which an item separates the students who performed well from those who did poorly on the test as a whole" [6]. The discrimination power of an item is calculated by categorizing the examinee into upper 27% and lower 27% according to their total test score. The difference between the upper and lower group is divided by the number of the examinee in the upper group or the larger group or by half of the total number of the examinee or even by the total number [4, 6, 58, 59]. Obon and Rey [12] calculated the discrimination index as the difference of difficulty index between the upper and lower groups [12]. In literature, both 25 and 27% were reported as possible percentages of examinee categorization [60, 61]. The 27% is commonly used to maximize differences in normal distributions and increase the number of examinees in each category. The discrimination index range from 1.0 to −1.0. The positive discrimination index indicates that high achievers answer the item correctly more than those in the lower ones, which is desirable. The negative discrimination index reflects that lower achiever examinees answer the item more correctly, while zero discrimination indicates equal numbers of students in the upper and lower groups [36, 37]. Negative discrimination is thought to be due to

item flaws or inefficient distractors, miss keys, ambiguous wording, gray areas of opinion, and areas of controversy [12, 62]. Nevid and McClelland [52] reported that items assessing evaluation and explanation domains could discriminate between high and low performers, while Kim et al. [51] comments that items assessing remembering and understanding levels have low discrimination power [52, 54].

It was reported that discrimination indices are positively associated with difficulty index and distractor efficiency [39, 63]. The discrimination power of the item is reduced by the increased number of non-functional distractors [36].

A test with poor discriminating power will not provide a reliable interpretation of the examinee's actual ability [6, 64]. In addition, discrimination power will not indicate item validity, and deletion of items with poor discrimination power negatively impacts validity due to a decrease in the item number [65].

#### **13. Discrimination coefficients**

Discrimination coefficients can evaluate item discrimination. The discrimination coefficients include point biserial correlation, biserial correlation, and phi coefficient. Although point biserial correlation is used interchangeably with the discrimination index, discrimination coefficients are considered superior to the discrimination index [24]. The superiority came from the fact that discrimination coefficients are calculated using all examinees' responses in the item rather than only 54% of the examinees such as in the discrimination index.

The difference between Point-biserial correlation (rBP) and discrimination indexes is that rBP is the correlation between an item in the exam and the overall student score [2, 66]. In cases of highly discriminating items, the examinees who responded to the item correctly also did well on the test. In general, the examinees who responded to the item incorrectly also tended to perform poorly on the overall test. It was suggested that point biserial can express the predictive validity better than Biserial correlation coefficients [61, 67].

#### **14. Interpretation of discrimination index**

Discrimination power of items more than 0.15 was reported as evidence of item validity [50, 53]. While any item with less than 0.15 or negative should be reviewed [50] (**Table 5**).

When interpreting the discrimination power of an item to decide about, especial consideration should be related to its difficulty. Items with a high difficulty index (most of the examinee answer it right) and those with low difficulty index (most of the examinee answer it wrong) commonly have low discrimination power [35, 63]. In both cases, such items will not discriminate examines as the majority are on one side. Thus items with a moderate difficulty index are more likely to have good discrimination power.

The common causes of poor discrimination power of item include technical or writing flaws, untaught or not well covered content material, ambiguous wording, gray areas of opinion and controversy, and wrong keys [12, 50, 62, 66].

In general, the statistical data obtained from item analysis can help item constructors and exam composers to detect defective items. The decision to revise an item or distractors must be based on the difficulty index, discrimination index, and distractor efficiency. Revision of items can lead to modification in the teaching method or the content material [68].

#### *Item Analysis: Concept and Application DOI: http://dx.doi.org/10.5772/intechopen.100138*


#### **Table 5.**

*Reference values and interpretation of discrimination index (power).*
