Upper/Lower Item Discrimination Simulator (CTT)

1

Form the groups using the corrected total score X_(−i)

First, respondents are ordered by the corrected total score X_(−i), that is, the test score excluding the item being analysed. The 27% with the lowest X_(−i) form the Lower group, and the 27% with the highest X_(−i) form the Upper group.

Lower
27%

Middle group
46%

Upper
27%

Lower X_(−i) Higher X_(−i)

Important: X_(−i) is used to define the groups. Discrimination is calculated for that specific item.

2

Examine responses to a specific item

Item being analysed: Item i

The two proportions below refer to the same item.

Upper group

27% with higher X_(−i)

p_U = 0.80

Proportion correct in Upper 80%

0.000.501.00

Correct responses: 80 Incorrect responses: 20

Lower group

27% with lower X_(−i)

p_L = 0.30

Proportion correct in Lower 30%

0.000.501.00

Correct responses: 30 Incorrect responses: 70

Correct responses in Upper

Correct responses in Lower

Incorrect responses

Separation between groups for Item i

Each marker's position represents its proportion correct. As the markers move farther apart, the magnitude of the difference between the groups increases.

Upper = .80

Lower = .30

0.000.250.500.751.00

D = +0.50

3

Calculate item discrimination

D_i = p_U − p_L The proportions correct for the two groups are compared for the same item.

D_i = 0.80 − 0.30 = 0.50

D for Item i = +0.50

The Upper group answered this item correctly more often than the Lower group.