100 respondents
pi = 0.53
Proportion correct (pi)
Acceptable range: 0.30 ≤ pᵢ ≤ 0.90
0.00
0.25
0.50
0.75
1.00
Correct responses
Incorrect responses
Within the acceptable range
0.30 ≤ pᵢ ≤ 0.90.
\( p_i=\frac{\displaystyle\sum_{p=1}^{N_i} X_{pi}}{N_i} \)
Where
pi = proportion correct for the item i (difficulty index)
Xpi = person's response p al item i: 1 = correct, 0 = incorrect
Ni = number of people with a valid response to the item i
Xpi = person's response p al item i: 1 = correct, 0 = incorrect
Ni = number of people with a valid response to the item i
Relationship with difficulty
pi ↑ → easier item
pi ↓ → more difficult item
pi ↓ → more difficult item
Correct
53
Incorrect
47
pi
0.53