Response to Item i by X(−i)
The points show the distribution of corrected scores among respondents who answer correctly and incorrectly.
M1: mean among correct responders
55.00
305070
M0: mean among incorrect responders
45.00
305070
Proportion correct (p)
p = 0.50
.10.50.90
\( r_{pbis}=\frac{M_1-M_0}{S_X}\sqrt{pq} \)
Expected criterion: rpbis > 0.30
Meets the expected criterion
The relationship is positive and rpbis > 0.30.
Derived or fixed values
q = 1 − p
0.50
M1 − M0
10.00
SX (fixed)
12.00
Where
M1 = mean X(−i) among respondents who answer the item correctly
M0 = mean X(−i) among respondents who answer the item incorrectly
SX = standard deviation of X(−i) across the full sample
p = proportion correct for the item
q = proportion incorrect for the item, \(q=1-p\)
M0 = mean X(−i) among respondents who answer the item incorrectly
SX = standard deviation of X(−i) across the full sample
p = proportion correct for the item
q = proportion incorrect for the item, \(q=1-p\)
In this demonstration, SX is held constant at 12.00 to isolate the effect
of M1, M0 and p on rpbis.