Page 142 - DEDU504_EDUCATIONAL_MEASUREMENT_AND_EVALUATION_ENGLISH

Educational Measurement and Evaluation

Notes 10.6.2 Kelley’s Formula
When the number of students is very large, in such a situation, Kelley’s top 27% and bottom 27%
formula proves convenient, which is as follows :
1 ⎧ W H ⎞ 1 ⎛ W L ⎞ 1 ⎫ ⎛
P = ⎨ R − H ⎟ + ⎜ R − L ⎟ ⎬⎜
c 2 ⎝ K 1 N − ⎠ ⎩ − H NR H K 1 N − − ⎝ ⎠ L NR L ⎭
Where, RH = Number of candidates in top group giving right response
W = Number of candidates in top group giving wrong response.
H
N = Number of total candidates in top group.
H
NR = Number of candidates in top group who have not attempted the item.
H
R = Number of candidates in bottom group giving right response.
L
W = Number of candidates in bottom group giving wrong response.
L
N = Number of total candidates in bottom group.
L
NR = Number of candidates in bottom group who have not attempted the item.
L
Example : An achievement test was administered upon a group of 380 students approximately.
The Test-administrator is interested in calculating Difficulty-Index of Item No. 75 by Kelleys, T-
B 27% method for which the different values are as under :
N = 100, R = 70, W = 20 and NR = 10
H H H H
N = 100, R = 20, W = 60 and NR = 20
L
L
L
L
Solution :
⎧ 20 60 ⎫
1 ⎪ 70 − 51 + 20 − 5 1 ⎪
−
−
−
−
∴ P c = 2 ⎨ ⎪ 100 10 100 20 ⎬ ⎪
⎩ ⎭
⎧ 70 − 20 20 − 60 ⎫
1 ⎪ 4 + 4 ⎪
= 2 ⎨ 90 80 ⎬
⎪ ⎪
⎩ ⎭
= { 90 − + 20 15 }
−
1 70 5
2
80
= { + 5 }
165
290 80
= { + }
15200 450
2 7200
1 5650
= ×
2 7200
1 113
= ×
2 114
113
=
228
= .39
= .39 × 100
= .39% (Difficulty-Index)

136 LOVELY PROFESSIONAL UNIVERSITY