Page 307 - DEDU504_EDUCATIONAL_MEASUREMENT_AND_EVALUATION_ENGLISH

Unit 26: Achievement Test: Concept, Types and Construction

Example Notes
Suppose, the following data are obtained in respect of question number 27 of a test :
R = 60, W = 30, N = 100, NR = 10,
H H H H
R = 20, W = 50, N = 100, NR = 30, K = 4
L L L L
So, the difficulty level of question number 27 will be :
1 ⎡ 30 ⎞ 1 ⎛ 50 ⎞ 1 ⎤⎛
DL = ⎢ ⎜ 60 – ⎟ + ⎜ 20 – ⎟ ⎥
2 ⎝ 4 – 1 100 – 10 ⎝ 4 – 1 100 – 30 ⎦ ⎠
⎠ ⎣
1 ⎡ 1 ⎛ 10 ⎞ 1 ⎤
= ⎢ ( )60–10 + ⎜ ⎟ ⎥
2 ⎣ 90 ⎝ 3 ⎠ 70 ⎦
150 1 ⎤ ⎡ 138 ⎤
⎡
= 290 + 21 ⎥ ⎦ = ⎢ ⎣ 263 ⎥ ⎦
⎢
⎣
19
= = .30
63
Difficulty level (in %) = 30%
Note :
Though no norm has been determined as regards difficulty level for the selection of
items in the construction of a test, yet most specialists consider the selection of items of
different level from 30% to 70% as suitable. Some of the specialists are of the opinion that
it should be limited from 40% to 60%. Katiz has written in this context that if only
proficiency of the students in a subject is to be found out, then the test should be constructed
using less difficult items; but if the students have to be divided into different classes as
high, medium and low then comparatively difficult items should be used to construct a
test. He has demonstrated it by the following table :

Form of Item Difficulty level (in %)
Essay type 50
Five choice type 60
Four choice type 62
Three choice type 66
Two choice type 75

(b) Discriminating Power of Items : Discriminating power of a question or item intimates
how far it can discriminate the students of higher and lower achievement. If a question
has not this quality, it is not selected for the test. If a question or item in a test is solved
by students of higher and lower levels in an equal or almost equal percentage, then its
discriminating power is zero and it is not considered worth for inclusion in the test.
However, if the percentage of the students of higher level is sufficiently more than the
students of lower level, the positive discriminating power of the question is high and
such a question is selected. The determination of high and low levels is done on the basis
of obtained scores of the test.
Finding out Discriminating Power of the Items : The following methods and formulae
are used to find out the discriminating power of the items :
First Method : When the group of students is of small size, the number of students
solving an item is known in percentage and the discriminating power is found out using
the following formula :

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