Page 153 - DEDU504_EDUCATIONAL_MEASUREMENT_AND_EVALUATION_ENGLISH

Unit 10 : Item Analysis : Item Difficulty, Discrimination index, Effectiveness of Distractors

• Correcting Difficulty Indices for Chance Errors Notes
• Guilford’s Formula : There is every possibility while administering a multiple items that
students will guess answers without actually knowing the right responses. In order to curb
this tendency, the correction formula is applied, which is are as follows :
• 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 ⎭
• Calculation of D.P. Using Chi-square Test Formula : When the values calculated by the
above formulae are different, it presents difficulty in their comparative study; therefore,
another formula is applied which is called Chi-square test formula. this formula has two
forms. The first form is applied in the situation when the value of R is more than R , and
H L
the second form is applied when the value of R is more than R .
L H
• Supposing the students’ responses in a multiple choice item has been noted down as below:
• Item Analysis :
(a) Determining the number of actual items 12
(b) Excluding weak and ambiguous items 8
(c) Ensuring that selected items represent the entire test 20
(d) All of the above 10
• Here, the alternative (c) is the greatest obstacle because it has attracted most of the students.
This is stronger than even alternative (d). So, Horst has determined some basic assumptions
for his formula S = D , which are as follows :
p
(a) All obstacles do not attract all students equally, though there is an arrangement in their
attraction.
(b) Here importance is given to the most potent obstacle, which is very important from the
viewpoint of multiple choice items.

(c) The most potent obstacle should not be more attractive than the right alternative. If it is
so, then another obstacle should replace it.
• Calculating Discriminating Value of Validity Index by Formula
• To calculate discriminating value of an item by the formula method, we arrange answer
books in a definite descending order after marking them. In this, the answer books with
higher scores will be at the top and those with lower scores will be at the bottom.
• 4.27% Top and 27% Bottom Right Response Method : This is a very popular method and it
was mentioned by Garrett in this way.
• Under this method, the answer books are arranged in the descending order, that is, the
answer book obtaining the highest marks is placed at the top and the one obtaining the
lowest marks is placed at the bottom. Then the top 27% and bottom 27% are allowed to be
the while the remaining answer books are taken out.
• The more difficult a question (or item) or easier the question (or item), the lower will be the
discrimination index. Stanley and Hopkins (1972) provide a theoretical model to explain the
relationship between the difficulty index and discrimination index of a particular question
or item. According to the model, a difficulty index of 0.2 can result in a discrimination index
of about 0.3 for a particular item (which may be described as an item of 'moderate
discrimination').

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