P : Difficulty level of all items.
b : Difficulty level of each item
∑ ; Sigma Total
N : Total number of test items.
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Score “FV” Facility value or item difficulty that we are looking for and “P” difficulty level of all items can be ranged from 0.00 to 1.00. If “FV” or “P”
is less than 0.30, it means almost the student from upper and lower groups cannot answer the item test correctly these items belong to difficult one. If “FV” or “P”
is 0.30 - 0.70, it means the proportion of students answering correctly is about halfway between a chance value and the point where no student misses the item
these items belong to moderate one. And if “FV” or “P” is more than 0.70, it means almost the students from upper and lower group can answer the item test
correctly these items belong to very easy one.
The level of difficulty shows the easiness or difficultness of item test for that group. So the level of difficulty is influenced by the students’ competence. It
will be different if the test is given to another group.
2. Discriminating Power
The discriminating power of a test item is its ability to differentiate between pupils who have achieved well the upper group and those who have
achieved poorly the lower group.
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Students with high scores on the test the upper group answered the item correctly more frequently than student with low
scores on the test the lower group. If the test items given to the students who have studied well, the score will be high and if they are given to those who have
not, the score will be low. On the contrary, if the test items yield the same score
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Asmawi zainul dan Noehi Nasution, Penilaian Hasil Belajar, Jakarta: PAU-PPAI, UT, 1993, p. 153.
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Wilmar Tinambunan, Evaluation of …, p. 139.
when they are given to the two groups, or even to the upper group yield the low
score and to the lower group yield the high score, so they are not good test items.
Effective and ineffective distracters can be identified from analysis, and those which are not working as planned can be rewritten or replaced. A change in
alternatives for a multiple choice item can increase discrimination. The formula is as follows:
Where: DP
: the index of item discriminating power. U
: the number of students in the upper group who answered the item correctly
L : the number of students in the lower group who answered
the item correctly T
: total number of students in upper and lower group.
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Item discrimination statistic is calculated by subtracting the number of students in the upper group who answered the item correctly from the number of
students in the lower group who answered the item correctly then it is divide by half of total number of students in upper and lower group.
3. Distracter Effectiveness
A good distracter will attract more students who have not studied well the lower group than the upper group. On the contrary, a weak distracter will not be
selected by any of the lower achieving students.
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Ngalim Purwanto, Prinsip-prinsip dan Teknik Evaluasi Pengajaran, Bandung: Remaja Rosdakarya, 1986, p.120.
DP = U - L ½ T
One important aspect affecting the difficulty of multiple choice test items is the quality of distracters. Some distracters, in fact, might not be distracting at
all, and therefore serve no purpose.
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Because the parts of multiple choice items include the item stem, or the main part of the item at the top, the options, which
are the alternative choices presented to the student, the correct answer, which is the option that will be counted as correct, and the distracters, which are the
options that will be counted as incorrect.
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In a good test item, the distracters must be functioned effectively, if the distracter are not functioned, they should be rewritten or discarded. Distracter
analysis is done by comparing the number of students in the upper group and the lower group who select each incorrect alternative.
D. The Importance of Item Analysis
