Item Analysis in Student Assessment Dr.Mehdi Sayyah Psychiatrist

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Item Analysis in Student AssessmentDr.Mehdi
SayyahPsychiatrist
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Item/Question Analysis

• Rank total scores in descending order for total
  group
• Divide into two groups HIGH and LOW group,
  normally about 25 both ways (Optimum27)

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Facility Index (FI)

• Defined as proportion in total group getting the
  item right
• If everybody in the group got the item right, the
  facility index (FI) 1 indicating a very easy
  item
• If everybody in the group got the item wrong, the
  facility index (FI) 0 indicating a very
  difficult item.
• Hence FI ranges from 0 to 1, the higher the
  value, the easier is the item.

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Discrimination Index (DI)

• Defined as the proportion in the HIGH group
  getting the item right MINUS the proportion in
  the LOW group getting the item right. DI pH-pL
• If everybody in the HIGH group got the item right
  and everybody in the LOW group also got the item
  right then DI pH-pL 1 1 0. The item has
  zero discrimination index. It is not
  discriminating at all!
• If everybody in the HIGH group got the item right
  and everybody in the LOW group got the item
  wrong then DI pH-pL 1 0 1. The item has
  positive 1 as DI, maximum discrimination which
  is ideal in the norm referenced sense.

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Discrimination Index (DI)

• If everybody in the HIGH group got the item wrong
  and everybody in the LOW group got the item
  right, then DIpH-pL 0 1 -1. The item has
  negative 1 as DI, maximum discrimination in the
  wrong direction. Bad in the norm-referenced
  sense.
• Hence DI ranges from 1 to 1, where negative
  values indicate discrimination in the wrong way
  but positive values for DI, indicate good
  discrimination. The higher the value of DI, the
  better or more discriminating is the item.

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Approximate Values for FI and DI

• In a class of about 40 students, take the first
  10 as the HIGH group and the bottom 10 as the
  LOW group.
• Then FI is approximately equal to
• (pH pL)/2.
• Then DI is pH - pL

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Matrix of student data on a twenty-one item test
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• The data for the student with lowest score was
  entered first, then the student with the next
  lowest score, and so on.

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Students divided into three groups according to
score
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• The position of the rows (item scores) has been
  altered so that the easiest item is at the top of
  the matrix and the other rows are arranged in
  descending order. Notice that the top right
  corner of the matrix has mostly entries of 1s,
  and the lower left corner has mostly entries of
  0s.

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• The students have been assigned to 3 (equal)
  groups. The highest 6 scorers will be called the
  High group the lowest 6 scorers will be called
  the Low group the Middle group of 6 has been
  shown underlined. (Note that to form three groups
  of equal size, the middle

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• We can investigate the patterns of success for
  each item (in an approximate way) by graphing the
  success rate of the Low group and the
  corresponding success rate of the High group.

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Correct answer responses for item 1
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Correct answer responses for item 4
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Correct answer responses for item 19
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• Now we return to considering the middle group.
  (If the middle group was not exactly the same
  size as the low and high groups,

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Correct answer responses for L, M and H groups on
items 1, 4, 19, and 21
Item 1
Item 4
Item 19
Item 21
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Acceptable and may be acceptable correct answer
response patterns
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Unacceptable correct answer response patterns
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Patterns for correct responses
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• Thank You !
• Any Question ?