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Item Analysis, Item Analysis Index - Basic Statistics for Behavioral Sciences - Lecture Notes, Study notes of Statistics for Psychologists

English and Foreign Languages UniversityStatistics for Psychologists

Item Analysis, Item Analysis Index, Distractor Analysis, Item Difficulty, Item Discrimination Index, Item Total Correlation, Item Reliability and Item Validity are some points from this helpful lecture notes.

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2011/2012

Uploaded on 11/21/2012

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Ch. 6. Item Analysis
I. Introduction: analyzing each item to check the strength and weakness of each item so
that the quality of each item can be enhanced.
II. Item analysis index
A. Distractor analysis: analyzing the response of incorrectly answered alternatives to
check if there is an equal distribution of incorrect responses.
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Ch. 6. Item Analysis

I. Introduction: analyzing each item to check the strength and weakness of each item so that the quality of each item can be enhanced. II. Item analysis index A. Distractor analysis: analyzing the response of incorrectly answered alternatives to check if there is an equal distribution of incorrect responses.

of persons answering an item incorrectly

  1. E(distractor) = -------------------------------------------------------

    of distractors

  2. an extremely popular distractor is likely to lower the reliability and alidity of the test.

B. Item difficulty

of persons answering item i correctly

  1. pi = ----------------------------------------------------- total # of persons taking the item

  2. an item with the p-value of 0 or 1 is useless.

  3. If pi = .5, the variance of item score, piqi is maximized, but if inter-item correlation is 1, the test will classify examinees only into two groups.

  4. Items with range of .3 - .7 and average pi = .5 will be ideal. C. Item discrimination index

  5. di = Ui/niU - Li/niL where, Ui: # of people in the upper group who have the item i correct, niU: # of people in the upper group, Li: # of people in the lower group who have the item i correct, and niL: # of people in the lower group.

  6. In many cases, the upper group and the lower group are equal in sample size, thus, di = (Ui - Li)/ni

  7. di is the difference between the proportion of high-scoring examinees who get the item correct and the proportion of low-scoring examinees who get the item correct.

  8. niU and niL range between 10% and 33%. If the test scores are normally distributed, 27% is optimum.

  9. the range of di is -1 to +1. If di is negative, the item should be discarded. D. Item-total correlation (point-biserial or biserial)

i

i X

i iX (^) p

p s

X X

r 1 where Xi : the mean of the test score for those who have item i correctly, X and sX are the mean and SD of all examinees, and pi is item difficulty index.

  1. If the item score and the test score are highly correlated, the coefficient becomes high.
  2. The easier the item and the larger the difference between Xi and X , the higher the correlation. E. Item reliability and item validity
  3. Assume a case where we want to select k-items from N-items (N k) to build a test.