Item & Test Statistics Psych 818 - DeShon

Binary Item Statistics Score an item or set of items as 0,1 1 represents “pass”, “agree”, or “endorse” Notation: Xj - jth item score xij - ith person’s score on item j j is the probability of a “1” on item j nj is the number of people in the sample who receive a “1” on the jth item

Binary Item Statistics Item difficulty = item mean sample mean for item j relative frequency of “1” (pass) in the sample proportion of people with a “1” on the jth item Estimates the “item difficulty” (j) Range: 0 -> 1 1 means easy 0 means hard

Binary Item Statistics Item Variance Mean (“difficulty”) and variance are not independent What does this imply about item discrimination or item information?

Binary Item Statistics Covariance Correlation

Quantitative Item Statistics Assume a 5 point rating scale frequency weighted approach X nc p  x x2 5 7 .07 .1 0.5 2.5 4 17 .17 .2 0.8 3.2 3 41 .41 .4 1.2 3.6 2 25 .25 0.4 1 10 .10 0.1

Quantitative Item Statistics Maximum variance of an item given the number of response options used as the basis for the rwg statistic k 2 3 4 5 6 7 8 9 10 0.25 1.00 2.25 4.00 6.25 9.00 12.25 16.00 20.25

Quantitative Test Statistics Forming test scores from quantitative items Usually accomplished by simply adding the scores for each item This is a unit weighted linear composite Can directly compute the resulting test mean and SD Variance is the sum of all elements in the var- covar matrix