## Blocks of Items

NAEP uses student weights, which account for NAEP's complex sampling of students, to calculate statistics for each item within a block. These statistics are then averaged across items. Weights are also used to calculate alpha reliability and the proportion of students attempting the last item in a block. Weighted summary statistics estimate the results for each block of items for the whole population of students in the NAEP sampling frame.

• The unweighted sample size is the number of students in the reporting sample who receive each block in the assessment. The other statistics provided in these descriptive item statistics tables are based on these counts of students.

• The weighted average item score for the block is the average, over items in the block, of the mean item score for each item, where the mean item score has been calculated using appropriate student sampling weights.

• The weighted average polyserial is the average, over items in the blocks, of the item-level polyserial (the biserial correlation for dichotomous items) between the item score and the total block score. For each item-level polyserial, the total block score (including the item in question, and with students receiving zero points for all not-reached items) is used as the criterion variable for the correlation. The total block score for each examinee is calculated by adding a one to each dichotomously scored item answered correctly plus the credit assigned to the examinee's response category for each polytomously scored item. Data from students classified as not reaching the item of interest are omitted from the calculation of the statistic.

• The weighted alpha reliability is Cronbach's coefficient alpha calculated using appropriate student weights for each block of items. Cronbach (1951) describes coefficient alpha when each student's responses are weighted equally in the calculation.

• The weighted proportion of students attempting the last item of a block (or, equivalently, one minus the proportion of students not reaching the last item) is often used as an index of the degree of speediness associated with the administration of that block of items. Mislevy and Wu (1988) discusses these conversions.

Last updated 11 July 2008 (DB)