8.7 Station Statistic Analysis

33% Discrimination

Item discrimination is the degree to which students with high overall exam scores also got a particular item correct.

The Station Statistic analysis uses 33% cohort to calculate the discrimination by:

• getting all correct answer and sorting it in order,

• selecting the top third correct answers and the bottom third correct answers,

• subtracting bottom from the top

Discrimination (point-biserial)

The item discrimination index is a point biserial correlation coefficient. Its possible range is -1.00 to 1.00. A positive result indicates that there is a high correlation between higher performing candidates giving a correct response to the item.

https://en.wikipedia.org/wiki/Point-biserial_correlation_coefficient

Facility (difficulty) of correct answer

Facility is a measure of how easy or difficult is a question for candidates. It is calculated as:
FI = (Xaverage) / Xmax
where Xaverage is the mean score obtained by all users attempting the item,
and Xmax is the maximum score achievable for that item.

Frequency

Frequency of answers

Quintile Graph

For SBA type items it works like this: all candidates sorted by score (from the highest to the lowest) are split to 5 groups and then the graph shows % of candidates who got the question correctly in each group. The graph should usually shows "steps down" because most of top scored candidates should get the question right.

Not the same for CPQ Graph.