Item Sampling in Educational Research

This paper introduces the concept of item sampling by considering the possible cases that can arise when making inferences from a sample of examinees and/or test items to a population of examinees and test items. Item sampling is the case in which both examinees and items have been randomly sampled from a population of examinees and items. Formulas have been worked out such that the data from the item sample can be used to estimate the mean and variance of the population. Computational examples are provided in the appendix to illustrate the cases discussed.

Several further cases involving item samples are introduced: (1) single item samples in a one-way ANOVA with two levels, (2) multiple item sampling for increased accuracy in inference, and (3) multiple item sampling in a one-way ANOVA with two levels plus extensions to a two-factor design.

Recommendations based on examinee score and item difficulty variance are made for deciding on the number of subjects vs. the number of items to sample from the population. Certain advantages as well as cautions pertaining to item sampling are discussed, and possible used of item sampling in educational research are proposed.