The application of latent trait theory to classroom tests necessitates the use of small sample sizes for parameter estimation. Computer generated data were used to assess the accuracy of estimation of the slope and location parameters in the two parameter logistic model with fixed abilities and varying small sample sizes. The maximum likelihood…

Estimating item parameters from a two-parameter normal ogive model is considered using Gibbs sampling to simulate draws from the joint posterior distribution of ability and item parameters. The method gives marginal posterior density estimates for any parameter of interest, as illustrated using data from a 33-item mathematics placement…

The third section of this two-volume report examines the utility of the model developed in section I for application in a classroom testing situation. The model was applied in arithmetic classes through a weekly testing program. The teacher specified the generic task being taught, tests were constructed using a table of random numbers to select…