Derivation and test of predictions of a discrete latent state model for signed number addition test performance

• Main Author: Yamamoto, Kentaro
• Format: Others
• Published: PDXScholar 1983
• Subjects: Prediction (Psychology); Mathematical ability > Testing; Discrete Mathematics and Combinatorics; Psychology
• Online Access: https://pdxscholar.library.pdx.edu/open_access_etds/3328; https://pdxscholar.library.pdx.edu/cgi/viewcontent.cgi?article=4332&context=open_access_etds

This study is an investigation of the performance of a discrete latent state model devised by Paulson (1982) to account for signed-number arithmetic test data gathered by Birenbaum and Tatsuoka (1980). One hundred twenty nine students took a test which consists of sixteen item types with four parallel arithmetic items of each type. The present study utilizes the five addition item types of four items each; hence, there are four parallel subtests. Responses to the addition items can be analyzed in terms of two components: the siqn component (is the sign correct?), and the absolute value component (is the size of the answer correct?). Paulson's model describes how students perform on the two components separately and how the component responses are related. This study examines the parallelism of the four subtests, in terms of equality of means, standard deviations, and correlations between all pairs of subtests. Decision consistency between subtests is another useful indicator of measurement reliability, particularly for tests of concept mastery. The model implies that the consistency between any two pairs of subtests should be equal; this implication is tested. The specific numerical values predicted by the model for the means, standard deviations, correlations, and decision consistency indices are tested against the corresponding observed statistics. All the analyses described so far are done separately for both the sign and the absolute value components of the responses. A method to synthesize overall correct response from estimated parameter values of two components is derived and tested against observed values. The results are that "parallel" items within item types are not all parallel and finer characterization would be needed to describe the items completely. However, the deviations from strict parallelism are slight. Paulson's model demonstrates good predictive ability; on both components and on the overall responses. Most of the deviations from the prediction can be attributed to not strictly parallel subtests and estimated parameter values not being the best possible estimates.