Matching G-Theory Analyses to the Numbers of Response Options Available

We used scores from a multi-dimensional self-concept measure to compare split-half versus item level scores in task-by-occasion, G-theory analyses that took multiple sources of measurement error into account. Split analyses were performed on raw-score metrics, and item analyses on both raw-score and continuous-latent-response-variable (CLRV) metrics. Reliability coefficients for raw-split and CLRV-item scores always exceeded those for raw-item scores, but differences diminished as number of scale points increased. Reliability coefficients for raw-split dichotomous scores were lower than those for CLRV dichotomous scores but comparable or higher as number of scale points increased. Overall, these results highlight advantages of using splits in G-theory analyses in practical settings in which raw scores are needed for decision making.