Multiple true–false items: a comparison of scoring algorithms

Felicitas-Maria Lahner, Andrea Carolin Lörwald, Daniel Bauer, Zineb Miriam Nouns, René Krebs, Sissel Guttormsen, Martin R. Fischer, Sören Huwendiek

Multiple true-false (MTF) items are a widely used supplement to the commonly used single-best answer (Type A) multiple choice format. However, an optimal scoring algorithm for MTF items has not yet been established, as existing studies yielded conflicting results. Therefore, this study analyzes two questions: What is the optimal scoring algorithm for MTF items regarding reliability, difficulty index and item discrimination? How do the psychometric characteristics of different scoring algorithms compare to those of Type A questions used in the same exams? We used data from 37 medical exams conducted in 2015 (998 MTF and 2163 Type A items overall). Using repeated measures analyses of variance (rANOVA), we compared reliability, difficulty and item discrimination of different scoring algorithms for MTF with four answer options and Type A. Scoring algorithms for MTF were dichotomous scoring (DS) and two partial credit scoring algorithms, PS50 where examinees receive half a point if more than half of true/false ratings were marked correctly and one point if all were marked correctly, and PS1/n where examinees receive a quarter of a point for every correct true/false rating. The two partial scoring algorithms showed significantly higher reliabilities (αPS1/n = 0.75; αPS50 = 0.75; αDS = 0.70, αA = 0.72), which corresponds to fewer items needed for a reliability of 0.8 (nPS1/n = 74; nPS50 = 75; nDS = 103, nA = 87), and higher discrimination indices (rPS1/n = 0.33; rPS50 = 0.33; rDS = 0.30; rA = 0.28) than dichotomous scoring and Type A. Items scored with DS tend to be difficult (pDS = 0.50), whereas items scored with PS1/n become easy (pPS1/n = 0.82). PS50 and Type A cover the whole range, from easy to difficult items (pPS50 = 0.66; pA = 0.73). Partial credit scoring leads to better psychometric results than dichotomous scoring. PS50 covers the range from easy to difficult items better than PS1/n. Therefore, for scoring MTF, we suggest using PS50.