The test of basic Mechanics Conceptual Understanding (bMCU): using Rasch analysis to develop and evaluate an efficient multiple choice test on Newton’s mechanics

International Journal of STEM Education

Table 2 Item difficulty D _i, standard error of D _i, 95% confidence interval of D _i, and outfit mean-square (MNSQ) for the 12 items

Item	Item difficulty D _i	Standard error	95% CI		Outfit MNSQ
Item	Item difficulty D _i	Standard error	LL	UL	Outfit MNSQ
1. Water glass	−2.12	0.17	− 2.46	− 1.79	0.92
2. Book	−1.24	0.14	− 1.52	− 0.97	0.97
3. Bus	−0.80	0.13	− 1.07	− 0.54	1.00
4. Train	−0.43	0.13	− 0.69	− 0.17	1.04
5. Hiker	−0.25	0.13	− 0.51	0.01	0.83
6. Cart	−0.04	0.13	− 0.30	0.22	1.12
7. Object motion	0.05	0.13	− 0.21	0.31	0.98
8. Stone	0.37	0.14	0.10	0.64	1.11
9. Inclined plane	0.58	0.14	0.30	0.85	0.96
10. Motorcycle	0.62	0.14	0.34	0.90	0.87
11. Balls	1.33	0.17	1.00	1.65	0.78
12. Skaters	1.95	0.20	1.57	2.34	0.84

Notes: CI confidence interval, LL lower limit, UL upper limit. Item difficulty parameter D _i and its standard error estimated according to the Rasch model. Higher positive values indicate higher difficulty. Confidence intervals provide an idea of the precision of the difficulty parameter estimation. Outfit MNSQ is a fit statistic comparing expected (based on the model) with observed data patterns that is sensitive to outliers. Values of approximately 1.00 (~ 0.50–1.50) indicate reasonable fit. The values obtained for the 12 items all fall within this range, indicating reasonable fit of the item data to the Rasch model (for information on less well-known conditional fit statistics, see Christensen and Kreiner, 2013; Müller and Kreiner, 2015)