Table 7.

Descriptive Statistics of Test Lengths Using the A-CDM.

		PWKL				MPWKL				GDI
Item quality	π(αc|Xi)	Minimum	Maximum	M	CV	Minimum	Maximum	M	CV	Minimum	Maximum	M	CV
HD-LV	0.65	6	13	6.99	0.10	6	13	6.92	0.08	6	12	6.93	0.08
	0.75	6	14	7.86	0.14	7	14	7.75	0.12	7	15	7.76	0.12
	0.85	9	18	9.98	0.14	9	19	9.74	0.13	9	20	9.79	0.13
	0.95	11	25	12.84	0.16	11	26	12.82	0.15	11	26	12.84	0.15
HD-HV	0.65	6	10	6.83	0.08	6	7	6.75	0.06	6	7	6.70	0.07
	0.75	6	14	7.18	0.12	6	8	6.83	0.06	6	8	6.80	0.06
	0.85	6	17	7.87	0.15	6	11	7.18	0.07	6	11	7.04	0.06
	0.95	6	17	8.71	0.16	6	15	8.79	0.09	7	16	8.79	0.10
LD-LV	0.65	10	32	12.67	0.21	10	30	12.65	0.22	10	29	12.62	0.22
	0.75	11	33	14.66	0.23	11	34	14.67	0.23	11	34	14.64	0.23
	0.85	12	50	17.80	0.24	12	49	17.84	0.24	12	52	17.82	0.24
	0.95	16	59	24.41	0.23	16	74	24.39	0.23	16	74	24.37	0.23
LD-HV	0.65	8	22	9.04	0.17	8	21	9.04	0.17	8	18	9.03	0.17
	0.75	9	26	11.25	0.19	9	24	11.30	0.19	9	24	11.26	0.19
	0.85	11	27	13.29	0.19	11	32	13.20	0.18	11	29	13.20	0.18
	0.95	13	39	17.43	0.20	13	38	17.49	0.19	13	41	17.48	0.20

Note. A-CDM = additive CDM; CDM = cognitive diagnosis model; PWKL = posterior-weighted Kullback–Leibler index; MPWKL = modified posterior-weighted Kullback–Leibler index; GDI = G-DINA model discrimination index; G-DINA = generalized DINA; DINA = deterministic inputs, noisy “and” gate; CV = coefficient of variation; HD-LV = high discrimination–low variance; HD-HV = high discrimination–high variance; LD-LV = low discrimination–low variance; LD-HV = low discrimination–high variance.