Table 5.

Descriptive Statistics of Test Lengths Using the DINA Model.

		PWKL				MPWKL				GDI
Item quality	π(αc|Xi)	Minimum	Maximum	M	CV	Minimum	Maximum	M	CV	Minimum	Maximum	M	CV
HD-LV	0.65	3	25	8.26	0.28	3	16	6.69	0.13	3	14	6.67	0.13
	0.75	3	28	8.92	0.28	4	18	7.32	0.17	4	19	7.34	0.16
	0.85	3	32	10.08	0.27	4	22	8.83	0.19	4	24	8.87	0.19
	0.95	4	35	12.05	0.25	4	26	10.99	0.19	4	31	10.99	0.19
HD-HV	0.65	2	19	7.76	0.22	2	14	6.55	0.11	2	10	6.52	0.12
	0.75	2	22	7.96	0.22	2	14	6.58	0.11	2	11	6.60	0.11
	0.85	2	23	8.45	0.22	2	14	6.72	0.10	2	14	6.73	0.10
	0.95	2	23	9.36	0.21	2	17	7.51	0.12	2	18	7.22	0.11
LD-LV	0.65	4	48	13.48	0.37	5	32	11.41	0.30	5	34	11.46	0.30
	0.75	4	50	15.21	0.36	6	40	13.02	0.29	6	38	13.08	0.29
	0.85	5	55	17.11	0.35	6	53	14.95	0.30	6	55	15.00	0.30
	0.95	5	73	21.43	0.32	7	56	19.40	0.28	7	64	19.46	0.28
LD-HV	0.65	3	35	10.45	0.32	4	28	8.60	0.24	4	28	8.57	0.24
	0.75	4	36	11.71	0.32	5	29	9.86	0.26	5	31	9.93	0.26
	0.85	4	42	13.41	0.31	5	32	11.78	0.26	5	32	11.77	0.26
	0.95	4	49	15.70	0.29	6	43	14.13	0.25	6	42	14.17	0.25

Note. DINA = deterministic inputs, noisy “and” gate; PWKL = posterior-weighted Kullback–Leibler index; MPWKL = modified posterior-weighted Kullback–Leibler index; GDI = G-DINA model discrimination index; G-DINA = generalized DINA; 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.