Table 5.

Chi-Square Test Statistics for Model 2 (10 Indicators, One Factor)

N	y* distribution		Full WLS				Robust WLS
	s	k	M	SD	RB	% reject	RB	% reject
100	0.00	0.00	59.68	19.94	70.50	63.80	8.42	6.40
	0.75	1.75	61.33	20.39	75.21	66.06	8.65	7.40
	0.75	3.75	63.14	21.49	80.41	70.68	10.17	8.00
	1.25	1.75	64.51	19.28	84.32	77.60	16.10	12.40
	1.25	3.75	60.19	18.69	71.99	70.42	7.68	5.00
200	0.00	0.00	44.55	12.88	27.28	28.60	4.25	5.60
	0.75	1.75	45.14	12.73	28.98	32.00	4.05	3.80
	0.75	3.75	45.40	12.19	29.70	33.60	4.46	6.40
	1.25	1.75	47.88	13.86	36.81	38.80	9.15	10.20
	1.25	3.75	45.37	12.52	29.64	33.20	5.34	4.00
500	0.00	0.00	38.53	10.11	10.08	13.80	1.85	6.00
	0.75	1.75	38.13	9.68	8.95	12.80	0.11	3.60
	0.75	3.75	38.61	9.79	10.31	13.00	1.02	3.80
	1.25	1.75	41.01	10.23	17.23	18.60	6.19	7.80
	1.25	3.75	38.30	9.90	9.42	11.40	1.62	6.20
1,000	0.00	0.00	36.52	9.31	4.35	8.40	−0.15	5.00
	0.75	1.75	36.54	9.51	4.39	9.40	−0.22	6.00
	0.75	3.75	36.77	9.46	5.06	9.40	0.13	5.80
	1.25	1.75	39.00	9.78	11.42	14.00	6.44	9.20
	1.25	3.75	36.98	9.38	5.67	8.60	1.59	6.00

Note. For full weighted least squares (WLS), expected value of the chi-square statistic is 35; expected standard deviation is 8.37. For robust WLS, expected value of the chi-square statistic varies within each cell, thus it is not appropriate to calculate the mean and standard deviation of chi-square statistics across replications within a given cell. s = skewness; k = kurtosis; RB = mean relative bias across replications; % reject values are Type I error rates at α = .05.