Table 7.

Chi-Square Test Statistics for Model 4 (20 Indicators, Two Correlated Factors)

N	y* distribution		Full WLS				Robust WLS
	s	k	M	SD	RB	% reject	RB	% reject
100	0.00	0.00	—	—	—	—	17.13	15.00
	0.75	1.75	—	—	—	—	15.46	14.40
	0.75	3.75	—	—	—	—	16.19	12.80
	1.25	1.75	—	—	—	—	19.45	17.60
	1.25	3.75	—	—	—	—	17.03	13.80
200	0.00	0.00	1235.67	317.21	631.16	100.00	8.21	8.20
	0.75	1.75	1271.38	327.99	652.29	100.00	7.93	7.80
	0.75	3.75	1388.40	404.18	721.54	100.00	7.73	7.60
	1.25	1.75	1279.96	322.21	657.37	100.00	10.97	11.00
	1.25	3.75	1292.71	369.64	664.92	100.00	9.07	10.00
500	0.00	0.00	272.76	37.90	61.39	97.80	3.94	7.80
	0.75	1.75	275.02	40.44	62.73	97.40	3.58	6.80
	0.75	3.75	279.43	42.22	65.34	97.80	2.92	6.20
	1.25	1.75	285.95	42.51	69.20	99.20	5.91	7.80
	1.25	3.75	273.99	38.48	62.13	99.00	3.58	6.80
1,000	0.00	0.00	210.55	26.49	24.59	63.80	1.53	6.40
	0.75	1.75	211.90	25.21	25.38	66.60	2.30	7.00
	0.75	3.75	211.82	25.63	25.34	65.00	1.98	5.80
	1.25	1.75	219.15	26.87	29.68	74.00	3.92	6.80
	1.25	3.75	211.43	24.62	25.11	67.40	2.96	7.20

Note. For full weighted least squares (WLS), expected value of the chi-square statistic is 169; expected standard deviation is 18.38. 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. Dashes indicate values that are not available because of noninvertible weight matrices. s = skewness; k = kurtosis; RB = mean relative bias across replications; % reject values are Type I error rates at α = .05.