Table 5.

Simulation Results: Unidimensional model, Power at .05 Alpha Level

K	N	df	null model			TKL10			TKL30
			M	RMSEA (90% CI)	rej	M	RMSEA (90% CI)	rej	M	RMSEA (90% CI)	rej
test statistic based on full one- and two-way marginal tables (M2)
2	750	90	90.9	.006 (.000,.019)	.053	100.1	.011 (.000,.023)	.186	180.7	.036 (.028,.044)	.997
	1500	90	89.9	.004 (.000,.013)	.044	100.2	.008 (.000,.016)	.189	180.1	.026 (.019,.032)	.998
3	750	405	399.8	.003 (.000,.011)	.032	425.5	.007 (.000,.015)	.194	620.1	.026 (.022,.031)	1.000
	1500	405	396.2	.002 (.000,.008)	.031	451.4	.008 (.000,.013)	.483	841.5	.027 (.024,.030)	1.000
4	750	930	904.8	.002 (.000,.008)	.010	937.2	.004 (.000,.011)	.077	1180.6	.019 (.015,.022)	.999
	1500	930	903.5	.001 (.000,.006)	.015	973.1	.005 (.000,.009)	.259	1462.2	.019 (.017,.022)	1.000
5	750	1665	1622.1	.001 (.000,.007)	.010	1663.9	.003 (.000,.009)	.047	1933.1	.015 (.011,.018)	.997
	1500	1665	1619.6	.001 (.000,.004)	.008	1699.9	.003 (.000,.007)	.159	2246.4	.015 (.013,.017)	1.000
test statistic based on reduced one- and two-way marginal tables ( $M_2^{\ast }$)
3	750	75	75.7	.006 (.000,.020)	.061	98.3	.019 (.000,.030)	.538	246.0	.055 (.046,.064)	1.000
	1500	75	75.5	.004 (.000,.014)	.053	119.4	.019 (.011,.026)	.886	413.0	.055 (.049,.061)	1.000
4	750	60	60.2	.006 (.000,.021)	.056	87.0	.023 (.007,.035)	.670	206.2	.057 (.045,.070)	1.000
	1500	60	60.4	.005 (.000,.015)	.056	113.9	.024 (.016,.031)	.971	337.8	.055 (.047,.064)	1.000
5	750	45	45.0	.007 (.000,.023)	.057	59.2	.018 (.000,.033)	.376	138.7	.052 (.041,.064)	1.000
	1500	45	45.1	.005 (.000,.016)	.052	73.8	.020 (.010,.028)	.799	232.7	.053 (.045,.060)	1.000

Notes. K is the number of categories. N is the sample size. The reference distribution of M₂ and $M_2^{\ast }$ statistics is central chi-square with df degrees of freedom. Note that M₂ is equivalent to $M_2^{\ast }$ when K is 2. Means are reported under M and the empirical rejection rates at alpha level of .05 are shown under column heading “rej.”