. Author manuscript; available in PMC: 2021 Mar 1.

Published in final edited form as: Multivariate Behav Res. 2019 Jul 2;55(2):231–255. doi: 10.1080/00273171.2019.1627659

Table 3.

The Power Simulation Results of Chi-square Tests from 500 Replications. The Values are Percentage of Power to Detect Outliers, and the Values in the Parenthesis are the False Detection Rates.

Factors			Joint ( $ρ_{i t}^{* 2}$ )			Independent
S-to-N^d	T	n	Total^a	Inn^b	Add^c	Inn ( $ρ_{η, i t}^{* 2}$ )	Add ( $ρ_{y, i t}^{* 2}$ )
High	60	100	.764 (.148)	.565 (.081)	.963 (.060)	.917 (.002)	.963 (.060)
	60	300	.764 (.148)	.566 (.081)	.963 (.060)	.917 (.002)	.977 (.041)
	100	60	.886 (.111)	.787 (.057)	.984 (.051)	.969 (.003)	.990 (.030)
	300	60	.967 (.047)	.939 (.024)	.995 (.023)	.993 (.006)	.997 (.014)
Low	60	100	.218 (.037)	.090 (.024)	.347 (.011)	.181 (.007)	.402 (.010)
	60	300	.219 (.038)	.090 (.025)	.347 (.011)	.181 (.006)	.401 (.010)
	100	60	.240 (.032)	.096 (.020)	.385 (.011)	.207 (.008)	.442 (.010)
	300	60	.268 (.025)	.111 (.014)	.425 (.011)	.249 (.009)	.484 (.010)

^a.

The power and the false detection rates for the joint chi-square statistics, when the total of the given 6 outliers (3 for latent and 3 for measurement component) were considered.

^b.

The abbreviation for innovative outliers.

^c.

The abbreviation for additive outliers.

^d.

The abbreviation for S-to-N.