A comparative study of the impacts of unbalanced sample sizes on the four synthesized methods of meta-analytic structural equation modeling

Table 3 Rejection frequency percentage (statistical power) of stage 1 in heterogeneous studies

k	\(\bar{n}\)	Types	Low heterogeneity (20%)				High heterogeneity (50%)
k	\(\bar{n}\)	Types	UNIr	UNIz	MGLS	TSSEM	UNIr	UNIz	MGLS	TSSEM
5
	50	E	40.1	37.6	44.6	47.6	39.0	35.3	40.4	43.9
		M	34.6	37.0	36.2	45.8	39.3	25.4	46.1	33.5
		H	22.9	11.3	29.6	18.4	38.6	20.0	45.8	25.6
	100	E	61.4	51.8	65.1	58.6	76.4	74.1	80.4	81.2
		M	46.3	31.1	52.0	37.1	71.1	58.1	78.1	65.0
		H	40.6	23.5	44.8	26.2	60.0	38.1	69.9	46.7
	200	E	93.6	90.6	96.3	92.9	98.5	98.3	99.4	99.4
		M	77.3	64.9	84.8	72.0	97.6	93.6	98.5	96.8
		H	63.0	45.7	69.6	50.6	89.7	79.9	93.0	83.6
	500	E	100	100	100	100	100	100	100	100
		M	99.5	99.3	100	100	100	100	100	100
		H	96.9	93.2	98.7	95.2	99.9	99.9	100	100
10
	50	E	45.0	36.6	47.2	44.4	57.8	59.3	59.6	67.7
		M	34.7	19.3	42.3	28.0	67.6	48.0	76.0	60.9
		H	32.5	14.4	40.0	23.0	63.0	39.9	76.7	57.5
	100	E	82.9	75.3	84.2	78.2	94.7	94.9	96.9	97.6
		M	63.9	47.1	73.9	56.1	93.6	86.1	96.3	92.1
		H	56.1	29.4	62.7	37.4	91.4	81.7	96.3	88.1
	200	E	99.5	99.0	99.6	99.3	100	100	100	100
		M	95.5	88.3	97.7	91.2	100	100	100	100
		H	86.4	69.7	90.3	72.9	99.8	99.5	100	99.9
	500	E	100	100	100	100	100	100	100	100
		M	100	100	100	100	100	100	100	100
		H	100	99.5	100	99.9	100	100	100	100
15
	50	E	56.8	42.7	59.4	55.9	72.5	72.6	76.0	81.5
		M	45.5	25.1	47.2	36.0	75.8	53.6	79.0	68.9
		H	35.9	14.1	39.9	27.9	73.3	40.8	77.0	59.4
	100	E	94.0	88.3	95.0	90.7	99.0	99.3	99.4	99.5
		M	77.3	57.8	78.7	65.3	98.4	95.5	98.9	96.4
		H	63.8	37.4	65.5	44.7	96.8	88.9	97.7	92.9
	200	E	100	100	100	99.9	100	100	100	100
		M	98.7	94.8	99.2	97.4	100	100	100	100
		H	94.4	82.7	96.4	85.4	100	100	100	99.9
	500	E	100	100	100	100	100	100	100	100
		M	100	100	100	100	100	100	100	100
		H	100	100	100	100	100	100	100	100

\(\bar{n}\) average sample sizes, k number of studies, UNIr univariate-r, UNIz univariate-z, MGLS modified generalized least squared, TSSEM two-stage structural equation modeling, E equally sized studies, M moderately unequal sized studies, H highly unequal sized studies

ISSN: 1756-0500