A Meta-Analysis on Differences and Associations between Alliance Ratings in Child and Adolescent Psychotherapy

Figures & data

Table 1. Results for the overall mean effect sizes for differences between child, parent, and therapist alliance ratings.

Type of difference	# studies^a	# es	Mean d (se)	95% ci	p	σ^2level2	σ^2level3	% var. level 1	% var. level 2	% var. level 3
Child ratings – therapist ratings	47	92	0.346 (0.062)	0.222, 0.469	<.001***	0.000	0.146***	17.8	0.0	82.2
Parent ratings – therapist ratings	23	47	0.715 (0.094)	0.527, 0.903	<.001***	0.000	0.176***	14.6	0.0	85.4
Child ratings – parent ratings	18	31	−0.406 (0.080)	−0.569, −0.243	<.001***	0.000	0.081**	32.2	0.0	67.8

ci = confidence interval; es = effect size; σ²_level2 = variance between effect sizes (within studies); σ²_level3 = variance between effect sizes (between studies); % var. = percentage of variance explained; ^aThe number of studies reflects the number of independent samples.

Table 2. Results for the overall mean effect sizes for the association between child, parent, therapist, and observer ratings.

Type of association	# studies^a	# es	mean r (se)	95% ci	p	σ^2level2	σ^2level3	% var. level 1	% var. level 2	% var. level 3
Child ratings – therapist ratings	43	59	.321 (0.025)	.275, .365	<.001***	0.019**	0.000	42.2	57.8	0.0
Parent ratings – therapist ratings	18	25	.225 (0.034)	.158, .290	<.001***	0.003	0.009	49.0	13.1	37.9
Child ratings – parent ratings	16	27	.256 (0.037)	.184, .327	<.001***	0.013	0.000	58.5	41.5	0.0
Child ratings – observer ratings	15	19	.425 (0.071)	.296, .539	<.001***	0.000	0.049*	36.7	0.0	63.3
Therapist ratings – observer ratings	7	10	.533 (0.062)	.426, .626	<.001***	0.000	0.000	99.9	0.0	0.1
Observer ratings parent alliance – observer ratings child alliance	5	5	.183 (0.135)	−.186, .507	.240	0.026	0.026	39.8	30.1	30.1

ci = confidence interval; es = effect size; σ²_level2 = variance between effect sizes (within studies); σ²_level3 = variance between effect sizes (between studies); % var. = percentage of variance explained; ^aThe number of studies reflects the number of independent samples.

Table 3. Results for publication bias analyses.

				Trim-and-fill analyses
Type of association	# k (# es)	Funnel plot test	Egger test	# es imp. l	# es imp. r	# es > cutoff
Child ratings – therapist ratings (d)	47 (92)	z = 0.01, p = .99	z = 0.56, p = .58	8	3	Yes
Parent ratings – therapist ratings (d)	23 (47)	z = 0.71, p = .48	z = −0.79, p = .43	3	0	No
Child ratings – parent ratings (d)	18 (31)	z = 1.56, p = .12	z = −1.39, p = .16	2	0	No
Child ratings – therapist ratings (r)	43 (59)	z = 0.55, p = .58	z = 0.21, p = .83	0	1	No
Parent ratings – therapist ratings (r)	18 (25)	z = −0.55, p = .58	z = 0.79, p = .43	0	0	No
Child ratings – parent ratings (r)	16 (27)	z = 0.00, p = 1.00	z = −1.53, p = .13	0	0	No
Child ratings – observer ratings (r)	15 (19)	z = 0.20, p = .84	z = −0.03, p = .98	0	0	No
Therapist ratings – observer ratings (r)	7 (10)	z = −1.65, p = .10	z = 1.55, p = .12	3	0	Yes
Observer ratings parent alliance – observer ratings child alliance (r)	5 (5)	z = −0.72, p = .47	z = 0.52, p = .60	0	0	No

#k = number of studies; #es = number of effect sizes; imp. l = number of effect sizes on the left side of the funnel plot distribution; imp. r. = number of effect sizes on the right side of the funnel plot distribution; #es > cutoff = the number of imputed es on the left side in relation to the cutoff value of the estimator of the trim-and-fill method proposed by Fernández-Castilla et al. (2021). this estimate is based on the population es and power (number of effect sizes).

Fernández-Castilla, B., Declercq, L., Jamshidi, L., Beretvas, S. N., Onghena, P., & Van den Noortgate, W. (2021). Detecting selection bias in meta-analyses with multiple outcomes: A simulation study. The Journal of Experimental Education, 89(1), 125–144. https://doi.org/10.1080/00220973.2019.1582470

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