Supplementary Material 1. Detailed Information on Quantitative Data Synthesis

Supplementary material 1. Detailed information on quantitative data synthesis

Within-group effect sizes (ESs) were calculated using the following formula:

 Y Y   1 2    S within Y d =   , where 1 is the pre-treatment sample mean, and Y2 is the post-

2 2 SD1  SD2  2r  SD1  SD2 S within  2(1 r) treatment sample mean. , where SD1 is the standard deviation of the pre-treatment sample mean, SD2 is the standard deviation of the post- treatment sample mean, and r is the correlation between pre-treatment and post-treatment scores. Hedges’ g can be computed by multiplying d by the correction factor J (df) =

3 1  4df 1 , where df refers to the degrees of freedom, to estimate the within-group standard deviation. The controlled ESs were computed using the following formula:

 PSY   CONT  3  g   1  2 2  4(n  n )  9  (nExp 1)SDCont  (nCont 1)SDExp  Exp Cont  (n  2) total , where  is the mean pre- to post-treatment change, SD is the standard deviation of post-treatment scores, n is the sample size, Exp refers to the experimental treatment condition, and Cont refers to the control group.

We used a test of significance based on the Q statistic, a measure of weighted squared deviations. If Q is significant, then the assumption of heterogeneity in the data set is confirmed, and random effects are recommended. In addition, we used the ratio of true heterogeneity to total observed variation I2 (Higgins, Thompson, Deeks, & Altman, 2003). I2 tests the level of inconsistency across studies, and the result indicates the percentage of total

100%, where 0% implies no heterogeneity, values below 25% indicate a low level of heterogeneity, values of 50% indicate moderate heterogeneity, and values above 75% indicates high heterogeneity (Higgins, et al., 2003). Moderator analyses can be conducted to help clarify the reason for the existence of heterogeneity in studies.

Q is determined by the following formula:

2 k W Y k 2  i1 i i  Q  W Y i   i1 i k W  i1 i , where Wi is the weight of the study, Yi is the ES of the study, and k is the number of studies included. To determine the expected value of Q, we used the degrees of freedom (df = k−1, where k is the number of studies included). A significant Q-test (a p-value less than alpha set at .05) indicates heterogeneity in the ES.

I2 is determined using the following formula:

 Q  df   x100% I2=  Q  .

I2 is expressed as a ratio with a range of 0% to 100% and reflects the proportion of observed variance reflecting a real difference in the ES. Values of 25%, 50%, and 75% can be considered low, moderate, and high, respectively (Higgins, et al., 2003).

Sensitivity analysis.

Meta-analysis results may be biased because studies reporting non-significant results are less likely to be published than those reporting significant results (Johnson & Eagly,

2000). We computed the fail-safe N (Rosenthal, 1993) to address potential publication bias.

ESs can be considered robust if the required number of studies (X) to reduce the overall ES to a non-significant level exceeds 5K + 10 (Rosenthal, 1993). In addition, we constructed funnel

Tweedie, 2000) to measure the robustness of the results. Meta-analysis results are considered unbiased and robust if the funnel plot is symmetrical, if the trim-and-fill method yields comparable original and re-calculated ESs, and if the fail-safe N exceeds 5K+10.

We computed the fail-safe N (Rosenthal, 1993) using the following formula:

2 K(K Z  2.706) X  2.706 .

In this formula, K is the number of studies in the meta-analysis, and Z is the mean Z obtained from K studies.

The trim-and-fill method is used to determine whether negative or positive trials are over- or under-represented by accounting for the sample size (i.e., where the missing studies would need to fall to make the plot symmetrical). This information can then be used to re- calculate the ES estimates if the funnel plot is asymmetrical. The divergence of the original

ES and the re-calculated ES indicates the results’ level of robustness.

Duval, S., & Tweedie, R. (2000). Trim and fill: A simple funnel-plot-based method of testing

and adjusting for publication bias in meta-analysis. Biometrics, 56(2), 455-463.

Higgins, J. P. T., Thompson, S. G., Deeks, J. J., & Altman, D. G. (2003). Measuring

inconsistency in meta-analyses. BMJ: British Medical Journal, 327(7414), 557-560.

Johnson, B. T., & Eagly, A. H. (2000). Quantitative synthesis of social psychological

research. In H. T. Reis & C. M. Judd (Eds.), Handbook of research methods in social

and personality psychology (pp. 496-528). London: Cambridge University Press.

Rosenthal, R. (Ed.). (1993). Meta-analytic procedures for social research. Newbury Park,

CA: Sage Publications.

Psychological Treatments for Symptoms of Posttraumatic Stress Disorder in Children and Adolescents: A Meta- Analysis, Clinical Child and Family Psychology Review, Gutermann, J., Schreiber, F., Matulis, S., Schwartzkopff, L., Deppe, J., Steil, R., Department of Clinical Psychology and Psychotherapy, Goethe University, Frankfurt am Main, Germany, [email protected] Psychological Treatments for Symptoms of Posttraumatic Stress Disorder in Children and Adolescents: A Meta- Analysis, Clinical Child and Family Psychology Review, Gutermann, J., Schreiber, F., Matulis, S., Schwartzkopff, L., Deppe, J., Steil, R., Department of Clinical Psychology and Psychotherapy, Goethe University, Frankfurt am Main, Germany, [email protected]