. Author manuscript; available in PMC: 2010 Mar 10.

Published in final edited form as: Except Child. 2009 Oct 1;76(1):31–51. doi: 10.1177/001440290907600102

TABLE 4.

Table of Chi-squares for Each Set of Correlations (r), Mean Aggregated Effects, and Confidence Intervals

Category of r	χ²	df	p <	N	k	Lower 95% Confidence Interval	Mean Correlation Coefficient	Upper 95% Confidence Interval	R²
Bivariate	28.21	15	.02	476	11	.19	.27	.36	.07
Autoregressor-only/lower estimate set	38.77	32	.19	1223	19	.11	.17	.22	.03
Autoregressor-only/upper estimate set	36.51	30	.19	1271	18	.11	.17	.22	.03
Autoregressor plus covariates/lower estimate set	21.23	30	.88	1569	20	.03	.08	.13	.006
Autoregressor plus covariates/upper estimate set	19.92	30	.92	1569	20	.06	.11	.16	.01

Note. In a small set of studies, both lower and upper estimates of effects were calculated to prevent bias that is due to choice of estimate. Lower and upper sets are reported separately. Degrees of Freedom (df) represent the number of independent pieces of information available to estimate the chi square test. df is larger than k because after testing the set of effects for homogeneity, we aggregated within studies to come up with a set of independent effects. The number of effects (k) represents the total number of independent studies or samples of students utilized to calculate the mean correlation coefficient.