Heterogeneity in Hedges

1. Heterogeneity in Hedges

2. Homogeneity Test When the null (homogeneous rho) is true, Q is distributed as chi-square with (k-1) df, where k is the number of studies. This is a test of whether Random Effects Variance Component is zero.

3. Q Chi-square ( ) is the sum of squared z scores, i.e., k scores drawn from the unit normal, squared, and summed. Q is the deviation of the observed effect size from the mean over the standard error, squared and summed. The expected value of Chi-square is its degrees of freedom.

4. Estimating the REVC If REVC estimate is less than zero, set to zero.

5. Random-Effects Weights Inverse variance weights give weight to each study depending on the uncertainty for the true value of that study. For fixed-effects, there is only sampling error. For random-effects, there is also uncertainty about where in the distribution the study came from, so 2 sources of error. The InV weight is, therefore:

6. I-squared Conceptually, I-squared is the proportion of total variation due to ‘true’ differences between studies. Proportion due to random effects.

7. Comparison

8. Confidence intervals for tau and tau-squared CI for See Borenstein et al., p 122. Formulas are long and tedious. Small numbers of studies and a large population value of tau-square make for broad confidence intervals.

9. Prediction or Credibility Intervals Makes sense if random effects. M is the random effects mean (summary effect). The value of t is from the t table with your alpha and df equal to (k-2) where k is the number of independent effect sizes (studies). The variance is the squared standard error of the RE summary effect.