Past exam of the mathematics course of the University of Cambridge 2012 iii Paper 41 2 c Solution Created 2026-10-03 Updated 2026-10-07
The I-squared statistic of is a small estimate of excess variation on the heterogeneity scale. It does not mean that of studies are different, nor that this percentage of patients responds differently. The Cochran's Q statistic compares the observed variation with that expected from the studies' sampling errors; its approximate null distribution has five degrees of freedom here. A heterogeneity-test p-value of provides no rejection of the common-effect hypothesis.
The individual confidence intervals in the forest plot overlap substantially, although some point estimates are larger than others. Taken together, there is little evidence of between-study heterogeneity in these six studies. Neither the nonsignificant test nor the small I-squared statistic proves equal effects: with only six studies, detecting moderate heterogeneity can be difficult. A study being individually significant while another is not is also not itself a test of their difference.
Past exam of the mathematics course of the University of Cambridge 2015 iii Paper 35 2 c Solution Created 2026-10-03 Updated 2026-10-06
Use for the inverse within-study variances, and . For Cochran's Q statistic, the DerSimonian–Laird estimator of the between-study variance isConsequently the estimated heterogeneity variance and standard deviation areThese describe dispersion of underlying study log odds ratios, not ordinary sampling error of a single trial. The between-study heterogeneity is additional to the within-study variances.
The I-squared statistic isIt estimates the share of variation beyond that expected from sampling error in this collection of studies. Approximately half the variation is attributed to heterogeneity on that scale; this is neither the percentage of trials with different effects nor a percentage change in mortality. The PDF omits the symbol naming its heterogeneity estimate, so both and are reported explicitly.