there was a high variation of standard errors across all studies owing to the high variability in water quality studies in Latin America and the Caribbean and multiple interventions in South Asia (Figure A6).

Finally, Group 5, which pertained to diarrhea and enteric disease, comprised 79 studies, the highest number of all groups, distributed comparatively evenly across subgroups and regions. The variation in correlations of estimated effects was relatively low across subgroups except for water supply, especially in Sub‐Saharan Africa. The variation in standard errors across all papers was high, especially for water quality in Latin America and the Caribbean (Figure A6).

In summary, all the groups showed low variations in correlations between outcome effects, making them highly suitable for pooling. However, slight heterogeneity was detected in Groups 4 and 5 because of the high variability in standard errors.

# **5.2 Bias of Subgroups**

Funnel plots were constructed for each subgroup (Figure A7 in Appendix A) to assess potential bias. There is no evidence of asymmetry for Groups 1 through 4, and bias is unlikely. In the case of Group 5, while the outcome effects are relatively evenly distributed when considering all studies, the distribution of larger, more precise studies is skewed, suggesting an absence of studies. However, since most of the missing studies fall within an area of high significance, asymmetry is unlikely to have resulted from reporting bias. Group 5 includes the six highly influential studies from North America, and thus aligns with the findings from the full data set and may be the source of asymmetry.

# **5.3 Meta‐Regression**

Table A1 (see Appendix A) presents the results of a meta‐regression of the correlation of study outcomes to study characteristics (variables) for each group; Table A2 presents the results of a meta‐regression of study characteristics on the pooled effects by group.

In the case of Group 1, studies conducted in Latin America and the Caribbean and South Asia were slightly correlated, indicating similar evidence bases in those regions. Sample size produced a slight, but significantly inverse, effect, which is somewhat counterintuitive given that larger sample sizes often lead to greater representation. Effectively, the number of studies is positively correlated with outcome effects, suggesting more studies may lead to improved results. Quasi‐experimental (or nonrandomized program assignment) designs are negatively correlated with outcome effects, suggesting experimental designs (RCTs) are more likely to produce reliable results. Similarly, studies undertaken in urban areas are positively correlated with outcome effects, suggesting urban studies may produce better results than their rural counterparts. This is not surprising, given that all four evaluations conducted in urban areas used randomized methods, and studies in rural areas predominantly used quasi‐experimental methods.

There was less evidence of correlation between papers in Group 2 than in all other groups except Group 3, which may indicate a lack of relationship between the different studies. Further, it may suggest that individual outcome effects are not easily explained by study characteristics. Indeed, none of the study characteristics evaluated was significantly correlated with outcomes in Group 2, which indicates a diverse set of studies that, when compared with Group 1, for example, exerts less influence on overall effects.

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