Table 2 Results of hierarchical Bayesian model for randomised and non-randomised datasets.

From: Quantifying and addressing the prevalence and bias of study designs in the environmental and social sciences

Term

Posterior mean

95% Credible Interval

Randomised (R-)

 σβ

0.746

[0.679, 0.813]

 λ

1.119

[0.980, 1.276]

 σ[BACI DiD]

0.029

[0.005, 0.097]

 σ[BACI CA]

0.005

[0.002, 0.008]

 σ[CI]

0.005

[0.002, 0.008]

 σ[BA]

0.773

[0.699, 0.846]

 Ω[BACI DiD, BACI CA]

0.268

[0.152, 0.379]

 Ω[BACI DiD, CI]

0.239

[0.122, 0.354]

 Ω[BACI DiD, BA]

0.849

[0.770, 0.914]

 Ω[BACI CA, CI]

0.995

[0.994, 0.996]

 Ω[BACI CA, BA]

−0.168

[−0.332, 0.002]

 Ω[CI, BA]

−0.184

[−0.349, −0.015]

Non-randomised

 σβ

0.700

[0.628, 0.776]

 λ

1.822

[1.595, 2.098]

 σ[BACI DiD]

0.017

[0.004, 0.049]

 σ[BACI CA]

0.049

[0.005, 0.128]

 σ[CI]

0.091

[0.008, 0.137]

 σ[BA]

0.645

[0.573, 0.720]

 Ω[BACI DiD, BACI CA]

0.140

[0.010, 0.263]

 Ω[BACI DiD, CI]

0.036

[−0.106, 0.176]

 Ω[BACI DiD, BA]

0.798

[0.718, 0.865]

 Ω[BACI CA, CI]

0.939

[0.923, 0.954]

 Ω[BACI CA, BA]

−0.127

[−0.285, 0.026]

 Ω[CI, BA]

−0.229

[−0.397, −0.061]

  1. In randomised datasets, BACI and CI terms refer to R-BACI and R-CI designs (denoted by ‘R-’). The \(\sigma\) terms are the standard deviations of the bias of each design, so larger \(\sigma\) values correspond to more biased designs. σβ refers to the standard deviation of the true effect across all datasets. \({\Omega}\) represents the within-response correlations between study design estimates, and λ models systematic underestimation (λ > 1) or overestimation (λ < 1) of the statistical error using GLM(M)s. See methods for more details on the model.
  2. BA before-after, BACI before-after-control-impact, CI control-impact.
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