Computes the sceptical Bayes factor
BFs(to, so, tr, sr, truncate = FALSE, zo = NULL, zr = NULL, c = NULL)The sceptical Bayes factor \(\mathrm{BF}_{\mathrm{S}}\). \(\mathrm{BF}_{\mathrm{S}} < 1\) indicates replication success, the smaller the value of \(\mathrm{BF}_{\mathrm{S}}\)
the higher the degree of replication success. It is possible that the
result of the replication is so inconclusive that replication success
cannot be established at any level. In this case, the sceptical Bayes
factor does not exist and the function returns NaN.
Original effect estimate
Standard error of the original effect estimate
Replication effect estimate
Standard error of the replication effect estimate
Logical indicating whether advocacy prior should be truncated
to direction of the original effect estimate (i.e., a one-sided test).
Defaults to FALSE
Original z-value zo = to/so (alternative
parametrization for to and so)
Replication z-value zr = tr/sr (alternative
parametrization for tr and sr)
Relative variance c = so^2/sr^2 (alternative parametrization
for so and sr)
Samuel Pawel
The sceptical Bayes factor is a summary measure of the following two-step reverse-Bayes procedure for assessing replication success:
Use the data from the original study to determine the standard deviation \(\tau_{\gamma}\) of a sceptical normal prior \(\theta \sim \mathrm{N}(0, \tau_{\gamma}^2)\) such that the Bayes factor contrasting the null hypothesis \(H_0: \theta = 0\) to the sceptic's hypothesis \(H_{\mathrm{S}}: \theta \sim \mathrm{N}(0, \tau_{\gamma}^2)\) equals a specified level \(\gamma \in (0, 1]\). This prior represents a sceptic who remains unconvinced about the presence of an effect at level \(\gamma\).
Use the data from the replication study to compare the sceptic's hypothesis \(H_{\mathrm{S}}: \theta \sim \mathrm{N}(0, \tau_{\gamma}^2)\) to the advocate's hypothesis \(H_{\mathrm{A}}: \theta \sim f(\theta \, | \, \mathrm{original~study})\). The prior of the effect size under \(H_{\mathrm{A}}\) is its posterior based on the original study and a uniform prior, thereby representing the position of an advocate of the original study. Replication success at level \(\gamma\) is achieved if the Bayes factor contrasting \(H_{\mathrm{S}}\) to \(H_{\mathrm{A}}\) is smaller than \(\gamma\), which means that the replication data favour the advocate over the sceptic at a higher level than the sceptic's initial objection. The sceptical Bayes factor \(\mathrm{BF}_{\mathrm{S}}\) is the smallest level \(\gamma\) at which replication success can be established.
The function can be used with two input parametrizations, either on the
absolute effect scale (to, so, tr, sr) or
alternatively on the relative z-scale (zo, zr, c). If
an argument on the effect scale is missing, the z-scale is automatically
used and the other non-missing arguments on the effect scale ignored.
Pawel, S. and Held, L. (2022). The sceptical Bayes factor for the assessment of replication success. Journal of the Royal Statistical Society Series B: Statistical Methodology, 84(3): 879-911. tools:::Rd_expr_doi("10.1111/rssb.12491")
BFsSMD, BFslogOR
to <- 2
tr <- 2.5
so <- 1
sr <- 1
BFs(to = to, so = so, tr = tr, sr = sr)
BFs(zo = to/so, zr = tr/sr, c = so^2/sr^2)
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