BFrSMD {BayesRep}

Generalized replication Bayes factor for SMD effect sizes

Description

Computes the generalized replication Bayes factor for standardized mean difference (SMD) effect sizes

Usage

BFrSMD(
  to,
  no,
  n1o = no,
  n2o = no,
  tr,
  nr,
  n1r = nr,
  n2r = nr,
  ss,
  type = c("two.sample", "one.sample", "paired")
)

Arguments

to

t-statistic from the original study

no

Sample size of the original study (per group)

n1o

Sample size in group 1 of the original study (only required for two-sample t-test with unequal group sizes)

n2o

Sample size in group 2 of the original study (only specify if unequal group sizes)

tr

t-statistic from the replication study

nr

Sample size of the replication study (per group)

n1r

Sample size in group 1 of the replication study (only required for two-sample t-test with unequal group sizes)

n2r

Sample size in group 2 of the replication study (only required for two-sample t-test with unequal group sizes)

ss

Standard devation of the sceptical prior under H_\mathrm{S}. Defaults to 0

type

Type of t-test associated with t-statistic. Can be "two.sample", "one.sample", "paired". Defaults to "two.sample"

Details

This function computes the generalized replication Bayes factor for standardized mean difference (SMD) effect sizes using an exact t-likelihood for the data instead of the normal approximation used in BFr (for details, see Section 4 in Pawel and Held, 2022). Data from both studies are summarized by t-statistics and sample sizes. The following types of t-tests are accepted:

• Two-sample t-test where the SMD represents the standardized mean difference between two group means (assuming equal variances in both groups).

• One-sample t-test where the SMD represents the standardized mean difference to the null value.

• Paired t-test where the SMD represents the standardized mean difference score.

Value

The generalized replication Bayes factor \mathrm{BF}_{\mathrm{SA}}. \mathrm{BF}_{\mathrm{SA}} < 1 indicates that the data favour the advocate's hypothesis H_{\mathrm{A}} (replication success), whereas \mathrm{BF}_{\mathrm{SA}} > 1 indicates that the data favour the sceptic's hypothesis H_{\mathrm{S}} (replication failure).

Author(s)

Samuel Pawel

References

Verhagen, J. and Wagenmakers, E. J. (2014). Bayesian tests to quantify the result of a replication attempt. Journal of Experimental Psychology: General, 145:1457-1475. doi:10.1037/a0036731

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. doi:10.1111/rssb.12491

See Also

BFr, BFrlogOR

Examples

data("SSRPexact")
morewedge2010 <- subset(SSRPexact, study == "Morewedge et al. (2010), Science")
with(morewedge2010,
     BFrSMD(to = to, n1o = n1o, n2o = n2o, tr = tr, n1r = n1r, n2r = n2r, ss = 0))