BFsSMD {BayesRep}

Sceptical Bayes factor for SMD effect sizes

Description

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

Usage

BFsSMD(
  to,
  no,
  n1o = no,
  n2o = no,
  tr,
  nr,
  n1r = nr,
  n2r = nr,
  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)

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 sceptical Bayes factor for standardized mean difference (SMD) effect sizes using an exact t-likelihood for the data instead of the normal approximation used in BFs (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 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.

Author(s)

Samuel Pawel

References

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

BFs, BFslogOR

Examples

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