pSceptical: Computes the sceptical p-value

In ReplicationSuccess: Design and Analysis of Replication Studies

Description

The sceptical p-value is computed based on the z-values of the original and the replication study and the corresponding variance ratio. If specified, a recalibration is applied.

Usage

pSceptical(zo, zr, c, alternative = "one.sided", type = "golden")

Arguments

zo	A vector of z-values from original studies.
zr	A vector of z-values from replication studies.
c	A vector of variance ratios of the original and replication effect estimates. This is usually the ratio of the sample size of the replication study to the sample size of the original study.
alternative	Either "one.sided" or "two.sided". Defaults to "one.sided". If "one.sided" then the sceptical p-value is based on a one-sided assessment of replication success in the direction of the original effect estimate. If "two.sided" then the sceptical p-value is based on a two-sided assessment of replication success regardless of the direction of the original and replication effect estimate.
type	Type of recalibration. Can be either "nominal", "liberal", "controlled" or "golden". Defaults to "golden". Setting type to "nominal" corresponds to no recalibration as in Held et al. (2020). A recalibration is applied if type is "liberal", "controlled" or "golden" and the sceptical p-value can then be interpreted on the same scale as an ordinary p-value (e.g. a one-sided sceptical p-value can be thresholded at the conventional 0.025 level). See ?levelSceptical for details about recalibration types.

Value

The sceptical p-value.

Author(s)

Leonhard Held

References

Held, L. (2020). A new standard for the analysis and design of replication studies (with discussion). Journal of the Royal Statistical Society: Series A (Statistics in Society). 183(2):431 - 448. https://doi.org/10.1111/rssa.12493

Held, L., Micheloud, C. & Pawel, S. (2020). The assessment of replication success based on relative effect size. https://arxiv.org/abs/2009.07782

See Also

sampleSizeReplicationSuccess, powerReplicationSuccess, levelSceptical

Examples

## no recalibration (type = "nominal") as in Held (2020)
pSceptical(zo = p2z(0.01), zr = p2z(0.02), c = 2, alternative = "one.sided",
           type = "nominal")
           
## recalibration with golden level as in Held, Micheloud, Pawel (2020)
pSceptical(zo = p2z(0.01), zr = p2z(0.02), c = 2, alternative = "one.sided",
           type = "golden")

## two-sided p-values 0.01 and 0.02, relative sample size 2
pSceptical(zo = p2z(0.01), zr = p2z(0.02), c = 2, alternative = "one.sided")
## reverse the studies
pSceptical(zo = p2z(0.02), zr = p2z(0.01), c = 1/2, alternative = "one.sided")
## both p-values 0.01, relative sample size 2
pSceptical(zo = p2z(0.01), zr = p2z(0.01), c = 2, alternative = "two.sided")

ReplicationSuccess documentation built on Dec. 2, 2020, 3 p.m.