powerReplicationSuccess: Computes the power for replication success
In florafauna/RStest: Design and Analysis of Replication Studies

Description Usage Arguments Details Value Author(s) References See Also Examples

Computes the power for replication success based on the result of the original study, the corresponding variance ratio, and the design prior.

powerReplicationSuccess(
  zo,
  c = 1,
  level = 0.025,
  designPrior = c("conditional", "predictive", "EB"),
  alternative = c("one.sided", "two.sided"),
  type = c("golden", "nominal", "liberal", "controlled"),
  shrinkage = 0,
  h = 0,
  strict = FALSE
)

`zo`	Numeric vector of z-values from original studies.
`c`	Numeric 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.
`level`	Numeric vector of replication success levels. The default is 0.025.
`designPrior`	Either "conditional" (default), "predictive", or "EB". If "EB", the power is computed under a predictive distribution, where the contribution of the original study is shrunken towards zero based on the evidence in the original study (with an empirical Bayes shrinkage estimator).
`alternative`	Either "one.sided" (default) or "two.sided". Specifies if the replication success level is one-sided or two-sided. If the replication success level is one-sided, then power calculations are based on a one-sided assessment of replication success in the direction of the original effect estimates.
`type`	Recalibration type can be either "golden" (default), "nominal" (no recalibration), "liberal", or "controlled". `type` = "golden" ensures that for an original study just significant at the specified `level`, replication success is only possible if the replication effect estimate is larger than the original one. See `levelSceptical` for details about recalibration types.
`shrinkage`	Numeric vector with values in [0,1). Defaults to 0. Specifies the shrinkage of the original effect estimate towards zero, e.g., the effect is shrunken by a factor of 25% for `shrinkage = 0.25`. Is only taken into account if the `designPrior` is "conditional" or "predictive".
`h`	Numeric vector of relative heterogeneity variances i.e., the ratio of the heterogeneity variance to the variance of the original effect estimate. Default is 0 (no heterogeneity). Is only taken into account when `designPrior` = "predictive" or `designPrior` = "EB".
`strict`	Logical vector indicating whether the probability for replication success in the opposite direction of the original effect estimate should also be taken into account. Default is `FALSE`. Only taken into account when `alternative` = "two.sided".

powerReplicationSuccess is the vectorized version of .powerReplicationSuccess_. Vectorize is used to vectorize the function.

The power for replication success.

Leonhard Held, Charlotte Micheloud, Samuel Pawel

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, 431-448. doi: 10.1111/rssa.12493

Held, L., Micheloud, C., Pawel, S. (2021). The assessment of replication success based on relative effect size. https://arxiv.org/abs/2009.07782

sampleSizeReplicationSuccess, pSceptical, levelSceptical

## larger sample size in replication (c > 1)
powerReplicationSuccess(zo = p2z(0.005), c = 2, level = 0.025, designPrior = "conditional")
powerReplicationSuccess(zo = p2z(0.005), c = 2, level = 0.025, designPrior = "predictive")

## smaller sample size in replication (c < 1)
powerReplicationSuccess(zo = p2z(0.005), c = 1/2, level = 0.025, designPrior = "conditional")
powerReplicationSuccess(zo = p2z(0.005), c = 1/2, level = 0.025, designPrior = "predictive")

powerReplicationSuccess(zo = p2z(0.00005), c = 2, level = 0.05, 
                        alternative = "two.sided",  strict = TRUE, shrinkage = 0.9)
powerReplicationSuccess(zo = p2z(0.00005), c = 2, level = 0.05, 
                        alternative = "two.sided", strict = FALSE, shrinkage = 0.9)