sampleSizeReplicationSuccess: Computes the required relative sample size to achieve...
In florafauna/RStest: Design and Analysis of Replication Studies

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

The relative sample size to achieve replication success is computed based on the z-value of the original study, the replication success level, the type of recalibration and either the power or the minimum relative effect size. When the approach based on power is used, the design prior also has to be specified.

sampleSizeReplicationSuccess(
  zo,
  power = NA,
  d = NA,
  level = 0.025,
  alternative = c("one.sided", "two.sided"),
  type = c("golden", "nominal", "liberal", "controlled"),
  designPrior = c("conditional", "predictive", "EB"),
  shrinkage = 0,
  h = 0
)

`zo`	Numeric vector of z-values from original studies.
`power`	The power to achieve replication success.
`d`	The minimum relative effect size (ratio of the effect estimate from the replication study to the effect estimate from the original study) to achieve replication success.
`level`	Numeric vector of replication success levels. The default is 0.025.
`alternative`	Either "one.sided" (default) or "two.sided". Specifies if the replication success level is one-sided or two-sided.
`type`	Type of recalibration. Can be either "golden" (default), "nominal" (no recalibration), "liberal", "controlled". "golden" ensures that for an original study just significant at the specified `level`, replication success is only possible if the replication effect estimate is at least as large as the original one. See `levelSceptical` for details about recalibration types.
`designPrior`	Is only taken into account when `power` is specified. 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).
`shrinkage`	Is only taken into account when `power` is specified. A number in [0,1) with default 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 when the `designPrior` is "conditional" or "predictive".
`h`	Is only taken into account when `power` is specified and `designPrior` is "predictive" or "EB". The relative between-study heterogeneity, i.e., the ratio of the heterogeneity variance to the variance of the original effect estimate. Default is 0 (no heterogeneity).

sampleSizeReplicationSuccess is the vectorized version of .sampleSizeReplicationSuccess_. Vectorize is used to vectorize the function.

The relative sample size for replication success. If impossible to achieve the desired power for specified inputs NaN is returned.

Leonhard Held, Charlotte Micheloud, Samuel Pawel, Florian Gerber

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

pSceptical, powerReplicationSuccess, levelSceptical

## based on power
sampleSizeReplicationSuccess(zo = p2z(0.0025), power = 0.8, level = 0.025,
                             type = "golden")
sampleSizeReplicationSuccess(zo = p2z(0.0025), power = 0.8, level = 0.025,
                             type = "golden", designPrior = "predictive")

## based on minimum relative effect size
sampleSizeReplicationSuccess(zo = p2z(0.0025), d = 0.9, level = 0.025,
                             type = "nominal")
sampleSizeReplicationSuccess(zo = p2z(0.0025), d = 0.9, level = 0.025,
                             type = "golden")