Computes the replication success level — levelSceptical • ReplicationSuccess

The replication success level is computed based on the specified alternative and recalibration type.

levelSceptical(
  level,
  c = NA,
  alternative = c("one.sided", "two.sided"),
  type = c("golden", "nominal", "controlled")
)

Arguments

level: Threshold for the calibrated sceptical p-value. Default is 0.025.
c: The variance ratio. Only required when type = "controlled".
alternative: Specifies if level is "one.sided" (default) or "two.sided". If "one-sided", then a one-sided replication success level is computed.
type: Type of recalibration. Can be either "golden" (default), "nominal" (no recalibration), or "controlled". "golden" ensures that for an original study just significant at the specified level, replication success is only possible for replication effect estimates larger than the original one. "controlled" ensures exact overall Type-I error control at level level^2.

Value

Replication success levels

Details

levelSceptical is the vectorized version of the internal function .levelSceptical_. Vectorize is used to vectorize the function.

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

Held, L. (2020). The harmonic mean chi-squared test to substantiate scientific findings. Journal of the Royal Statistical Society: Series C (Applied Statistics), 69, 697-708. doi:10.1111/rssc.12410

Held, L., Micheloud, C., Pawel, S. (2022). The assessment of replication success based on relative effect size. The Annals of Applied Statistics, 16, 706-720. doi:10.1214/21-AOAS1502

Micheloud, C., Balabdaoui, F., Held, L. (2023). Assessing replicability with the sceptical p-value: Type-I error control and sample size planning. Statistica Neerlandica. doi:10.1111/stan.12312

Author

Leonhard Held

Examples

levelSceptical(level = 0.025, alternative = "one.sided", type = "nominal")
#> [1] 0.025
levelSceptical(
  level = 0.025,
  alternative = "one.sided",
  type = "controlled",
  c = 1
)
#> [1] 0.06530978
levelSceptical(level = 0.025, alternative = "one.sided", type = "golden")
#> [1] 0.06167928