levelSceptical: Computes the level for the sceptical p-value

In ReplicationSuccess: Design and Analysis of Replication Studies

Description

The level for the sceptical p-value is computed based on the specified alternative and calibration type.

Usage

levelSceptical(level, alternative = "one.sided", type = "golden")

Arguments

level	The required significance level. This can be a vector.
alternative	Either "one.sided" or "two.sided". Defaults to "one.sided". Specifies if the significance level is one-sided or two-sided. If the significance level is one-sided, then a one-sided level for the sceptical p-value is computed.
type	Type of calibration. Can be either "nominal", "liberal", "controlled" or "golden". Defaults to "golden". This type ensures that for an original study just significant at the specified level, replication success is only possible if the replication effect estimate larger than the original one. If "type" is "controlled" then the type-I error rate is equal to level^2 (for alternative = "two.sided") or 2 *level^2 (for alternative = "one.sided") if the variance ratio is equal to 1. The type "nominal" ensures that the type-I error rate is always smaller than level^2. Significance of both the original and replication study at level is then a necessary but not sufficient requirement for replication success. If "type" is "liberal" then significance of both studies is a sufficient requirement for replication success if the variance ratio is equal to 1.

Value

The level for 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, 431-448. https://doi.org/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. https://doi.org/10.1111/rssc.12410

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

pSceptical, T1EpSceptical

Examples

levelSceptical(level = 0.025, type = "nominal")
levelSceptical(level = 0.025, type = "liberal")
levelSceptical(level = 0.025, type = "controlled")
levelSceptical(level = 0.025, type = "golden")

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