thresholdSceptical {ReplicationSuccess}R Documentation

Computes the threshold for the sceptical p-value

Description

The threshold for the sceptical p-value is computed.

Usage

thresholdSceptical(level, alternative = "one.sided", type = "nominal")

Arguments

level

The required one-sided significance level. This can be a vector.

alternative

either "one.sided" or "two.sided". Defaults to "one.sided". Specifies if the threshold is for one-sided or two-sided sceptical p-values.

type

Type of threshold. Default is "nominal" as in Held (2020). This ensures that the Type-I error 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. If "type" is "controlled" then the Type-I error is equal to level^2 if the variance ratio is equal to 1. If "type" is "golden", this ensures that any significant original study can achieve replication success with a replication effect estimate smaller than the original one, provided the replication sample size is sufficiently large.

Value

The threshold 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

Examples

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

[Package ReplicationSuccess version 0.1-3 Index]