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

The project power of the sceptical p-value is computed for a specified level of replication success, the relative variance, significance level and power for a standard significance test of the original study, and the alternative hypothesis.

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`level` |
Numeric vector of levels of replication success. |

`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. |

`alpha` |
Significance level for a standard significance test in the original study. |

`power` |
Power to detect the assumed effect with a standard significance test in the original study. |

`alternative` |
Either "one.sided" (default), "two.sided", "greater", or "less". If "one.sided", the type-I error rate is computed based on a one-sided assessment of replication success in the direction of the original effect estimate. If "two.sided", the type-I error rate is computed based on a two-sided assessment of replication success regardless of the direction of the original and replication effect estimate. If "greater" or "less", the type-I error rate is computed based on a one-sided assessment of replication success in the pre-specified direction of the original and replication effect estimate. |

`type` |
Type of recalibration. Can be either "golden" (default),
"nominal" (no recalibration), "liberal", or "controlled".
"golden" ensures that for an original study just significant
at the specified |

`PPpSceptical`

is the vectorized version of `.PPpSceptical_`

.
`Vectorize`

is used to vectorize the function.

The project power.

Samuel Pawel, Leonhard Held

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. (2021). The assessment of replication success based on relative effect size. https://arxiv.org/abs/2009.07782

Maca, J., Gallo, P., Branson, M., and Maurer, W. (2002). Reconsidering some aspects
of the two-trials paradigm. *Journal of Biopharmaceutical Statistics*, **12**,
107-119. doi: 10.1081/bip-120006450

`pSceptical`

, `levelSceptical`

, `T1EpSceptical`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | ```
## compare project power for different levels of replication success
levels <- c("nominal" = levelSceptical(level = 0.025, type = "nominal"),
"liberal" = levelSceptical(level = 0.025, type = "liberal"),
"controlled" = levelSceptical(level = 0.025, type = "controlled"),
"golden" = levelSceptical(level = 0.025, type = "golden"))
c <- seq(0.4, 5, by = 0.01)
alpha <- 0.025
power <- 0.9
pp <- sapply(X = levels, FUN = function(l) {
PPpSceptical(level = l, c = c, alpha, power, alternative = "one.sided",
type = "nominal")
})
## compute project power of 2 trials rule
za <- qnorm(p = 1 - alpha)
mu <- za + qnorm(p = power)
pp2TR <- power*pnorm(q = za, mean = sqrt(c)*mu, lower.tail = FALSE)
matplot(x = c, y = pp*100, type = "l", lty = 1, lwd = 2, las = 1, log = "x",
xlab = bquote(italic(c)), ylab = "Project power (%)", xlim = c(0.4, 5),
ylim = c(0, 100))
lines(x = c, y = pp2TR*100, col = length(levels) + 1, lwd = 2)
abline(v = 1, lty = 2)
abline(h = 90, lty = 2, col = "lightgrey")
legend("bottomright", legend = c(names(levels), "2TR"), lty = 1, lwd = 2,
col = seq(1, length(levels) + 1))
``` |

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