sampleSizeSignificance: 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 significance of the replication study is computed based on the z-value of the original study, the significance level and either the power or the minimum relative effect size. When the approach based on power is used, the arguments design prior, shrinkage, and relative heterogeneity also have to be specified.

sampleSizeSignificance(
  zo,
  power = NA,
  d = NA,
  level = 0.025,
  alternative = c("one.sided", "two.sided"),
  designPrior = c("conditional", "predictive", "EB"),
  h = 0,
  shrinkage = 0
)

`zo`	A 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).
`level`	Significance level. Default is 0.025.
`alternative`	Either "one.sided" (default) or "two.sided". Specifies direction of the alternative. "one.sided" assumes an effect in the same direction as the original estimate.
`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).
`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).
`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 towards zero (e.g., `shrinkage = 0.25` implies shrinkage by a factor of 25%). Is only taken into account when `designPrior` is "conditional" or "predictive".

sampleSizeSignificance is the vectorized version of .sampleSizeSignificance_. Vectorize is used to vectorize the function.

The relative sample size to achieve significance in the specified direction. If impossible to achieve the desired power for specified inputs NaN is returned.

Leonhard Held, Samuel Pawel, Charlotte Micheloud, 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

Pawel, S., Held, L. (2020). Probabilistic forecasting of replication studies. PLoS ONE. 15, e0231416. doi: 10.1371/journal.pone.0231416

Held, L., Micheloud, C., Pawel, S. (2021). The assessment of replication success based on relative effect size. https://arxiv.org/abs/2009.07782

powerSignificance

sampleSizeSignificance(zo = p2z(0.005), power = 0.8)
sampleSizeSignificance(zo = p2z(0.005, alternative = "two.sided"), power = 0.8)
sampleSizeSignificance(zo = p2z(0.005), power = 0.8, designPrior = "predictive")

sampleSizeSignificance(zo = 3, power = 0.8, designPrior = "predictive",
                       shrinkage = 0.5, h = 0.25)
sampleSizeSignificance(zo = 3, power = 0.8, designPrior = "EB",  h = 0.5)

# sample size to achieve  0.8 power as function of original p-value
zo <- p2z(seq(0.0001, 0.05, 0.0001))
oldPar <- par(mfrow = c(1,2))
plot(z2p(zo), sampleSizeSignificance(zo = zo, designPrior = "conditional", power = 0.8),
     type = "l", ylim = c(0.5, 10), log = "y", lwd = 1.5, ylab = "Relative sample size",
     xlab = expression(italic(p)[o]), las = 1)
lines(z2p(zo), sampleSizeSignificance(zo = zo, designPrior = "predictive", power = 0.8),
      lwd = 2, lty = 2)
lines(z2p(zo), sampleSizeSignificance(zo = zo, designPrior = "EB", power = 0.8),
      lwd = 1.5, lty = 3)
legend("topleft", legend = c("conditional", "predictive", "EB"),
       title = "Design prior", lty = c(1, 2, 3), lwd = 1.5, bty = "n")

sampleSizeSignificance(zo = p2z(0.005), d = 1)
sampleSizeSignificance(zo = p2z(0.005), d = 0.5)
# sample size based on minimum relative effect size of 0.8
zo <- p2z(seq(0.0001, 0.05, 0.0001))
plot(z2p(zo), sampleSizeSignificance(zo = zo, d = 0.8, level = 0.025),
     type = "l", ylim = c(0.5, 10), log = "y", lwd = 1.5, ylab = "Relative sample size",
    xlab = expression(italic(p)[o]), las = 1)
par(oldPar)