Description Usage Arguments Details Value Note References Examples

Transforms a two-sided p-value to a minimum Bayes factor. That minimum Bayes factor is obtained by modelling the distributions of the p-value under the null and the alternative hypothesis, respectively.

1 | ```
pCalibrate(p, type="exploratory", transform="id")
``` |

`p` |
a vector of two-sided p-values |

`type` |
either |

`transform` |
either |

If `type="exploratory"`

is used,
the so-called "- e p log(p)" calibration (Sellke et al., 2001)
is applied.

If `type="confirmatory"`

is used,
the the so-called "- e q log(q)" calibration with q=1-p (Held & Ott, 2018)
is applied.

`type="exploratory"`

gives a larger minimum Bayes factor than `type="confirmatory"`

.

Under the null hypothesis, the distribution of the p-value
is assumed to be uniform.
Under the alternative, the p-value is assumed to have a beta-distribution
with monotonically decreasing density function under both alternatives,
with different parameters however.
If `type="exploratory"`

, the prior sample size
does not exceed 2, whereas for `type="confirmatory"`

,
the prior sample size is at least 2.
The latter calibration may be appropriate for small sample size,
but for larger sample size it is too conservative (Held & Ott, 2018).

Note that for the "- e p log(p)" calibration, alternative derivations which do not assume a beta-distribution under the alternative have also been given, see Sellke et al. (2001).

A numeric vector of minimum Bayes factors for the specified p-values

The argument `type`

replaces the argument `alternative`

in version 0.1-1 of this package.

`type="exploratory"`

corresponds to `alternative="noninformative"`

and

`type="confirmatory"`

corresponds to `alternative="informative"`

.

Held, L. and Ott, M. (2018). On p-values and Bayes factors.
*Annual Review of Statistics and Its Application*, **5**, 393–419.

Sellke, T., Bayarri, M. J. and Berger, J. O. (2001). Calibration of p values for testing precise null hypotheses.
*The American Statistician*, **55**, 62–71.

Vovk, V. G. (1993). A logic of probability, with application to the foundations of statistics (with discussion and a reply by the author). *Journal of the Royal Statistical Society, Series B*, **55**, 317–351.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 | ```
pCalibrate(p=c(0.05, 0.01, 0.001))
pCalibrate(p=c(0.05, 0.01, 0.001), type="confirmatory")
# plot the 2 calibrations as a function of the p-value
par(las=1)
p <- exp(seq(log(0.0001), log(0.3), by=0.01))
minBF1 <- pCalibrate(p=p)
minBF2 <- pCalibrate(p=p, type="confirmatory")
plot(p, minBF1, type="l", log="xy",
xlab="Two sided p-value", ylab="Minimum Bayes factor",
axes=FALSE, lwd=2, col=1)
lines(p, minBF2, col=2, lwd=2)
axis(1, at=c(0.0001, 0.0003, 0.001, 0.003, 0.01, 0.03, 0.1, 0.3),
as.character(c(format(c(0.0001,0.0003), nsmall=4, digits=4,
scientific=FALSE),
c(0.001, 0.003, 0.01, 0.03, 0.1, 0.3))))
my.values <- c(3000, 1000, 300, 100, 30, 10, 3, 1)
my.at <- 1/my.values
my.ylegend <- c(paste("1/", my.values[-length(my.values)], sep=""), "1")
axis(2, at=my.at, my.ylegend)
box()
legend("bottomright", lty=1, lwd=2,
legend=c("- e p log(p)", "- e q log(q)")
, col=c(1,2))
``` |

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