saviTTestStat: Computes E-Values Based on the T-Statistic
In safestats: Safe Anytime-Valid Inference

saviTTestStat

R Documentation

Computes E-Values Based on the T-Statistic

Description

A summary stats version of saviTTest() with the data replaced by t, n1 and n2, and the design object by parameter

This is saviTTestStat() based on t-densities instead of hypergeometric functions.

Evidence for practical equivalence requires the e-value to be small, i.e. smaller than alphaRelevance. If the alternative holds true, i.e. deltaTrue >= relevanceSize, then there is no more than alphaRelevance probability of ever seeing eRelevance <= alphaRelevance.

Usage

saviTTestStat(
  t,
  n1,
  n2 = NULL,
  parameter,
  alternative = c("twoSided", "less", "greater"),
  tDensity = FALSE,
  paired = FALSE,
  nuMin = 2,
  eType = c("mom", "eGauss", "imom", "eCauchy", "grow", "lai"),
  ...
)

saviTTestStatNEffNu(
  t,
  nEff,
  nu,
  parameter,
  alternative = c("twoSided", "less", "greater"),
  tDensity = FALSE,
  paired = FALSE,
  nuMin = 2,
  eType = c("mom", "eGauss", "imom", "eCauchy", "grow", "lai"),
  ...
)

saviTTestStatNEffNuMom(
  t,
  nEff,
  nu,
  parameter,
  alternative = c("twoSided", "less", "greater"),
  tDensity = FALSE,
  paired = FALSE,
  k = 1,
  ...
)

saviTTestStatNEffNuGrow(
  t,
  nEff,
  nu,
  parameter,
  alternative = c("twoSided", "less", "greater"),
  tDensity = FALSE,
  paired = FALSE,
  ...
)

saviTTestStatTDensity(
  t,
  parameter,
  nu,
  nEff,
  alternative = c("twoSided", "less", "greater"),
  paired = FALSE,
  ...
)

saviRelevanceTStatNEffNu(
  t,
  nEff,
  nu,
  parameter = NULL,
  alternative = c("twoSided", "less", "greater"),
  eType = "grow",
  tDensity = FALSE,
  paired = FALSE,
  relevanceSize,
  nuMin = 2,
  ...
)

Arguments

`t`	numeric that represents the observed t-statistic.
`n1`	integer that represents the size of the (first) sample. Default n2=`NULL` implies a one-sample T-test.
`n2`	an optional integer that represents the size of the second sample, which implies a two-sample t-statistic
`parameter`	numeric > 0, the savi test defining parameter, see `matchEParameterWith` for details.
`alternative`	a character string specifying the alternative hypothesis. Must be one of "twoSided" (default), "greater" or "less".
`tDensity`	Uses the the representation of the savi T-test as the likelihood ratio of t densities.
`paired`	a logical, if `TRUE` then pair the data.
`nuMin`	numeric > 0, the minimum degrees of freedom under which the results are trivial, thus, 1.
`eType`	character one of "mom", "grow", "eGauss", and "eCauchy". "mom" is default and uses a non-local moment prior with bump(s) at meanDiffMin, "grow" uses point prior(s) at meanDiffMin, "eGauss" a zero-centred normal prior, "eCauchy" a zero centred Cauchy prior.
`...`	further arguments to be passed to or from methods, but mainly to perform do.calls.
`nEff`	numeric > 0, the effective sample size. For one sample tests, this is just n.
`nu`	numeric > 0, the degrees of freedom.
`k`	the moment used for the non-local moment prior. Default 1
`relevanceSize`	numeric, the minimal clinical relevant mean difference that we do not want to miss under the alternative. Default relevanceSize=NULL implies relevanceSize=abs(meanDiffMin)

Value

Returns a numeric that represent the e10, that is, the e-value in favour of the alternative over the null

References

Grünwald, P. D., de Heide, R., & Koolen, W. (2024). Safe testing. Journal of the Royal Statistical Society. Series B (Methodological), 86(5), 1091-1128. (With discussions), https://doi.org/10.1093/jrsssb/qkae011. Ly, A, Boehm, Grünwald, P. D., Ramdas, A., & van Ravenzwaaij, D. (2024). Safe Anytime-Valid Inference: Practical maximally flexible sampling designs for experiments based on e-values. PsyArXiv Preprint, https://doi.org/10.31234/osf.io/h5vae. Pérez-Ortiz, M. F., Lardy, T., de Heide, R., & Grünwald, P. D. (2024). E-statistics, group invariance and anytime valid testing. The Annals of Statistics, 52(4), 1410-1432, http://dx.doi.org/10.1214/24-AOS2394. Wang, H., & Ramdas, A. (in press). Anytime-valid t-tests and confidence sequences for Gaussian means with unknown variance. Sequential Analysis, https://doi.org/10.48550/arXiv.2310.03722.

Examples

saviTTestStat(t=1, n1=100, parameter=0.4)
saviTTestStat(t=3, n1=100, parameter=0.3)
# evidence for the alternative over minimal efficacy
saviRelevanceTStatNEffNu(t=3, nEff=100, nu=60, parameter=0.4)
# evidence for minimal efficacy over the alternative
saviRelevanceTStatNEffNu(t=0.35, nEff=100, nu=60, parameter=0.4)

safestats documentation built on Sept. 6, 2026, 1:06 a.m.