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E-values for the +1 hypergeometric urn model

find_e_two_types.Rd

Compute e-values for the DrBristol +1 hypergeometric urn model by first obtaining the conservative upper bound on the p-value under the rival theory and then calibrating that p-value into an e-value.

Concretely, this function:

  1. Calls find_p_two_types() with interpretation = FALSE to obtain the upper bound \(p_{\max}\) on the p-value under the +1 urn model. oai_citation:4‡p_value_process_tracing.pdf

  2. Applies e_from_p() to \(p_{\max}\) using the chosen calibration (inverse or κ-calibrator).

Because \(p_{\max}\) is conservative, the resulting e-value is likewise conservative: it is the minimum e-value consistent with the +1 urn model and the chosen calibrator.

Usage

find_e_two_types(
  obs_support,
  total_obs,
  weights = NULL,
  odds = 1,
  method = c("inverse", "kappa"),
  kappa = 0.5,
  cap = Inf,
  interpretation = FALSE
)

Arguments

obs_support

An integer representing the number of observations in favor of the working hypothesis. Must be less than or equal to total_obs.

total_obs

An integer representing the total number of observations made. It can be greater than or equal to the obs_support.

weights

Double vector. Default is equal weight for each observation when weights=NULL is rep(1,obs_support). To indicate that one observation should have twice the weight of any other one might use rep(c(2,1),c(1,obs_support-1))

odds

The odds of observing a rival versus working-theory observation. This can be interpreted as "bias" in observation. Or "relative ease" of observation.

method

Character; passed to e_from_p() (either "inverse" or "kappa").

kappa

Numeric; κ parameter for the "kappa" method.

cap

Upper cap for the returned e-value; passed to e_from_p().

interpretation

Logical. If FALSE (default), return a numeric e-value. If TRUE, return a list with the e-value and a human-readable character string summarizing the result.

Value

If interpretation = FALSE, a single numeric e-value. If interpretation = TRUE, a list with components:

  • e: the e-value (numeric scalar).

  • interp: a character string describing the result.

See also

find_p_two_types(), e_from_p(), sens_urn_evalue()

Examples

# Basic: 7 supportive observations out of 10 total
find_e_two_types(obs_support = 7, total_obs = 10)
#> [1] 53.625

# With textual interpretation
res <- find_e_two_types(
    obs_support = 7, total_obs = 10,
    interpretation = TRUE
)
res$e
#> [1] 53.625
res$interp
#> [1] "Under the +1 hypergeometric urn model, the upper bound on the p-value is p <= 0.01865. Using method='inverse', this corresponds to an e-value of e = 53.62."

# Using κ-calibration
find_e_two_types(
    obs_support = 7, total_obs = 10,
    method = "kappa", kappa = 0.5
)
#> [1] 3.661455