coin (version 1.0-24)

pvalue-methods: Extract P-Values

Description

Extracts the p-value from objects representing null distributions of independence tests.

Usage

pvalue(object, ...)

Arguments

object

an object inheriting from class IndependenceTest-class.

...

additional arguments: method, a character specifying the type of adjustment (global, single-step, step-down or discrete) should be used. The default is global

Details

Univariate p-values for maximum-type statistics come with associated 99% confidence interval when resampling was used to determine the null distribution (which may be the case even when distribution = "asypmtotic" was used).

By default, a global p-value is returned. When method = "single-step", adjusted p-values are obtained from a single-step max-T procedure (Westfall & Young, 1993, algorithm 2.5 and formula 2.8). Note that the minimum of the adjusted p-values always controls the familywise error rate (FWER) but the maximum type I error, i.e. the error for each of the individual tests, is only controlled when the subset pivotality condition holds.

When method = "step-down" the free step-down resampling method (algorithm 2.8 and formula 2.8 in Westfall & Young, 1993) is used, the above comments apply as well.

With method = "discrete", the Bonferroni adjustment as suggested by Westfall & Wolfinger (1997) with improvements for highly discrete permutation distributions is available, however, without taking correlations between the test statistics into account. Here, the p-values are valid even without assuming subset pivotality.

References

Peter H. Westfall & S. Stanley Young (1993). Resampling-based Multiple Testing. New York: John Wiley & Sons.

Peter H. Westfall & Russell D. Wolfinger (1997). Multiple tests with discrete distributions. The American Statistician 51, 3--8.

Examples

### artificial 2-sample problem
  df <- data.frame(y = rnorm(20), x = gl(2, 10))
 
  ### Ansari-Bradley test
  at <- ansari_test(y ~ x, data = df, distribution = "exact")
  at

  pvalue(at)

  ### bivariate 2-sample problem
  df <- data.frame(y1 = rnorm(20) + c(rep(0, 10), rep(1, 10)), 
                   y2 = rnorm(20), 
                   x = gl(2, 10))

  it <- independence_test(y1 + y2 ~ x, data = df, 
                          distribution = approximate(B = 9999))
  pvalue(it, method = "single-step")
  pvalue(it, method = "step-down")
  pvalue(it, method = "discrete")