asht (version 1.0.1)

tukeyWelsch: Tukey-Welsch Pairwise Tests

Description

Calculate pairwise comparisons between groups levels using step down correction for multiple testing.

Usage

tukeyWelsch(y, g, method = c("aov", "kw", "sr", "user"), 
    pvalfunc = NULL, padjfunc = padjTW, maxnTest=10^4,nTestMessage=FALSE, ...)

Value

An object of class 'tukeyWelsch', a list with elements:

fullResults

a list of all the intermediate p-values (unadjusted and adjusted). Not printed by default

method

description of method

data.name

description of input data

ksample.pvalue

p-value for k-sample test

pairwise.pvalues

vector of adjusted p-values for pairwise comparisons

Arguments

y

response vector

g

grouping vector or factor

method

type of method for tests, one of 'aov' (ANOVA which is a t-test for the pairwise comparisons) 'kw' (Kruskal-Wallis test, which is a Wilcoxon-Mann-Whitney test for the pairwise comparisons), 'sr' (studentized range test), or 'user' (user supplied function, see details).

pvalfunc

function to test for effects and return a p-value. Used if method='user'. See details.

padjfunc

function that takes the unadjusted p-value vector from a stage, and returns the adjusted p-value vector for that stage (see details)

maxnTest

maximum number of tests, if the number of tests is larger than maxnTest then gives an error

nTestMessage

logical, print a message at the start of calculations telling how many tests will be calculated

...

additional arguments to pass to XXX (if method='aov'), YYY (if method='kw') or pvalfunc (if method='user')

Author

Michael P. Fay

Details

This function does a k-sample test (either one-way ANOVA [method='aov'] or Kruskal-Wallis test [method='kw']) on the responses when the g vector has k levels. Then it does all the pairwise comparisons (either t.tests [method='aov'] or Wilcoxon-Mann-Whitney tests [method='kw']) giving multiple comparison adjusted p-values. The adjustment uses a step-down method, that is different from (and potentially more powerful than) the single step procedures in pairwise.t.test and pairwise.wilcox.test. The method is described in Einot and Gabriel (1975) [for the anova case] and Campbell and Skillings (1985) for the Kruskal-Wallis case. See also Hochberg and Tamhane (1987, p. 111 for 'aov' case, and p. 247-248 for the 'kw' case).

Here are the details. First, the k-sample test is done, where the type of test is determined by the method. The function repeats that type of test k-1 times, leaving out a different level of the group each time. These are k-1 tests, each having k-1 levels. This process repeats itself (i.e., do choose(k,k-2) tests each having k-2 levels, then do choose(k,k-3) tests each having k-3 levels, etc) until we get to the choose(k,2) pairwise tests. Reject at level aj = 1- (1-alpha)^(j/k), for all tests where there are j groups, for j=2,..,k-2 and at level aj=alpha for j=k-1 and k. These adjusted significance levels are known as the Tukey-Welch (see Hochberg and Tamhane, p. 111) or Ryan (see Einot and Gabriel, 1975) levels. Then we only reject each pairwise comparison, if we reject at all null hypotheses that contain that pair.

We convert this procedure into adjusted p-values, by finding the lowest alpha level such that each pairwise comparison would be rejected, that is its adjusted p-value. The padjfunc is a function that takes the unadjusted p-values and gives the adjustment for each level by itself. For example, the default uses the Tukey-Welch adjusted significance levels, and the function solves for alpha as a function of aj (i.e., inputs unadjP and returns either 1-(1-unadjP^(k/j) for j=2,3,...k-2 or unadjP for j=k-1 or k)). Then taking the individual level adjusted p-values, we define the step-down adjusted p-value for each pairwise comparison as the maximum of all the individual level adjusted p-values for each hypothesis that contains the pair as part of its groups tested.

When k=3, this method gives an adjusted p-value for each pairwise comparison that is the maximum of the k-sample test p-value and the unadjusted p-value for the two-sample test using that pair of levels.

When method='user' the function uses the pvalfunc function to test for p-values. The function must input y and g and output the p-value for the j-sample test, where j is the number of levels present in g. So the function must be defined when j=2,3,...,k.

References

Campbell and Skillings (1985) JASA 998-1003.

Einot and Gabriel (1975) JASA 574-583.

Hochberg, Y and Tamhane, AC (1987) Multiple Comparison Procedures. Wiley: New York.

See Also

pairwise.wilcox.test and pairwise.t.test

Examples

##
createData<-function(n,props,shifts,ry=rnorm){
  k<-length(props)
  if (round(sum(props),8)!=1) stop("sum of props must be 1")
  props<- props/sum(props)
  if (length(shifts)!=k) stop("length of shifts must equal length of props")
  g<-rep(1:k,as.vector(rmultinom(1,n,props)))
  y<-ry(n)
  for (i in 1:k){
    y[g==i]<-y[g==i]+shifts[i]
    }
  list(y=y,g=g)
}
set.seed(1)
d<-createData(100,c(.2,.3,.2,.3),c(0,0,0,1))
tukeyWelsch(d$y,factor(d$g),method="kw")
tukeyWelsch(d$y,factor(d$g),method="aov")
tukeyWelsch(d$y,factor(d$g),method="sr")
TukeyHSD(aov(d$y~factor(d$g)))[[1]][,"p adj"]