tamhaneT2Test {PMCMRplus} | R Documentation |
Performs Tamhane's T2 (or T2') all-pairs comparison test for normally distributed data with unequal variances.
tamhaneT2Test(x, ...) ## Default S3 method: tamhaneT2Test(x, g, welch = TRUE, ...) ## S3 method for class 'formula' tamhaneT2Test(formula, data, subset, na.action, welch = TRUE, ...) ## S3 method for class 'aov' tamhaneT2Test(x, welch = TRUE, ...)
x |
a numeric vector of data values, a list of numeric data vectors or a fitted model object, usually an aov fit. |
... |
further arguments to be passed to or from methods. |
g |
a vector or factor object giving the group for the
corresponding elements of |
welch |
indicates, whether Welch's approximate solution for
calculating the degree of freedom shall be used or, as usually,
df = N - 2. Defaults to |
formula |
a formula of the form |
data |
an optional matrix or data frame (or similar: see
|
subset |
an optional vector specifying a subset of observations to be used. |
na.action |
a function which indicates what should happen when
the data contain |
For all-pairs comparisons in an one-factorial layout with normally distributed residuals but unequal groups variances the T2 test (or T2' test) of Tamhane can be performed. A total of m = k(k-1)/2 hypotheses can be tested. The null hypothesis H_{ij}: μ_i(x) = μ_j(x) is tested in the two-tailed test against the alternative A_{ij}: μ_i(x) \ne μ_j(x), ~~ i \ne j.
T2 test uses Welch's approximate solution for calculating the degree of freedom. T2' test uses the usual df = N - 2 approximation. A warning message appears in the modified T2' test, if none of in Tamhane (1979) given conditions for nearly balanced sample sizes and nearly balanced standard errors is true.
The p-values are computed from the t-distribution and adjusted according to Dunn-Sidak.
A list with class "PMCMR"
containing the following components:
a character string indicating what type of test was performed.
a character string giving the name(s) of the data.
lower-triangle matrix of the estimated quantiles of the pairwise test statistics.
lower-triangle matrix of the p-values for the pairwise tests.
a character string describing the alternative hypothesis.
a character string describing the method for p-value adjustment.
a data frame of the input data.
a string that denotes the test distribution.
T2 test is basically an all-pairs pairwise-t-test. Similar results
can be obtained with pairwise.t.test(..., var.equal=FALSE, p.adjust.mehod = FALSE)
.
Thanks to Sirio BolaƱos for his kind suggestion for adding T2' test into this function.
Tamhane, A. C. (1979) A Comparison of Procedures for Multiple Comparisons of Means with Unequal Variances, Journal of the American Statistical Association 74, 471–480.
fit <- aov(weight ~ feed, chickwts) shapiro.test(residuals(fit)) bartlett.test(weight ~ feed, chickwts) # var1 = varN anova(fit) ## also works with fitted objects of class aov res <- tamhaneT2Test(fit) summary(res) summaryGroup(res) res ## compare with pairwise.t.test WT <- pairwise.t.test(chickwts$weight, chickwts$feed, pool.sd = FALSE, p.adjust.method = "none") p.adj.sidak <- function(p, m) sapply(p, function(p) min(1, 1 - (1 - p)^m)) p.raw <- as.vector(WT$p.value) m <- length(p.raw[!is.na(p.raw)]) PADJ <- matrix(ans <- p.adj.sidak(p.raw, m), nrow = 5, ncol = 5) colnames(PADJ) <- colnames(WT$p.value) rownames(PADJ) <- rownames(WT$p.value) PADJ ## same without Welch's approximate solution summary(T2b <- tamhaneT2Test(fit, welch = FALSE))