| % File src/library/stats/man/friedman.test.Rd |
| % Part of the R package, https://www.R-project.org |
| % Copyright 1995-2007 R Core Team |
| % Distributed under GPL 2 or later |
| |
| \name{friedman.test} |
| \alias{friedman.test} |
| \alias{friedman.test.default} |
| \alias{friedman.test.formula} |
| \title{Friedman Rank Sum Test} |
| \description{ |
| Performs a Friedman rank sum test with unreplicated blocked data. |
| } |
| \usage{ |
| friedman.test(y, \dots) |
| |
| \method{friedman.test}{default}(y, groups, blocks, \dots) |
| |
| \method{friedman.test}{formula}(formula, data, subset, na.action, \dots) |
| } |
| \arguments{ |
| \item{y}{either a numeric vector of data values, or a data matrix.} |
| \item{groups}{a vector giving the group for the corresponding |
| elements of \code{y} if this is a vector; ignored if \code{y} |
| is a matrix. If not a factor object, it is coerced to one.} |
| \item{blocks}{a vector giving the block for the corresponding |
| elements of \code{y} if this is a vector; ignored if \code{y} |
| is a matrix. If not a factor object, it is coerced to one.} |
| \item{formula}{a formula of the form \code{a ~ b | c}, where \code{a}, |
| \code{b} and \code{c} give the data values and corresponding groups |
| and blocks, respectively.} |
| \item{data}{an optional matrix or data frame (or similar: see |
| \code{\link{model.frame}}) containing the variables in the |
| formula \code{formula}. By default the variables are taken from |
| \code{environment(formula)}.} |
| \item{subset}{an optional vector specifying a subset of observations |
| to be used.} |
| \item{na.action}{a function which indicates what should happen when |
| the data contain \code{NA}s. Defaults to |
| \code{getOption("na.action")}.} |
| \item{\dots}{further arguments to be passed to or from methods.} |
| } |
| \details{ |
| \code{friedman.test} can be used for analyzing unreplicated complete |
| block designs (i.e., there is exactly one observation in \code{y} |
| for each combination of levels of \code{groups} and \code{blocks}) |
| where the normality assumption may be violated. |
| |
| The null hypothesis is that apart from an effect of \code{blocks}, |
| the location parameter of \code{y} is the same in each of the |
| \code{groups}. |
| |
| If \code{y} is a matrix, \code{groups} and \code{blocks} are |
| obtained from the column and row indices, respectively. \code{NA}'s |
| are not allowed in \code{groups} or \code{blocks}; if \code{y} |
| contains \code{NA}'s, corresponding blocks are removed. |
| } |
| \value{ |
| A list with class \code{"htest"} containing the following components: |
| \item{statistic}{the value of Friedman's chi-squared statistic.} |
| \item{parameter}{the degrees of freedom of the approximate |
| chi-squared distribution of the test statistic.} |
| \item{p.value}{the p-value of the test.} |
| \item{method}{the character string \code{"Friedman rank sum test"}.} |
| \item{data.name}{a character string giving the names of the data.} |
| } |
| \references{ |
| Myles Hollander and Douglas A. Wolfe (1973), |
| \emph{Nonparametric Statistical Methods.} |
| New York: John Wiley & Sons. |
| Pages 139--146. |
| } |
| \seealso{ |
| \code{\link{quade.test}}. |
| } |
| \examples{ |
| ## Hollander & Wolfe (1973), p. 140ff. |
| ## Comparison of three methods ("round out", "narrow angle", and |
| ## "wide angle") for rounding first base. For each of 18 players |
| ## and the three method, the average time of two runs from a point on |
| ## the first base line 35ft from home plate to a point 15ft short of |
| ## second base is recorded. |
| RoundingTimes <- |
| matrix(c(5.40, 5.50, 5.55, |
| 5.85, 5.70, 5.75, |
| 5.20, 5.60, 5.50, |
| 5.55, 5.50, 5.40, |
| 5.90, 5.85, 5.70, |
| 5.45, 5.55, 5.60, |
| 5.40, 5.40, 5.35, |
| 5.45, 5.50, 5.35, |
| 5.25, 5.15, 5.00, |
| 5.85, 5.80, 5.70, |
| 5.25, 5.20, 5.10, |
| 5.65, 5.55, 5.45, |
| 5.60, 5.35, 5.45, |
| 5.05, 5.00, 4.95, |
| 5.50, 5.50, 5.40, |
| 5.45, 5.55, 5.50, |
| 5.55, 5.55, 5.35, |
| 5.45, 5.50, 5.55, |
| 5.50, 5.45, 5.25, |
| 5.65, 5.60, 5.40, |
| 5.70, 5.65, 5.55, |
| 6.30, 6.30, 6.25), |
| nrow = 22, |
| byrow = TRUE, |
| dimnames = list(1 : 22, |
| c("Round Out", "Narrow Angle", "Wide Angle"))) |
| friedman.test(RoundingTimes) |
| ## => strong evidence against the null that the methods are equivalent |
| ## with respect to speed |
| |
| wb <- aggregate(warpbreaks$breaks, |
| by = list(w = warpbreaks$wool, |
| t = warpbreaks$tension), |
| FUN = mean) |
| wb |
| friedman.test(wb$x, wb$w, wb$t) |
| friedman.test(x ~ w | t, data = wb) |
| } |
| \keyword{htest} |