Nemenyi Test

Performs Nemenyi's test of multiple comparisons.

NemenyiTest(x, ...)

# Default S3 method
NemenyiTest(x, g, dist = c("tukey", "chisq"), out.list = TRUE, ...)

# S3 method for class 'formula'
NemenyiTest(formula, data, subset, na.action, ...)

Arguments

x: a numeric vector of data values, or a list of numeric data vectors.
g: a vector or factor object giving the group for the corresponding elements of x. Ignored if x is a list.
dist: the distribution used for the test. Can be tukey (default) or chisq.
out.list: logical, defining if the output should be organized in listform.
formula: a formula of the form lhs ~ rhs where lhs gives the data values and rhs the corresponding groups.
data: an optional matrix or data frame (or similar: see model.frame) containing the variables in the formula formula. By default the variables are taken from environment(formula).
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 NAs. Defaults to getOption("na.action").
...: further arguments to be passed to or from methods.

Details

Nemenyi proposed a test based on rank sums and the application of the family-wise error method to control Type I error inflation, if multiple comparisons are done. The Tukey and Kramer approach uses mean rank sums and can be employed for equally as well as unequally sized samples without ties.

Value

A list of class htest, containing the following components:

statistic: Nemenyi test
p.value: the p-value for the test
null.value: is the value of the median specified by the null hypothesis. This equals the input argument mu.
alternative: a character string describing the alternative hypothesis.
method: the type of test applied
data.name: a character string giving the names of the data.

References

Nemenyi, P. B. (1963) Distribution-Free Multiple Comparisons New York, State University of New York, Downstate Medical Center

Hollander, M., Wolfe, D.A. (1999) Nonparametric Statistical Methods New York, Wiley, pp. 787

Friedman, M. (1937) The use of ranks to avoid the assumption of normality implicit in the analysis of variance Journal of the American Statistical Association, 32:675-701

Friedman, M. (1940) A comparison of alternative tests of significance for the problem of m rankings Annals of Mathematical Statistics, 11:86-92

Author

Andri Signorell <andri@signorell.net>

Examples

## Hollander & Wolfe (1973), 116.
## Mucociliary efficiency from the rate of removal of dust in normal
##  subjects, subjects with obstructive airway disease, and subjects
##  with asbestosis.
x <- c(2.9, 3.0, 2.5, 2.6, 3.2) # normal subjects
y <- c(3.8, 2.7, 4.0, 2.4)      # with obstructive airway disease
z <- c(2.8, 3.4, 3.7, 2.2, 2.0) # with asbestosis

NemenyiTest(list(x, y, z))
#> 
#>  Nemenyi's test of multiple comparisons for independent samples (tukey)  
#> 
#>     mean.rank.diff   pval    
#> 2-1            1.8 0.7972    
#> 3-1           -0.6 0.9720    
#> 3-2           -2.4 0.6686    
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 

## Equivalently,
x <- c(x, y, z)
g <- factor(rep(1:3, c(5, 4, 5)),
            labels = c("Normal subjects",
                       "Subjects with obstructive airway disease",
                       "Subjects with asbestosis"))

NemenyiTest(x, g)
#> 
#>  Nemenyi's test of multiple comparisons for independent samples (tukey)  
#> 
#>                                                                   mean.rank.diff
#> Subjects with obstructive airway disease-Normal subjects                     1.8
#> Subjects with asbestosis-Normal subjects                                    -0.6
#> Subjects with asbestosis-Subjects with obstructive airway disease           -2.4
#>                                                                     pval    
#> Subjects with obstructive airway disease-Normal subjects          0.7972    
#> Subjects with asbestosis-Normal subjects                          0.9720    
#> Subjects with asbestosis-Subjects with obstructive airway disease 0.6686    
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 

## Formula interface.
boxplot(Ozone ~ Month, data = airquality)

NemenyiTest(Ozone ~ Month, data = airquality)
#> 
#>  Nemenyi's test of multiple comparisons for independent samples (tukey)  
#> 
#>     mean.rank.diff     pval    
#> 6-5    12.02991453  0.88737    
#> 7-5    41.21153846 0.000097 ***
#> 8-5    38.53846154  0.00035 ***
#> 9-5    11.99734748  0.67819    
#> 7-6    29.18162393  0.16373    
#> 8-6    26.50854701  0.24773    
#> 9-6    -0.03256705  1.00000    
#> 8-7    -2.67307692  0.99853    
#> 9-7   -29.21419098  0.01136 *  
#> 9-8   -26.54111406  0.02867 *  
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 

# Hedderich & Sachs, 2012, p. 555
d.frm <- data.frame(x=c(28,30,33,35,38,41, 36,39,40,43,45,50, 44,45,47,49,53,54),
                    g=c(rep(LETTERS[1:3], each=6)), stringsAsFactors=TRUE)

NemenyiTest(x~g, d.frm)
#> 
#>  Nemenyi's test of multiple comparisons for independent samples (tukey)  
#> 
#>     mean.rank.diff   pval    
#> B-A       5.583333 0.1658    
#> C-A      10.416667 0.0021 ** 
#> C-B       4.833333 0.2595    
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>