Dunnett's Test for Comparing Several Treatments With a Control

Performs Dunnett's test for comparing several treatments with a control.

DunnettTest(x, ...)

# Default S3 method
DunnettTest(x, g, control = NULL, conf.level = 0.95, ...)

# S3 method for class 'formula'
DunnettTest(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.
control: the level of the control group against which the others should be tested. If there are multiple levels the calculation will be performed for every one.
conf.level: confidence level of the interval.
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

DunnettTest does the post hoc pairwise multiple comparisons procedure.

If x is a list, its elements are taken as the samples to be compared, and hence have to be numeric data vectors. In this case, g is ignored, and one can simply use DunnettTest(x) to perform the test. If the samples are not yet contained in a list, use DunnettTest(list(x, ...)).

Otherwise, x must be a numeric data vector, and g must be a vector or factor object of the same length as x giving the group for the corresponding elements of x.

Value

A list of class c("PostHocTest"), containing one matrix named after the control with columns diff giving the difference in the observed means, lwr.ci giving the lower end point of the interval, upr.ci giving the upper end point and pval giving the p-value after adjustment for the multiple comparisons.

There are print and plot methods for class "PostHocTest". The plot method does not accept xlab, ylab or main arguments and creates its own values for each plot.

Author

Andri Signorell <andri@signorell.net>, the interface is based on R-Core code

References

Dunnett C. W. (1955) A multiple comparison procedure for comparing several treatments with a control, Journal of the American Statistical Association, 50:1096-1121.

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

DunnettTest(list(x, y, z))
#> 
#>   Dunnett's test for comparing several treatments with a control :  
#>     95% family-wise confidence level
#> 
#> $`1`
#>       diff     lwr.ci    upr.ci   pval    
#> 2-1  0.385 -0.6901497 1.4601497 0.5832    
#> 3-1 -0.020 -1.0336608 0.9936608 0.9982    
#> 
#> ---
#> 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"))

DunnettTest(x, g)
#> 
#>   Dunnett's test for comparing several treatments with a control :  
#>     95% family-wise confidence level
#> 
#> $`Normal subjects`
#>                                                            diff     lwr.ci
#> Subjects with obstructive airway disease-Normal subjects  0.385 -0.6901497
#> Subjects with asbestosis-Normal subjects                 -0.020 -1.0336608
#>                                                             upr.ci   pval    
#> Subjects with obstructive airway disease-Normal subjects 1.4601497 0.5832    
#> Subjects with asbestosis-Normal subjects                 0.9936608 0.9982    
#> 
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 

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

DunnettTest(Ozone ~ Month, data = airquality)
#> 
#>   Dunnett's test for comparing several treatments with a control :  
#>     95% family-wise confidence level
#> 
#> $`5`
#>          diff    lwr.ci   upr.ci     pval    
#> 6-5  5.829060 -22.43792 34.09604  0.96467    
#> 7-5 35.500000  15.22870 55.77130  0.00011 ***
#> 8-5 36.346154  16.07486 56.61745 0.000095 ***
#> 9-5  7.832891 -11.90719 27.57297  0.73511    
#> 
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 

DunnettTest(Ozone ~ Month, data = airquality, control="8", conf.level=0.9)
#> 
#>   Dunnett's test for comparing several treatments with a control :  
#>     90% family-wise confidence level
#> 
#> $`8`
#>            diff    lwr.ci     upr.ci     pval    
#> 5-8 -36.3461538 -54.26925 -18.423062 0.000067 ***
#> 6-8 -30.5170940 -55.50965  -5.524537   0.0298 *  
#> 7-8  -0.8461538 -18.76925  17.076938   0.9999    
#> 9-8 -28.5132626 -45.96667 -11.059853   0.0018 ** 
#> 
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>