anova.art: Aligned Rank Transform Analysis of Variance

Description

Conduct analyses of variance on aligned rank transformed data.

Usage

# S3 method for art
anova(object, response = c("art", "aligned"), type = c("III",
  "II", "I", 3, 2, 1), factor.contrasts = "contr.sum", test = c("F",
  "Chisq"), all.rows = FALSE, ...)
# S3 method for anova.art
print(x, verbose = FALSE, digits = 5, ...)

Arguments

object

An object of class art.

response

Which response to run the ANOVA on: the aligned responses ("aligned") or the aligned and ranked responses ("art"). This argument is passed to artlm. See 'Details'.

type

Type of ANOVAs to conduct. If type is 1 or "I", then conducts Type I ANOVAs using anova. Otherwise, conducts Type II or Type III ANOVAs using Anova.

factor.contrasts

The name of the contrast-generating function to be applied by default to fixed effect factors. See the first element of options("contrasts"). The default is to use "contr.sum", i.e. sum-to-zero contrasts, which is appropriate for Type III ANOVAs (also the default). This argument is passed to artlm.

test

Test statistic to use. Default "F". Note that some models and ANOVA types may not support "Chisq".

all.rows

Show all rows of the resulting ANOVA tables? By default (FALSE), shows only the rows that are relevant depending on the type of response.

An object of class art.

verbose

When TRUE, sums of squares and reisdual sum of squares in addition to degrees of freedom are printed in some Anova types (e.g. repeated measures Anovas). Default FALSE, for brevity.

digits

Digits of output in printed table; see print.

…

Additional arguments passed to Anova or anova by anova.art or to print by print.anova.art.

Value

An object of class "anova", which usually is printed.

Details

This function runs several ANOVAs: one for each fixed effect term in the model object. In each ANOVA, the independent variables are the same, but the response is aligned by a different fixed effect term (if response is "aligned") or aligned and ranked by that fixed effect term (if response is "art"). These models are generated using artlm.

From each model, only the relevant output rows are kept (unless all.rows is TRUE, in which case all rows are kept).

When response is "art" (the default), only one row is kept from each ANOVA: the row corresponding to fixed effect term the response was aligned and ranked by. These results represent nonparametric tests of significance for the effect of each term on the original response variable.

When response is "aligned", all rows except the row corresponding to the fixed effect term the response was aligned by are kept. If the ART procedure is appropriate for this data, these tests should have all effects "stripped out", and have an F value of ~0. If that is not the case, another analysis should be considered. This diagnostic is tested by summary.art and a warning generated if the F values are not all approximately 0.

References

Wobbrock, J. O., Findlater, L., Gergle, D., and Higgins, J. J. (2011). The Aligned Rank Transform for nonparametric factorial analyses using only ANOVA procedures. Proceedings of the ACM Conference on Human Factors in Computing Systems (CHI '11). Vancouver, British Columbia (May 7-12, 2011). New York: ACM Press, pp. 143-146.