On this webpage, we describe Real Statistics support for Two-Factor ART ANOVA.
Worksheet Function
Real Statistics Function: The Real Statistics Resource Pack supports the following array function:
Std2Art(R1, head): takes the data in R1 in standard two-factor ANOVA format (i.e. a three-column array whose first two columns consist of the row and column factor labels, and whose third column consists of the corresponding values of the dependent variable) and returns an array with five columns, the first two columns are identical to the first two columns of R1 and the other columns are the ART ranks for rows, columns and interactions; if head = TRUE (default FALSE) then both R1 and the output contain column headings.
You can obtain the results shown in range J25:L42 of Figure 1 of Two-Factor ART ANOVA by using the array formula =Std2Art(A25:C42).
Data Analysis Tool
Real Statistics Data Analysis Tool: ART ANOVA can be performed by using the ART ANOVA option of the Two-Factor ANOVA data analysis tool.
For Example 1 of Two-Factor ART ANOVA, press Ctrl-m and choose the Two-Factor ANOVA option from the Anova tab. This brings up the dialog box shown in Figure 1.
Figure 1 – ART option of Two-Factor ANOVA dialog box
Now, fill in the dialog box as shown in the figure and click on the OK button. The output is displayed in Figure 2.
Figure 2 – ART ANOVA output
References
Wobbrock, J. O., Findlater, L., Gergle, D., Higgins, J. J. (2011) The Aligned Rank Transform for Nonparametric Factorial Analyses Using Only ANOVA Procedures. Conference: Proceedings of the International Conference on Human Factors in Computing Systems, CHI 2011, Vancouver, BC, Canada
https://faculty.washington.edu/wobbrock/pubs/chi-11.06.pdf
Leys, C. and Schumann, S. (2010) A nonparametric method to analyze interactions: The adjusted rank transform test
http://cescup.ulb.be/wp-content/uploads/2015/04/Leys_and_Schumann_nonparametric_interactions.pdf