Download Art-ANOVA here.
Open the file in Microsoft Excel.
Copy the data into the sheet named "Data" according to the instruction below, and the adjusted rank-transformed values could be found in the sheet named "ART Rank".
Insert the adjusted rank-transformed values into statistical packages like the SPSS and you may run factorial-ANOVA as you typically do.
In the Sheet of "Data":
A1...A10 are the columns for placing values of the first independent variable with 10 levels.
B1...B5 are the columns for placing the values of the second independent variable with 5 levels.
• To give you an example of how we input the values in Art-ANOVA, I use the data by Leys and Schumann (2010).
| Group A Time 1 | Group A Time 2 | Group B Time 1 | Group B Time 2 |
Participant 1 | 6 | 2 | 1 | 1 |
Participant 2 | 1 | 3 | 2 | 3 |
Participant 3 | 7 | 2 | 3 | 2 |
Participant 4 | 8 | 1 | 3 | 7 |
Participant 5 | 9 | 1 | 4 | 8 |
• If you input the values as the table above such that A represents Group, and B represents Time:
◦ Group A Time 1 --> A1/B1
◦ Group A Time 2 --> A1/B2
◦ Group B Time 1 --> A2/B1
◦ Group B Time 2 --> A2/B2
In the Sheet of "ART Rank":
The values of rank adjusted transformation are found in the sheet of "ART Rank".
Art-ANOVA, at the present format, can serve a dataset of up to 200 participants, which is typically be adequate for the datasets of most "small" sample experiment. However, the maximum number of participants could be increased by the following method:
In the Sheet of "Data":
Highlight the cells A202 to AY202
Drag the highlighted cells downwards until it reaches the no of participants in your dataset
In the Sheet of "ART Rank":
Highlight the cells A202 to AY202
Drag the highlighted cells downwards until it reaches the no of participants in your dataset
ANOVA is one of the most frequently used statistical methods in research, but it posses assumptions on the sampling and distribution of the dependent variables. Specifically, ANOVA is a parametric test that is supposed to work when the following conditions are met:
Distribution of the dependent variable is normal (i.e., an inverted-U distribution)
Random sampling - independent observations (i.e., no correlation in error terms)
Variances of the dependent variable in separate groups are comparable (i.e., homogeneity of variances)
Violation of these assumptions would lead to increased type I and/or type II error. However, the normality of the data is not easy to uphold, particularly when the sample size is small and the error-variance of the dependent variables is remarkably high (e.g., biological data with the presence of outliers). When the distributions of the dependent variables are deviant from normal distribution, or even when your statistical power in parametric tests is not adequate, Kruskal-Wallis test is a non-parametric test that may do the job of a one-way ANOVA involving 3 levels/groups (or more), however, it can only handle one independent variable in a single analysis. In other words, Kruskal-Wallis test is unable to test the the effects of 2 (or more) independent variables and their interaction. How could we handle non-parametric data involving two (or more) independent variables?
A recent paper by Christophe Leys and Sandy Schumann (Leys & Schumann, 2010) offers us a feasible solution. They applied an adjusted rank-transformation to turn a typical two-way ANOVA into a non-parametric test, and it should theoretically work for two-way or multi-way ANOVA. Though I haven't come across any studies that require me to use adjusted rank transformation in factorial ANOVA, I am inspired by this approach and would like to have a crack of this useful statistical method.
Art-ANOVA is an excel-based spreadsheet written for doing the tedious adjusted rank-transformation procedures outlined by Leys and Schumann (2010). The example given by Leys and Schumann is a 2x2 ANOVA, but I realise the number of levels in the independent variable could sometimes be more than 2. Thus, I have top-up the capacity of Art-ANOVA by allowing an adjusted rank-transformation of a 10x5 ANOVA.
References
The citation looks funny because it's not a software. However, I would be appreciated if you let me know you are using it.
Chan, D. K. C. (2013). Art-ANOVA [Computer software]. Available from www.derwinchan.com.