What is the appropriate level for the independent variable in a one-way between groups ANOVA?

The independent variable in a one-way between groups ANOVA must be at a level that allows for group comparisons. A categorical level is ideal because it divides the data into distinct groups or categories based on the independent variable. This distinction is crucial, as the purpose of a one-way ANOVA is to assess whether there are any statistically significant differences between the means of these groups.

In a one-way ANOVA, the independent variable should define the groups being compared, which is characteristic of categorical variables. For instance, you might compare the effectiveness of different therapeutic approaches (e.g., cognitive behavioral therapy vs. psychodynamic therapy) where the approach is categorized.

The other levels listed, such as ordinal, interval, and nominal, do not meet the requirements for the independent variable in a one-way ANOVA. Ordinal variables rank values but do not provide distinct categories suitable for comparative analysis of means in the context of ANOVA. Interval variables offer numerical scales but typically refer to the dependent variable being measured. Nominal variables are classifications without a specific order, but they can be considered a subset of categorical variables. Therefore, while nominal might seem relevant, it is not as descriptive of the role of the independent variable in terms of distinct group categorization as 'categorical