In factorial ANOVA results write-up, what does 'df' stand for?

In the context of factorial ANOVA, 'df' represents degrees of freedom. Degrees of freedom are a critical concept in statistical analysis, reflecting the number of independent values that can vary in the analysis. In factorial ANOVA, degrees of freedom are associated with the number of levels of the factors involved, as well as the total sample size. The calculation of degrees of freedom informs the statistical tests, such as F-tests, used to determine whether there are significant effects of the factors on the dependent variable.

Understanding degrees of freedom is essential because they help to define the distribution that will be used for hypothesis testing. Specifically, they are used in determining critical values from the F-distribution, allowing researchers to make inferences about the data. Without a proper understanding of degrees of freedom, interpreting the results of an ANOVA may lead to incorrect conclusions about the effects of the independent variables on the dependent variable.