Conditions for ANOVA – Learn It 3

  • Check the conditions for a one-way ANOVA hypothesis test

Variability

The third condition is about the variability within groups.

The groups being compared should have equal or similar variability within their groups. There are formal tests that can be used to assess the similarity of variability among ANOVA groups, but they are beyond the scope of this course.

Instead, we can visually estimate variability by comparing boxplots of data or numerically comparing the standard deviations provided in summary statistics. Remember that the box in a boxplot visually represents the middle [latex]50\%[/latex] of the data and is the size of the interquartile range. While this is not a measurement of the standard deviation, a boxplot allows us to visually compare the spread or variability in each group.

variability in ANOVA

A good rule of thumb is:

  • If the sample sizes are equal, the largest standard deviation can be no more than two times the smallest standard deviation.
  • If the sample sizes are different, the standard deviations need to be really similar.