Robustness of Normality
According to the lecture and handout, ANOVA is robust to normality with relatively equal cell sizes, no outliers, dferror>= 20, and two tailed test.
1. What it is meant to be relatively equal cell sizes? My model has n=40, 45, and 49. Is it relatively equal?
2. If so, do I still need to do QQ plot to check normality? Do I still need to do transformation if the line is not straight?
1. What it is meant to be relatively equal cell sizes? My model has n=40, 45, and 49. Is it relatively equal?
2. If so, do I still need to do QQ plot to check normality? Do I still need to do transformation if the line is not straight?
posted by Sun @ 12:01 PM
6 Comments:
At 1:13 PM,
Justin said…
Those cell sizes seem relatively equal. Things start to get crazy when cell sizes differ 4:1 or more.
If you believe your model to be robust to normality, you do not need to run a Q-Q plot or histogram, because ANOVA can handle any deviation from normality (if there is any).
Be sure to note in your section on assumptions that ANOVA was robust to normality and that is why you did not check it.
At 3:01 PM,
Mari said…
Let me temper that just a tiny bit. ANOVA is robust to the assumption of normality, which means that MINOR deviations from normality will not wreck it. SEVERE deviations are still problematic, so you should still check the assumption...
At 6:55 PM,
Amy said…
Would a 5:1 ratio be considered relatively equal? I'm looking at an analysis with that approximate break down and am wondering whether this is problematic for homogeneity of variance.
At 9:01 PM,
Mari said…
5:1 is pretty discrepant.
Some would argue that 3:1 is as discrepant as you'd want to get and call it roughly equal. However, given that Fmax uses 4:1 as a criteria, you can go with that one, as Justin suggested above.
Note that the ratio, in and of itself, isn't problematic for normality or for homogeneity of variance. It is when you have (a) very unequal cell sizes AND a markedly nonnormal distribution by Q-Q plot or histogram (for normality) or (b) very unequal cell sizes AND a violation of Levene's/Fmax (for homogeneity of variance) that trouble arises.
At 9:36 AM,
Amy said…
This comment has been removed by the author.
At 10:43 AM,
Amy said…
What would you consider a "markedly" nonnormal distribution? My DV distribution is slightly negatively skewed and not helped by transformations. Since my cell sizes differ 4:1, is this problematic? And if so, do I just report the problem and continue on with the analysis, or do I need to pick a different hypothesis?
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