# How to present a one-way ANOVA when one of the group's variance is “unequal.”

I'm writing a research paper in entomology that compares 6 categorical variables (species) in terms of one dependent anatomic continuous variable. My samples look very normal by box-plots, etc. Looking at the "largest standard deviation can't be more than twice the smallest standard deviation rule of thumb, one of the six samples has a standard deviation that is less than half the largest $0.01847$ vs. $0.05181$). The other st. deviations are all "OK". Sample sizes range from 13 for several species to 32 for another.

Doing a one-way ANOVA on the six samples and ignoring the one species too small st. dev. I get $F > 40$ and a $p$ value of $9.6 \times 10^{-24}$, so I am sure the result is significant.

Can I just do the ANOVA anyway. What comment should I make about the one "smallish" variance? Is it a problem to have very unequal sample sizes? (Mine are 25, 22, 13, 13, 13, 32.)

• @PeterFlom Given that in one-way ANOVA there's no difference between variance of the observations within a level and variance of the error term within a level, what distinction are you drawing there? – Glen_b Jun 2 '14 at 0:48

You have heteroscedasticity, sometimes called "heterogeneity of variance" in ANOVA. This makes the standard confidence intervals and $p$-values invalid. There are many ways to address this issue. I discuss them here: Alternatives to one-way ANOVA for heteroscedastic data. You should read that. Regarding the question of how to present this, you just state the approach you used. There may be subject- or journal-specific conventions for discussing the analyses used, but they should all amount to pretty much the same thing. For example, you could simply say that you used the Welch correction to the degrees of freedom and list the resulting df with your results.