# I want to do an nested ANOVA but my variances are very unequal

I have data that were collected at a number of sites, and each site was located within one of three zones (Lake Ontario, Erie and the St. Lawrence), so I was hoping to do nested ANOVAs to compare between sites and zones. Unfortunately I have an unequal number of sites in each zone (3, 4 and 5 respectively) due to not enough data being collected at a couple sites. Also, my variances and sample sizes are also not equal between sites (sample size running from 3 to 43, I know, terrible!). The total number of observations for all sites was 182. Most sites had around 15 observations

My question is, is it possible for me to do nested analysis of some sort? I can't find much information on nested analysis with unequal variances.

I have tried transforming, the closest I can get to homoscedasticity is with $x_{new}=\frac{1}{(x+2)}$, and that gives me a $p \approx 0.02$

• You can fit a mixed model with lme() in R or PROC MIXED in SAS. I do not understand your last sentence, what is X_new and x ? – Stéphane Laurent Apr 23 '12 at 17:38
• Sorry, I meant that I tried transforming my data to stabilize the variances, where X_new was the transformed data and x was the original data. I will try your suggestions. Do you know of anything similar in SPSS? I am trying to consistant in my program usage, but I will try the other two anyway. Thanks! – Jess Apr 23 '12 at 17:49
• As Stephane suggests, multilevel/mixed models are probably the way to go with this - no need to have equal sample sizes at each site nor equal numbers of sites in each zone. I listed a few resources in this old answer, of which I'd probably start with Gelman and Hill. There are also many other questions on this site about this kind of analysis - search for [multilevel-analysis], [mixed-models], and [repeated-measures]. – Matt Parker Apr 23 '12 at 17:51
• And here's an intro to mixed models in SPSS (PDF). – Matt Parker Apr 23 '12 at 17:52