# Non-homogeneity in 2-way ANOVA in SPSS

I am trying to determine differences in fish weights from 1st to 2nd sampling between a control group and 4 different treatment groups. My groups are unbalanced (control = 1 group, t1= 2 groups, with t2,t3,t4 = 3 groups). Originally I was told this shouldn't be a problem.

I've run a 2-way ANOVA and the Levene's test in SPSS is significant (0.017) but ANOVA is (0.018) and the significant factor is (.001). Is there a way to adjust for this or do I need to run a different stats test?

Otherwise I was thinking I may need to simplify and combine all the treatment groups and run a t-test, then run another t-test for the control to demonstrate there are differences between treated and non-treated fish. What do you think?

Ok so there are a total of 21 tanks of fish i.e. n= 21. We didnt have room for 22 tanks so one treatment group only had to 2 tanks. We attempted to run everything in triplicate so 3 of the treatment groups are triplicated. 1 treatment group is duplicated, and 1 group is the control (single). The weights of fish are tanks averages. The largest difference is a total of 22 grams, the smallest is a difference of less than 1 between tanks

• This isn't at all clear. Can you say more about your study & your data? How can treatment group 1 have 2 groups? How much heterogeneity do you have? Ie, what are the variances of the groups w/ the largest & smallest variances? – gung - Reinstate Monica Jan 23 '14 at 2:31
• Can you give a sense of what the total overall $n$ is in this sample? – AdamO Jan 23 '14 at 5:33
• Ok so there are a total of 21 tanks of fish i.e. n= 21. We didnt have room for 22 tanks so one treatment group only had to 2 tanks. We attempted to run everything in triplicate so 3 of the treatment groups are triplicated. 1 treatment group is duplicated, and 1 group is the control (single). The weights of fish are tanks averages. The largest difference is a total of 22 grams, the smallest is a difference of less than 1 between tanks. – user37695 Jan 27 '14 at 23:38
• @user37695 how many fish in each tank? Can they be measured at baseline and then at follow-up? Or can they be measured multiple times (as opposed to, say, being sacrificed to measure liver volume) – AdamO Jan 28 '14 at 19:13
• Hi Adam, they are sacrificed at time point 1 (start) and 2 (end). I have already run some a GLMM and determined that for mortality rates there are insignificant cluster effects. I spoke to the Uni stats guys here and he said the averaging of the weight should not be a problem. Each tank had 6 fish measured at the start and the end of the trial. – user37695 Jan 30 '14 at 4:27

If I am interpreting your question correctly, there are 5 treatment levels. One group is control, one group is, say, standard treatment, and 3 groups are investigational treatment at 3 different doses. You have a sample of fish that have been randomized 1:2:1:1:1 in this experiment for the 5 groups. You are interested in whether the investigational treatment is better than standard treatment and/or control.

If indeed your experiment follows as I've described, you ought to break this out into multiple comparisons. No need for Bonferroni correction, since the substantive question "Is treatment better?" is approximately the same in all possible comparisons. T-tests do indeed handle unequal variances. However, just as ordinary linear regression adjusting for a binary predictor is an analogue of a t-test with equal variances, generalized estimating equations is an analogue of the t-test with unequal variances. You can correct for heteroscedasticity by calculating robust standard errors which is either easily supplied as an option in SPSS or else SPSS is horribly outdated.

This just goes to show that when you test for assumptions, it's very difficult to interpret the meaning of the p-value. The assumption was a problem, you find the assumptions aren't met, now you have two problems. Better to have no assumptions at all.

• Hi Addam, thanks for that! Yes you are correct, I am trying to work out which, if any, treatments are better than the control/standard treatment. So to make sure I understand correctly, I can either run multiple t-tests comparing all the different groups or do a GEE? – user37695 Jan 27 '14 at 23:45