Regression analysis or ANOVA for unequal sample sizes

#1
Hello everyone :)

First I want to apologize for my Eniglish, I´m not a native speaker.

I am currently working on a research for school purposes, as I can´t write what my research is about I describe example equal to my research: I study relationship between eating bananas and extraversion.

I have 3 groups, heavy eaters, light eaters and noneaters. My first problem is, that these group are unequal in size (eg. HE=150, LE= 70, NE= 300). I´m currently using one-way ANOVA, Brown-Forsythe test and post hoc Games-Howell test because of unequality.

But I started to think if this is a good method to analyse ma data. I though about regression analysis, but I´ve read in my lecture notes that there is a problem with unequal sample sizes and correlation. And as I searched internet I found that many states that ANOVA and regression analysis are the same thing.

I am really confused by this "one-way ANOVA and regression are the same method" thing.

At school, we only had basic of statistics, so now I really struggle whenever I have to analyse data because I´m not sure when to use certain type of methods.

My second problem is that I have to compare my groups by gender also. Normaly, I would use two-way ANOVA, but same problem here, unequal sample sizes, and in Levene´s test, Sig. is lower than 0.05. But there is no nonparametric equivalent to two-way ANOVA, so I don´t know if I can still use two-way ANOVA despite Levene´s.

I´m using SPSS to analyse data.

Thanks in advance for every response :)
 

noetsi

Fortran must die
#2
ANOVA and regression are different forms of the same general family of methods called general linear models. You should come up with the same substantive results using the two. They are different simply because different groups developed them in isolation from each other.

I have never seen unequal sample size raised in regression other than needing a specific number of each sample (Agresti says you need a specific number of cases to run regression for example, this minimum size is tied to the least common type of case). Not all agree these minimum sample sizes, really rules of thumb, are actually neccessary, however. That said if unequal sample size is an issue for ANOVA it should be for regression as well. It simply does not come up in discussion of regression or not that I have seen anyhow.

The bottom line is if something is a problem for ANOVA it should be for regression as well. But the people who use the two methods may not consider the problem identified in the other method to be important.
 
#4
So If I understand it right, my method (using Brown-Forsythe and Post hoc Games-Howell instead of one-way anova because of unequal sample sizes) is correct in this case? I only needed to know if I wasn´t completely off the track.
 
#5
And yes, they are normaly distributed, if you mean in this case ig. extraversion, than yes. English is not my primary language, nor is language of statistic so it is possible that I didn´t understand you correctly.