Short answer: Your readings are wrong. But you need to worry about
homogeneity of variance more.
Long answer: In the old days, this mattered. Fisher's great innovation
when inventing ANOVA was to find a way to fit regression models for
uncorrelated categorical variables (which you get from equal groups)
without doing matrix algebra - because matrix algebra was really,
really hard. He called that ANOVA, and generations of psychologists
believe that ANOVA and regression are different things. And when they
read about them in text books, the textbooks describe how to do ANOVA,
because the authors feel like they didn't write a proper textbook if
they didn't include equations, and the matrix algebra equations are
really hard.
Nowadays we have computers, so we don't care. Every stats package in
the world does ANOVA by doing regression, and then fiddling with the
output so it looks like ANOVA again. It does this with matrix algebra,
which is really easy, if you're a computer.
So we don't care about unbalanced groups.
However, homogeneity of variance is a problem with unbalanced groups.
The books tell you that HoV is an assumption of ANOVA. And that ANOVA
is robust to violation of that assumption. Both these are true if the
sample sizes are equal, if the sample sizes are not equal, the second
is not true.
Jeremy
On 15 July 2013 10:43, Rebecca Pepper <[log in to unmask]> wrote:
> Hi all,
>
> I have unequal group sizes with a ratio > 4:1 for largest:smallest group
> size and wish to conduct a univariate ANOVA comparing their scores. Based on
> my readings I believe I need to perform some sort of correction for this
> sample size discrepancy. The discrepancy was due to recruiting fewer members
> of some samples than others and was not due to random factors such as data
> loss etc. As such, I think the approach I need is the weighted least squares
> approach but cannot find information on how to calculate weightings for this
> analysis - is anyone able to help?
>
> Thanks,
> Rebecca
|