Katja Wunderlich wrote:
>
> Hi!
>
> Is it OK to do a regression analysis, when the sizes of the sub
> samples are very unequal?
>
> This is our sample with the sub samples:
>
> Germany GB France Italy Denmark Poland Total
>
> Interviewed (absolute) 500 407 420 343 101 253 2024
Katja, you clearly have "nationality" as one variable (categorical);
what are your others?
If your only other variable is the one you want to consider as a
dependent variable, you won't be doing a regression in the usual sense
at all - you would be doing, perhaps:
an ANOVA or something similar if your dependent variable was
continuous, (eg, income as a function of nationality). [ANOVA is
basically the same thing as regression on a set of n-1 dummy variables
but that isn't usually how it's done.] You do not need equal sample
sizes here if your software is any good at all.
a chisquare test if it was discrete (eg, favorite Beatle as a function
of nationality). Equal sample sizes are not needed.
If you had other continuous predictor variables (income as a function
of hours worked AND nationality) then a regression approach in which
cross terms were considered might be a good way to go. You do not need
equal sample sizes but must be careful that your variables are not too
strongly correlated (for instance, if the work week were different in
different countries.)
With other discrete predictor variables you would use multi-way ANOVA
with nationality as a predictor; there are versions of this that *do*
need equal sample sizes, though there are ways of doing the same thing
that don't.
With unequal sample sizes, any inference that does NOT give a way to
distinguish the effect of nationality would be invalid. For instance,
you would not pool all your data and then regress income on hours
worked!
-Robert Dawson
.
.
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