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I'm a bit new to statistics; I know some general info about ANOVA, but I'm wondering if it's applicable in the following situation.

Let's say I have a group of people who have taken a test, and the group is broken down into different races. However, the number of people of each race is different (30% Caucasian, 50% Asian, 20% African American). I measure the scores on a test for each person, and I want to see if the average score on the test is correlated with race. I know ANOVA is generally used to compare means of different groups, but I'm not entirely sure if it's applicable in this situation when the racial groups are of different size. What kind of analysis do you think I could do to answer this question?

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    $\begingroup$ ANOVA applies to different sized groups. It's sometimes called 'unbalanced ANOVA'. The balanced case has some nice properties but it deals just fine with the unequal-sample-size case. There may be some other issues to consider, but unequal sample sizes isn't an issue. $\endgroup$ – Glen_b Feb 10 '13 at 23:45
  • $\begingroup$ Thanks Glen_b. I've also learned that simple regression using dummy variables for the races is also another analysis, but to be honest, I'm not entirely sure which to use in this situation. $\endgroup$ – rottentomato56 Feb 11 '13 at 2:02
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    $\begingroup$ It's actually precisely the same analysis. ANOVA and regression are subsets of the general linear model, all of which can be implemented in a multiple regression package. So it's really not a matter of choosing between them. It's more a matter of how you view what you're doing. If my predictors are factors and interest is more on testing for differences in factor-levels than effect sizes, I think of it as ANOVA. If my predictors are not factors or interest is on effect sizes, I tend to think of it as regression. But that's a difference in attitude, not in the estimation. $\endgroup$ – Glen_b Feb 11 '13 at 3:08
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    $\begingroup$ I agree with @Glen_b that different group sizes are in principle not a problem with ANOVA. However, if the statistical assumptions of ANOVA (normally distributed and homoskedastic errors) are not met, a balanced ANOVA is pretty robust... while an unbalanced one may yield misleading results. So you may want to pay particular attention to your residuals (which we should all do, anyway): rer.sagepub.com/content/42/3/237 $\endgroup$ – Stephan Kolassa Feb 11 '13 at 8:47
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    $\begingroup$ I know that Kruskal-Wallis analysis of variance (KW-anova) can be used to determine differences among several groups; each group can have different size. This is a non-parametric method, which is different to the ANOVA parametric (groups must be equal in size,afaik). After you determine that there are significant differences using KW-anova, then you do a second test, such as unpaired T test to compare two means at the same time; you can do also multiple comparison using a non parametric test; the name escapes now from my mind. Hope this helps. $\endgroup$ – user35246 Nov 24 '13 at 14:24

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