[[ Please ignore the last email which was sent incomplete ]] Lets say there are 10 students in the first group and denote x1 as (say) the number of red balls for student 1 and s1 the total balls. Then I was calculating the average the proportion ( x1/s1 + x2/s2 + ... + x10/s10 ) and you were calculating the average number of events (x1+x2 +...+x10)/(s1+s2+...+s10).
It is just by chance that your calculation and mine agrees. When the numbers are highly unbalanced, you may get very different results. On second thoughts I think it is much better to calculate the a weighted average of the proportions. The weights should reflect the variance of the estimate of the proportions. Assuming that your outcome of interest is proportions, the summary effect size might look something like p_hat = ( w1*p1 + w2*p2+ ... + w10*p10 ) where p1 = x1/s1 and w1=1/var(p1). You should be able to obtain the standard errors for this estimate. Using this you can build a confidence interval and see if they overlap with proportion of reds in other groups. There is a big field called meta-analysis that deals with this kind of issue. You might want to read up more about this area. However I am not too familiar with the meta-analysis of proportion Perhaps someone on the mailing list can advise you if this approach is appropriate for your situation and perhaps even some references. Regards, Adai <SNIP> ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html