I would like to compare the proportion of an outcome (overweight yes/no) in my dataset for different age groups with normative population data that I found publicly available online. I have overweight prevalence for age groups 20-30y, 30-40y, 40-50y and 50-55y for men and women for my data and the control data. The challenge is that for the control data I only have an estimation of the total sample size (it's based on four yearly questionnaires that were completed by 9000-9500 each year, so in total about 37000 subjects, that's all they published, so it's unknown how large the separate age groups are). I do have frequency, standard error and confidence interval for each data point. Is there a way to perform a chi square test (or another test) to compare two proportions with unknown exact sample size, but known SE/CI in one group? Thank you for your suggestions, Best wishes, Vincent
1 Answer
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Given that you have the standard error of each proportion, you should be able to infer the respective sample size
$SE = \sqrt{p(1-p)/n}$
$n = \frac{p(1-p)}{SE^2}$
