Margins of error - proportions

#1
Hi everyone,
could somebody please explain
- I surveyed males and females (together) (71F, 189M, 260 total).
I have preferences (choices of A, B, C, D, E) that I want to review by gender.
(i.e. Females - A -2, B -40, C -28, D - 1, E - 0; Males - A - 5, B -35, C-100, D-4, E - 45).
When I want to show error margins and standard deviation, should I do it based on the entire sample (260) and (!)
should I treat each choice - Female A, Female B, Male A, Male B as i.e. % (proportion of Females A) and NOT A (all males and other females not A)?

Or maybe should I process males separately (189M - A-5, B-35, C-100, D-4, E-45) and calculate standard deviation and errors based on 189M only.
Then process females separately?

Personally, I think I need to calculate altogether, based on 260 sample. But I do not know for certain.

In other words, what is the right way to show error margins for this type of proportions?

Thank you before hand!
 
Last edited:

staassis

Active Member
#2
Since you want to estimate probabilities of A - E by gender, you have process males and females separately. So in calculating the sample proportion P you would be dividing by the number of participants of the same gender (N). Then the confidence interval would equal

[ P - Critical Value * sqrt(P * (1 - P) / N), P + Critical Value * sqrt(P * (1 - P) / N) ],

where Critical Value would depend on the confidence level.