# How to determine sample size for a binary variable

If you need to determine sample size for your survey when a variable of interest is a binary outcome, you can use power analysis and decide how many subjects you need before collecting data.

You can ignore this one, if too confusing=> You should adjust the sample size by expected response missing rate (e.g., you aim to collect data from 100 people; you expect only 95 will reply; then you use 95 as the sample size for power evaluation).

I wrote an Excel file for sample size calculation, but let me write a bit more here about what I did in there:

https://drive.google.com/file/d/0B7AoA5fyqX_sMkZJOUZxN3JvbUk/view?usp=sharing

If you have expectation as to what %s you will be looking at after your experiment, use those %s (% for the treatment group and % for the control/comparison group) and decide the sample size you will need to evaluate the two %s with confidence.

Often we don't have such expectations -- probably because no one has done a similar study like yours. You can just assume  the two percentages are close to 50%, which will give you the most conservative power analysis results. So if you want to see if the group difference of 5% will give you sufficient statistical confidence, given a certain sample size, you can set the two %s to be 47.5% and 52.5% (the difference being 5%).

If you want to see if the group difference of 10% will give you a good enough statistical confidence, given a certain sample size, you can set the two %s to be 45% and 55% (the difference being 5%).

I wish I could write this more tightly.

Reference:

http://www.surveysystem.com/sscalc.htm

Thanks: Mr. George Ohashi for showing me the function that adjusts sample sizes by expected missing rate.