I have a question about something that is probably very basic to statistics but I feel I don't fully understand
I've found that generally it is much harder to get high power (smaller) confidence intervals with binomial data (0,1s)
When I want to calculate the difference between two proportions it is hard to get a high p value and confidence intervals. However, with studies with the same amount of participants for which I can calculate means (because the variables are measured continuously rather than as 0 or 1 choice) the power is much higher. I think I have a good sense of why this is but i'd like someone to explain it to me in a basic way so that I can check my understanding.
Is there are graph which anyone can point me to (or some general rule) that links sample size with power when using binomial vs continuous data. I feel like I should avoid collecting binary outcomes where ever possible because of the lack of power. Is this correct
Additional comment added 11.05.2014 12:04
TO CLARIFY: My question is - if we are measuring exactly the same thing but with 2 different ways of collecting data. One is binary (e.g. do you prefer B 'more' or 'less' than A), one is continuous (do you prefer A or B. Please rate preference for A on scale of 0-1, where B is 0.5), then do I get higher power with the continuous measurement method - and if so why? I seem to, because I get a mean scores from the continuous method rather than proportions, and the std error of the mean scores generally seem to be lower than that of the proportions, when expected values are the same (e.g mean of 0.5, proportion of 0.5), and number of participants doing the test is the same.