I am planning a study and for that I need to use power analysis to estimated the sample size. Now, I do not have any estimates for the desired effect and standard deviation required to do the power calculation. I also cannot do a pilot study. Given these constraints, how do I estimate the sample size for my study?
The short answer is that you can't. Like other answers mentioned you need to assume a fixed effect size, fixed significance level and a desired statistical power in order to estimate the needed sample size.
Now if you don't know the mean difference and standard deviation - you can guess them based on some information.
And if you cannot reasonably do that then the next best thing is to calculate required sample sizes for a whole range of possible mean differences and standard deviations. This would allow you to at least imply on a range of possibilities. And you would be able to answer questions such as "what kind of effects can I reasonably (i.e. with power = 80%) expect to detect with a sample size of n".
I don't know, how hungry I will be, nor, how many people will join the meal. How much food should I buy?
You cannot do any reasonable computation without suitable data. You could probably try to guess reasonably. Or you need to look for similar investigations that have been done by others or you have yourself guided by what $n$ is reasonably achievable. Or maybe a descriptive analysis is in order?
While Bernhard is right that having some more info or a pilot would be ideal, a pragmatic approach in a situation where neither is available would be
- Fix your question
- Fix your statistical analysis
- Decide on the minimal effect size that is of SCIENTIFIC significance, i.e. that you want to be able to pick up if it is there, and use this as effect size in the power analysis
- Get an estimate about variability from the literature / colleagues (very unlikely that there is no precedence for a measurement method)