# Calculating "sample size"/power when I already have a group

I am doing a project on carpal tunnel syndrome. I am looking at electrophysiological and symptomatic data before surgical intervention and again afterwards to assess whether symptomatic relief correlated with electrophysiological data. For numbers my clinic takes about 3000 referrals to investigate CTS. From this about half have carpal tunnel, and about a third go on to surgery.

My understanding was I didn't need to calculate sample size as my sample is limited by time/resources. In my proposal I stated:

It is anticipated that we will assess around 100 patients initially. From this, those who have a diagnosis of CTS and are listed to surgery will be invited to participate in follow up. The number of patients seen will vary somewhat depending on time constraints and may increase with time permitting.

The feedback I was given stated:

Why? Have you done a power calculation to ascertain the numbers needed in order to make a statistically valid judgement?"

My understanding was I didn't need to calcualte sample size as my sample is limited by time/resources.

This is where you go wrong. Would you just start building a house without budgeting first and seeing whether you have enough money to build enough bedrooms? If you just start building until your resources are exhausted, you may end up with the foundations, a basement and half a kitchen - and broke, so worse off than before.

You need to make sure your resources are sufficient for your aim. In planning a study, this means deciding beforehand what clinically significant effect size you want to be able to detect, at what alpha and beta level. Then you can determine what your necessary sample size is. Then you can apply for funding.

Look at this from the point of view of the funding agency. Why should they fund an underpowered study? Much better for them to concentrate their limited funds on studies that are adequately funded.

If you find out (beforehand!) that the sample size you would need is prohibitively large, you can reduce beta or increase alpha, but this of course reduces the likely scientific payoff. Alternatively, you could reduce the effect size you want to be able to detect, for instance by reducing the prospective variance in your data, e.g., by using better instruments, or by controlling your enrollees better (which may mean that you can only look at subpopulations, and your results may not be generalizable).

• Hi, thanks for the information here. This is a small student project so as such funding is not an issue per se. Whilst I know it is not good statistical practice, our limiting factor is that we won't be able to see more than 100 patients. Can I "work backwards" to state what the power would be from this? Jul 18, 2016 at 14:05
• You can certainly work backwards in this case. Essentially, you have the following variables: (1) sample size, (2) effect size, (3) alpha level, (4) beta level. Typically, you'd fix (2)-(4) to certain values, then calculate (1). But of course you can also fix (1), (3) and (4) and calculate (2), i.e., the minimum effect size you will be able to detect given your sample size, alpha and beta. I usually approach such problems by simulating the experiment, then tweaking the effect size until it fits. Jul 18, 2016 at 14:19