Power analysis: How many subjects do I need?

power analysi Power analysis is an essential part of any expriemental design. Specifically, we need to be able to figure out how many subjects we will need to be confident we will be able to reject the null-hypothesis if there is a real effect.  This is REALLY important in animal research, as it avoids wasting animals, as no matter how good an experimental protocol is:
YOU WILL NOT BE ABLE TO DETECT A DIFFERENCE IF THE SAMPLE SIZE IS SMALL RELATIVE TO THE MAGNITUDE OF THE DIFFERENCE!

Power analysis allows us to do two things:
  1. To determine the sample size required to uncover a significant result for a given effect size with a given degree of confidence.
  2. To work out, if our sample size is limited, the probability of acheiving a significant result with a given effect size.
Both of these are essential parts of planning an experiment. You will usually have some idea of how large your effect is likely to be based on previous research, or on related data. For example, you may have carried out a pilot study or taken other measurements that can be used for estimating effect size. In the event that there really are no more data available, use the theoretical basis of your hypothesis to estimate if the expected effect will be high/medium/low.

IT IS YOUR RESPONSIBILITY AS A RESEARCHER TO ENSURE THAT YOU HAVE SUFFICIENT STATISTICAL POWER TO CARRY OUT YOUR EXPERIMENT.

So, we have the sample size (how many subjects in each treatment), the effect size (the magnitude of the treatment on the response), the α-level (P(Type-I error), which means falsely rejecting the null hypothesis), and the power (1 - P(Type-II error), which means falsely accepting the null hypothesis). If we have any three of these bits of information, we can calculate the fourth. To give you a heads-up, the α-level is typically p < 0.05, and the power should typcially be no less than 0.8.