How do I calculate my minimum sample size (number of horses) for a study testing reliability of an outcomes measure for epaxial muscle activity?
If you have no hypothesis to formulate or to comply the best approach is a confidence interval.
You need to set the confidence level (the probability that the real value of the mean will be within the interval) and the estimation error E (the accuracy of the measure).
The sample size is n= ((Z_(α⁄2) σ)/E)^2 where Z_(α⁄2) is the quantile of a normal distribution leaving at its right a probability α⁄2 if you want a confidence level (1-α) with a two sided test. σ is the standard deviation (supposing it known).
If you have no estimation of σ you should plan a pilot study with a minimum sample to get a σ estimation, for instance m=8 and use the following formula:
n= ((t_(α⁄2,m-1) s)/E)^2, where t_(α⁄2,m-1) is the quantile for the student distribution with m-1 degrees of freedom and s is the sample standard deviation obtained with the sample m.
Mr. Vast is right if you want only to establish reliability of the mean.
However if you want to verify that epaxial muscle activity is within tolerances (e.g. healthy or not ?) then I suggest using Tolerance Interval Analysis (TIA). See
1.1. Engineering statistics handbook NIST SEMATECH, 2006.
Guidelines for setting up the minimum sample size you can find in :
1.1. Mary Gibbons Natrella (1963). Experimental Statistics, NBS Handbook 91, US Department of Commerce.
1.2. Pass - Sample Size Software Manual Chapter 830.
I recently used this in a study for FDA qualification.
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