In my study, I used single proportion formula:
Sample size, n = Z2 P (1-P) / d2
Where Z = 1.96, d = 10%
P = 10%, which is the increment in postprandial metabolic rate after consumption of LCS (Mourao, Bressan, Campbell, & Mattes, 2007)
Thus, n = 35 subjects.
However, due to some issue, i only manage to finish 28/ 35 subject, so now, I need to calculate the power of study to justify my sample size. How to calculate it?
Dear Faiz,
For calculating statistical power you can visit this link:
https://www.psychologie.hhu.de/arbeitsgruppen/allgemeine-psychologie-und-arbeitspsychologie/gpower.html
Laila had some good points, but I dont see where she followed through to say what the confidence limit values were. Remember it is centered around p= 0.1. That might make the distribution noticeably asymmetric since it is so close to 0. If symmetric enough, I'd use a t distribution - i.e., use t instead of z - with such small sample sizes.
I'd suggest just showing the standard error of p.
Also note that you are assuming that the population size is large so no finite population correction is needed. You are also assuming simple random sampling.
For the original sample, the standard error wanted/hoped for p is sqrt(pq/35) = 0.051. (This seems rather large.) If you had wanted a sample size of n= 28, that would have been good for a desired standard error for p of sqrt(0.1×0.9/28)= 0.057.
If you expect that p is about 0.1, and want to find it with two standard errors of about 0.11, then I'm not sure that gives you the accuracy you might require. The original sample size was probably too small, but if it wasnt, then this is hardly worse.
And don't forget: this is for simple random sampling from a large or infinite population.
I suggest you look at section 4.4 "The Formula for n in Sampling for Proportions," pages 75 and 76, in W.G. Cochran, Sampling Techniques, 3rd ed, 1977, Wiley, or some similar text. Also, online, Penn State has a lot of good material made available to all. They should cover this. I suggest you try searching for your topic and "Pennsylvania State University."
In general, sample sizes are found by determining, under a given sampling methodology and a given corresponding estimation or prediction (regression) methodology, what sample size paired with what standard deviation will attain a desired standard error. This gets more complex with some methodologies than others. For stratified sampling, for example, standard deviations are needed by stratum, though it may be well worth it as stratified sampling can more efficiently estimate overall total or mean, with the desired standard error. Thus the overall sample size requirement may be substantially smaller.
In this question, the methodology apparently is simple random sampling from a large population, with probability-of-selection-based estimation, which is the simplest case. Standard deviation for p is approximately sqrt(pq). Standard error for p is approximately sqrt(pq/n). Thus for a given standard deviation, increasing n will determine the approximate standard error one will likely achieve.
Thus your required standard error should be approximately met if you have a good idea of the standard deviation, and use a large enough sample size, for given sampling and estimation/prediction methodologies.
[This is also the general basis behind power analyses for hypothesis tests, though interpretation there can be more convoluted, and often misunderstood. But always, as sample size goes up, standard error goes down. Some hypothesis tests get rather involved, however.]
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