1. I'm trying to use a sample dataset (attached) to estimate the optimal sample size.
I'm using the linked book chapter as a guide, using formula 7.1 (7.2) gives a similar result.
The resulting n is similar to the sample size. In fact, if I make random sub-sets the estimated n will be close to the actual sub-set size every time.
I was expecting a fairly stable value for n after a certain sampling size (which I want to determine). Instead the result points to the sample size used for the estimation: there is no conclusion to be taken, every tested sample size is the correct one.
The desired absolute error seems to be the most sensitive variable, but I'm unsure how to calculate a robust/adequate value for the sample, independent of variations in the test sample size.
2. The sample is not normally distributed, it's skewed to the left. The averaged values will be subject to a t-test. There are samples both in control and treatment that do not pass a normality test. But for this purpose, only the averages need to conform to a normal distribution, or the underlying values also need to be normal?
http://www.zoology.ubc.ca/~krebs/downloads/krebs_chapter_07_2013.pdf
Hi Nuno,
I think the mistake in your calculation lies in the desired absolute error d. d needs to be established by you. As an example I use your first random subset calculation: m=0,542, sd=0,129. Now let's say you are interested in finding n so that in 95% of the time you draw a sample of size n your sample mean will be between m+/-0,05. This 0,05 is the d you have to use in the formula.
I did the calculations for your examples and the sample size would be around 30 for d = 0,05.
Best,
Felix
1) Normality of the observations (underlying values) is what is needed.
2) I think that you took equation 7.1 and substituted the unnumbered equation that appears just before 7.1 into 7.1. However, equation 7.1 is just the previous equation rearranged, so you have substituted the equation into itself.
You should use G*Power to help. Your assumed effect size seems small. A sample of 30 seems too small for a t-test anyway. If you don't meet the assumptions for the t-test, simply do a Mann Whitney U.
http://www.gpower.hhu.de/en.html
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