Sample size for segmentation validation I've created a automatic algorithm liver segmentation and the next step is the method validation. I have 16 exams with a mean of 40 slices each and my doubt now is how many of these slices would have a technician to hand segment to compare with my algorithm.
I've read about Hypotesis test but I can't figure out how to calculate its variables,
here's the link from the source of the test.
http://circ.ahajournals.org/content/114/10/1078.full#disp-formula-6
here's the equation,

 A: I understand that you want to compare your automatic and manual segmentation methods. I don't know much about liver segmentation, so I don't know exactly what you will be comparing between the automatic and manual methods. I assume that you have some number that each of the segmentation methods produces for each case.
Use the "paired tests" formula in the reference you cite instead of the formula for the one-sample test you quote in your question. (It's like your formula, but with "d" in the numerator.) Calculate the difference between the automatic and manual methods for each case. Calculate the mean and standard deviation of those differences. The mean difference is the "d", the standard deviation of the differences is "s", and "n" is the number of cases. The t-value will tell you whether there is a significant difference between the two methods; the "degrees of freedom" in the table of t values for significance testing is one less than the number of cases you compare.
How many cases you have to compare depends on how big a difference you want to be able to detect, and how variable you expect the differences between the methods to be. If you have estimates of these, then you can use standard power analysis formulas to determine how many cases to examine. My guess is that you will be best off if you compare all 16 available cases, and use your results on those to guide your future choice of method.
Also, the differences between the methods may come from errors in either of the methods. If there is a significant difference between the two methods, look carefully into why they differ; manual methods aren't necessarily the most accurate.
A: It seems that author currently asks not about how to compare, but how many test observations are needed to do the comparison (possibly to show that the algorithm is no worse as manual segmentation by technician). The answer is "The more is always better". However, it is possible to construct the hypothesis "The difference between two methods is no more than some fixed value". The difference can be measured as the total area of wrong segmentation. Then the sample size $n=(\delta/d)^2$, where $\delta$ is taken from the table (considering significance level and desired power of test), and $d=(\bar X-\mu)/S$, with $\mu$ - the desired fixed value of difference and S - sample standard deviation. Note that in this case you are working with one-tailed one-sample t-test.
Here is good introduction to sample size calculations.
P.S. Have you any relationship to this article? If no, it'll be interesting for you.
