I need to compare two alternative methods of manufacturing a product, say
B. I wanted first to dermine the sample size of the measurings, and found this post in a sister site. There, it says that the number of samples is a function of the Z-value for a desired confidence, the standard deviation and the expected difference between alternatives. At first, it seemed to solve my problem, but then it sparked more questions than I had before. That's why I come here for help (I think the subject belongs more to the specialized CV site that to the general Mathematics, that's why I came with it here instead of there):
- What should I use for standard deviation? The post contains σ which is normally used to designate the population's standard deviation. Obviously I don't have it, so I assume I should use the sample's instead (see here, for example). The problem is, those two are different for small sample sizes, so there comes a "recursive" what sample size should I take?
- There's only one standard deviation, and I want to compare two alternatives. Does it mean that I should determine a sample size for each alternative, depending on its sd? or I should define the sample size as the max of the two estimated numbers.
- Is there any comparisson (preferably numerical) to determine that indeed there's one alternative that is better than the other? If so, what test should I run?
====== EDIT TO ADD =======
At a factory there are two operators, A and B who perform the same assembly operation. The sequence each of them uses is slightly different (I call them "methods" A and B), but take about the same time. I want to find the fastest of the two methods, and mathematically support my decision.
Method A takes 4:34 minutes in a 4-sample average, and the standard deviation is of about 1:50 minutes (for the same 4 registries). Method B takes 5:01 in average, with a standard deviation of 0:13 (over 3 measurements).
I'd like to know which of the methods could be considered "faster" with a confidence of, say, 90%. That's why I landed reading about sample sizes, because intuition tells me that my 3 and 4 trials aren't enough to make a call. I hope this provide further details about what I need to achieve.