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May 26, 2022 at 18:39 comment added cbeleites I also usually tell everyone that they need larger sample size to draw the conclusions they'd like to draw. However, there are case studies, and many projects can never acquire more than n = 1 (well, maybe 2) harvest season or locations. Plus, outside the stats discussed here, e.g. developing a wet-lab method to measure something (particular soil) can also be research worth a publication or an entire thesis. In some cases, even getting a particular method to work reliably in another lab may be worth a publication.
May 25, 2022 at 21:14 comment added gerrit @StephanKolassa $n=1$ is a small sample size, but when data collection is very expensive, it may be all we have to work with.
May 25, 2022 at 9:10 comment added user104446 @Daniel R. Collins Yes, n can vary a lot with skewness. The correct n value can be simulated for a variety of underlying distributions in tools like Matlab, Mathematica and Maple. Yet it's clear from previous comments that z-tests are not on here: t-tests it has to be. But OP can get more precise guidance on all this from his university's statistics advice center.
May 25, 2022 at 5:13 comment added Daniel R. Collins @Trunk: FWIW, my textbooks warn about using even the z-test (which assumes population variance is known exactly) with a sample less than 15, unless the variable is known to be "very close" to normal.
May 24, 2022 at 23:50 comment added user104446 @Daniel R. Collins If that's what he's got, he'll be fine. I think Student-t for population mean will run with reasonable precision with sample size of ~ 5. n = 30 is the textbook cut-off for people want to apply Normal stats to the sample mean for "well-behaved" underlying population distributions. But OP can estimate pop variance using Chi-squared distribution if the population is distributed with reasonable "Normality". Anyway he'll have to get pro advice on all this stuff as he reads up on it all.
May 24, 2022 at 19:33 comment added Daniel R. Collins @StephanKolassa: FWIW, in a comment to Bryan's answer, OP writes, "I wont tell actual number of samples here but they are within 10. Now I require to make bar graphs annova students-t etc.". So I read that as "1 group with ~10 individual samples". Given that inferences for a mean (like student's t-test) usually recommend a minimum size of around 30, maybe advisers are saying "you should have 3 groups of that size". (And possibly OP's first language is non-English.)
May 24, 2022 at 18:30 comment added user104446 I think that this answer is the best that can be salvaged from the existing sample data. And for God's sake find someone outside the influence of your current advisers to advise you on this statistical approach. Obviously there needs to be a recommendation in your final write-up for a greater number of samples. No only for reasons of confidence in the final estimates but also to evaluate the efficacy of your Bayesian analysis of singular samples.
May 24, 2022 at 14:14 comment added Random PhD Student @StephanKolassa yes, you are absolutely right. My answer is made on the premise of fully accepting the described circumstances.
May 24, 2022 at 13:19 comment added Stephan Kolassa Fellow statistician here. I upvoted your answer, but to be honest, either $n=1$ or $n=3$ sounds like a horrendously too small sample size. Yes, one can possibly salvage something using a Bayesian analysis. Nevertheless, it would have been useful to consult with a statistician before the experiment was even planned. I know, that is not useful at this point in time... but it may help others in the future. Recall R. A. Fisher's quote about consulting the statistician after the experiment.
S May 24, 2022 at 12:31 review First answers
May 24, 2022 at 12:38
S May 24, 2022 at 12:31 history answered Random PhD Student CC BY-SA 4.0