Good day.

We do not know what type of data in your case it is.

I recommend: https://www.researchgate.net/publication/11287641_The_Statistical_Analysis_of_Data_from_Small_Groups

Regards Marián :)

Thank you very much Marian

Non-parametric tests and small samples don't go well together. For instance, with n=5, the lowest possible p-value the signed rank test can give is 0.0625. If you consider that you will have to even adjust for mutiple testing in your screening approach, you don't even need to start the analysis as ther cannot become anything significant.

If you can make reasonable assumptions about the distribution of the data, they allow you to much better extract useful information from the data. I think, for instance, the assumption that HR is approximately lognormal and BP is approximately normal is surely reasonable and can be supported by rich data that should be available.

What Jochen Wilhelm has suggested--i.e., using what you know about the outcome variables from other studies--is one of the key points raised by Bland & Altman in their 2009 BMJ note on "analysis of continuous data from small samples". HTH.

Article Practice Statistics Notes Analysis of continuous data from s...

Thank you Bruce Weaver , I wasn't aware of this paper. Good to have a reference backing up my advice :D

Bruce Weaver and Jochen Wilhelm are assuming that your goal is testing a null hypothesis, and as they note this is under-powered and I think may not have been what your study was designed to do (otherwise your power analysis would have lead you to either have more people or conduct a different study). I assume your study's goal was to collect data, report the data descriptively, and allow these to become part of a wider collection of research to allow inferences to be made. With that in made, I would present the data as a scatterplot with after scores on the y axis and before scores on the x-axis, denote the groups differently (and I don't know what your individual measurements are, but perhaps those too), AND then make your data publicly available.

If you did a small randomized experiment, with the pretest being the same as the posttest, you could increase the power of a statistical test by adding the pretest as a covariate in an analysis of covariance (ANCOVA) (Hox, 2020).

Hox, J. (2020). Important yet unheeded: Some small sample issues that are often overlooked. In R. van de Schoot & M. Miočević (Eds.), Small sample size solutions: A guide for applied researchers and practitioners (pp. 255–265). Routledge. https://www.taylorfrancis.com/chapters/oa-edit/10.4324/9780429273872-21/important-yet-unheeded-joop-hox

Chapter Important yet unheeded: Some small sample issues that are of...

Good luck,

Thanks for sharing that link, Mohialdeen Alotumi. The entire book is available for free download here:

https://www.taylorfrancis.com/books/oa-edit/10.4324/9780429273872/small-sample-size-solutions-rens-van-de-schoot-milica-mio%C4%8Devi%C4%87?refId=7e34e721-aaf2-4095-ba77-eaca5556fc6d

Thank you so very much, Bruce Weaver , Mohialdeen Alotumi , Daniel Wright and Jochen Wilhelm for all your valuable advice I will study all options carefully.

Coming late to the party but eager to give my two cents: I totally agree with Jochen Wilhelm , the sample is simply too small to use non-parametric methods. Nina Shchemenok , with a sample of 5 to 10 subjects in each group, I would argue that only Bayesian methods (with properly elicitated priors) will provide sensitive results and conclusions - particularly if the goal is to test a hypothesis. See for example JASP, which is a cool and easy app developed by people from UvA (free publicity for JASP, I am not in any way related to UvA or the developers):

https://jasp-stats.org/

Rolando Gonzales Martinez , good point to mention Bayesian analysis. This requires and uses even more assumptions (or prior "knowledge") than the "standard" (parametric) analyses, and the information provided by a small sample adds a bit to the amount of information that is coded in the model an in the prior. I just want to note that the Bayesian inference using small samples is as good as the prior information that is used. I mean to say: it pays off only if there is such information. Using "non-informative" or "flat" priors won't bring much of an advantage.

Thank you for mentioning JASP. This is a cool tool, not only for Bayesian analysis. I can add JAMOVI (https://www.jamovi.org/), which is quite similar to JASP (I am also not related to these software in any way, I just think these are good free alternatives to the proprietary and costly programs out there).

Jochen Wilhelm , I totally agree with you. When I said with properly elicitated priors I mean properly elicitated informative priors. I can bet a beer Nina Shchemenok has some experts around to properly elicitate the priors, if she plans to take a Bayesian road - but of course, I agree too, the results will be highly dependent on the prior information given the small sample - which in my opinion is correct.

Thanks for the link to JAMOVI, quite interesting, too.

Oh, yes: "with properly elicitated priors". You said it, I have overseen this. This is a very important point (for small samples, not so for large samples).

Thank you Jochen Wilhelm and Rolando Gonzales Martinez very interesting discussion!

Can apply parametric test like Paired "t" and Unpaired "t" test to compare within the group and between the group

use t-test to compare before and after results in each group

Mohammed Ahmed Alkailany thank you, but T-test doesn't really work for small groups

Sorry Nina Shchemenok, OK. I did not notice the sample size.