It depends on the question? For an experience sampling method (ESM) also referred as a daily diary method, or ecological momentary assessment (EMA). ESM is an intensive longitudinal research methodology and can be used in a very small size.

See regarding my interest https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7870718/pdf/fpsyt-12-598434.pdf

Simple https://en.wikipedia.org/wiki/Experience_sampling_method

The smallest statistical sample is the smallest sample large enough to give you the precision you require. In the simplest case, where you are measuring a mean or a proportion in a single sample, then the size of the resulting confidence interval determines your sample size. If you can life with a margin of error of ±10% around a prevalence, for example, then 100 participants will achieve this.

If you are looking at measures of effect size, such as differences between groups or risk ratios, then the smallest sample is the one that gives adequate (≥90%) power to detect the smallest effect size that is of real-life interest (in health research, we say the smallest clinically-significant difference).

This is an explanation offered by Deborah Rumsey: is this helpful?

About the Author

Deborah J. Rumsey, PhD, Professor of Statistics and Statistics Education Specialist at Ohio State University. Author of Statistics Workbook For Dummies, Statistics II For Dummies, and Probability For Dummies.

How to Determine the Minimum Size Needed for a Statistical Sample

The margin of error of a confidence interval (CI) is affected by size of the statistical sample; as the size increases, margin of error decreases. Looking at this the other way around, if you want a smaller margin of error (and doesn’t everyone?), you need a larger sample size.

Suppose you are getting ready to do your own survey to estimate a population mean; wouldn’t it be nice to see ahead of time what sample size you need to get the margin of error you want? Thinking ahead will save you money and time and it will give you results you can live with in terms of the margin of error — you won’t have any surprises later.

The formula for the sample size required to get a desired margin of error (MOE) when you are doing a confidence interval.

Always round up the sample size no matter what decimal value you get. (For example, if your calculations give you 126.2 people, you can’t just have 0.2 of a person — you need the whole person, so include him by rounding up to 127.)

In this formula, MOE is the number representing the margin of error you want, and z* is the z*-value corresponding to your desired confidence level (from the below table; most people use 1.96 for a 95% confidence interval).

z*–values for Various Confidence Levels Confidence Level z*-value80%1.2890%1.645 (by convention)95%1.9698%2.3399%2.58

Note that these values are taken from the standard normal (Z-) distribution. The area between each z* value and the negative of that z* value is the confidence percentage (approximately). For example, the area between z*=1.28 and z=-1.28 is approximately 0.80. Hence this chart can be expanded to other confidence percentages as well. The chart shows only the confidence percentages most commonly used.

If the population standard deviation is unknown, you can put in a worst-case scenario guess for it or run a pilot study (a small trial study) ahead of time, find the standard deviation of the sample data (s), and use that number. This can be risky if the sample size is very small because it’s less likely to reflect the whole population; try to get the largest trial study that you can, and/or make a conservative estimate for

Often a small trial study is worth the time and effort. Not only will you get an estimate to help you determine a good sample size, but you may also learn about possible problems in your data collection.

Here’s an example where you need to calculate n to estimate a population mean. Suppose you want to estimate the average number of songs college students store on their portable devices. You want the margin of error to be no more than plus or minus 20 songs. You want a 95% confidence interval. How many students should you sample?

Because you want a 95% CI, z* is 1.96 (found in the above table); you know your desired MOE is 20. Now you need a number for the population standard deviation.

This number is not known, so you do a pilot study of 35 students and find the standard deviation (s) for the sample is 148 songs — use this number as a substitute.

Using the sample size formula, you calculate the sample size you need

which you round up to 211 students (you always round up when calculating n). So you need to take a random sample of at least 211 college students in order to have a margin of error in the number of stored songs of no more than 20. That’s why you see a greater-than-or-equal-to sign in the formula here.

You always round up to the nearest integer when calculating sample size, no matter what the decimal value of your result is (for example, 0.37). That’s because you want the margin of error to be no more than what you stated. If you round down when the decimal value is under .50 (as you normally do in other math calculations), your MOE will be a little larger than you wanted.

Dear colleague Remco FP De Winter, thank you so much for your answer.

Thank you for the scientific publication you sent me, I will read it very carefully. If I have additional questions I will ask you. Thanks again!

Useful days!

Sincerely yours, Julia D.

Thank you very much dear colleague Ronán Michael Conroy!

In particular, can there be a sample of 3 people, for example?

Have a nice days!

Best wishes: Julia D.

Dear Jutta Eschle thanks!

Thank you very much for the useful information.

I wish you controversial and fruitful days!

Sincerely, Julia D.

Julia Doncheva a sample can indeed be three people. However, the degree of precision with which they can represent the parent population is very low.

However, when you can't go wide, you can go deep. Freud's published case histories are just six in number, and they are all case histories of failed treatments. And each one gets a book-length history, because Freud wanted to transmit the challenges, the puzzles, the unresolved questions that had led to these failed treatments. (I admire someone who publishes their failures in far more detail than their successes!)

Hello, Prof. Conroy, Ronán Michael Conroy, I am extremely impressed and grateful for the answer to my question. Thank you very much! I'm really impressed!

I wish you controversial and fruitful days!

With sincere and deep respect: Julia Doncheva

.

There has been a special section devoted to "small sample research" in Prevention Science 2015

https://link.springer.com/journal/11121/volumes-and-issues/16-7

.

see http://europepmc.org/backend/ptpmcrender.fcgi?accid=PMC4943852&blobtype=pdf , for the introduction to the special section

.

I found the contributions by KE Etz and JA Arroyo quite interesting :

Article Small Sample Research: Considerations Beyond Statistical Power

.

Dear Prof. Fabrice Clerot, thank you so much for this useful information!

Thanks!

Wish you all the best!

Julia Doncheva

Most statisticians agree that the minimum sample size to get any kind of meaningful result is 100. If your population is less than 100 then you really need to survey all of them. http://www.tools4dev.org/resources/how-to-choose-a-sample-size/

Check https://measuringu.com/small-n/

Dear colleague Chinaza Godswill Awuchi, I am extremely grateful to you for this useful information. I will read it very carefully. Thanks again!

I wish you controversial and fruitful days!

With sincere respect: Julia Doncheva

Dear Julia Doncheva,

Let me convey my deep appreciation for introducing such an interesting and yet important question. It is specially important for medical researchers.

Thirty five years ago, when as young endocrinologist, I received an overseas call, requesting me to send one of our patients with pituitary tumor to Uk. The researchers were looking desperately all over the world for such 6 cases, which they thought should be the no for sample size. So there is need (from the medical researchers views) , for rare diseases or procedures, the smallest no of patients that can serve as sample size. For this reason, the science of small sample sizes_the whole science is very much required.

I have been benefitted a lot from information that I could gather from the answers to your questions.

Till then I only knew the Fisher exact test from the 'world of small sample size Science'.

Dear Prof. Chowdhury/Chaudhury Meshkat Ahmed, thank you so much! Thank you very much for your extremely accurate and complete comment.I really appreciate the opinion and professional comments of colleagues, because everyone has their own knowledge, which when shared with many scientists becomes useful for each other. Thank you colleague! I bet we will continue to help each other with whatever we can!

I wish you health and much success!

With sincere and deep respect: Julia Doncheva

Dear Julia Doncheva . Most statisticians agree that the minimum sample size to get any kind of meaningful result is 100. If your population is less than 100 then you really need to survey all of them. See the link: https://tools4dev.org/resources/how-to-choose-a-sample-size/#:~:text=The%20minimum%20sample%20size%20is,to%20survey%20all%20of%20them.

Kindly see also the following useful RG link: Article Sample size: how many participants do I need in my research?

Also check please the following useful link: https://greatbrook.com/survey-statistical-confidence-how-many-is-enough/

The following RG link is also very useful: Article Sample Size Policy for Qualitative Studies Using In-Depth Interviews

Visit kindly the following useful link: https://www.itl.nist.gov/div898/handbook/prc/section2/prc222.htm

Sampling of small size - https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&cad=rja&uact=8&ved=2ahUKEwjlluaGp-72AhUuqFYBHQhTBPUQFnoECBwQAQ&url=https%3A%2F%2Furegina.ca%2F~morrisev%2FSociology%2FSampling%2520from%2520small%2520populations.htm&usg=AOvVaw1OEXF9DluuZ6T9yx_LK_cS