There is no specific and fixed answer to this question.However Sample size depends on number of things like level of significance,power of the test and previous experimentation and above all expertise in the field.

To add to what Tariq A Raja wrote above, in addition to significance level and power, adequate sample size also depends on which statistical test you intend to conduct.

I recommend downloading the free software G*Power. https://www.psychologie.hhu.de/arbeitsgruppen/allgemeine-psychologie-und-arbeitspsychologie/gpower.html

Using this software, you can conduct an a priori power analysis. You can specify which type of statistical test you want to conduct, the desired significance level, the statistical power desired, etc, and the software will compute a recommended sample size.

Best,

Blaine

The truth is that there is no rule of thumb about N. Think of your sample size as an collection of evidence so you can make up a decision. The more information you acquire, the more confidence in your decision you can have. Sample until you are pretty sure that the effect size won't change.

I have to disagree with Igor Eloi . A larger sample is not necessarily a better sample. Sample size is important to an extent, but what matters more is the method of selection.

For instance, if I want to get an idea of the voting attitudes among the population of registered voters in the state of Illinois, a random sample of 1000 individuals from all across the state is better than a sample of 10,000 individuals all living in the city of Chicago.

Yes Blaine Tomkins. Perhaps I have written in a quite unclear way, but I did so supposing there was no bias in the sampling or obvious flaws in the method. You are absolutely correct about it. Thank you highlighting it.

Igor Eloi No worries. It's so easy to get seduced into the "more is better" line of reasoning when it comes to n-size, so I just wanted to make sure it doesn't happen to Md.Ishtiaq Ahmed Talukder

Thanks to all for such quick responses. I am really going through hard time to make a standardized or scientific sample size determination, as I have to come up with a right justification for the sample size. thanks again to Blaine Tomkins , Igor Eloi and Tariq A Raja .

The answer depends on the population properties and the kind of sample you wish to take. See: https://b-ok.cc/book/2468581/f6ddd3

for full details. This is the standard reference. Look for sample size in TOC and Index. Contact me if you need assistance. Best of luck, David Booth

I am astonished that nobody (except for Igor Eloi ) mentions the importance of the effect size. If you really want to do a priori power analysis for hypothesis testing you not only have to set alpha and beta, but a priori also an effect size. Optimally, this should not be a typically found effect size, but the minimal effect size of relevance/importance for your field (Smalles Effect Size O Interest, SESOI, see for example the short section in the attached article, to get an impression, the main topic is different). It is also possible to do it the other way around, assess the ressources available (how many participants are possible to analyze with your money) and make a sensitivity analysis, how large the smallest effect size it that you are able to detect (and decide if this is useful for you). And be aware, that there are no simple caclulations for power/sample size for more complex models. In that case you should simulate your model and test at which sample size would reach a desired power level.

Blaine Tomkins and Igor Eloi regarding you comment on larger sample sizes: I agree that bias has to be avoided, but by now I have the impression and opinion that I want to have a well collected sample from the population of interest and as large as possible to have stable estimates for coefficients of interest and neglect more and more p-values. It is the interpretation of coefficients I am interested in, not the p-values. This impression grew even stronger in the last years, where I more and more discovered and used bayesian analyses. But please, share your opinion on this topic.

Rainer Duesing Absolutely. If one were uninterested in p-values, as in Bayesian analyses, I don't see any harm in getting as large of sample size as is feasible. Thank you for sharing this article as well.

I really enjoyed the discussion started after my question which made my task structured. I went through all the articles and book references provided here above and I found from different sources; that it is clear, there is no single rules or rule of thumb to determine the sample size. But for a exploratory study it is again confusing to come to an understanding. Thanks to all again.

You are welcome! Good if it somehow helped you! Good luck for your research.

Blaine Tomkins , for research, it is always important to get "as large of sample size as is feasible", no matter if you go for p-values or Bayesian posteriors. You can use p-values to check if the amount of information provided by the data is sufficient for any directional statement (if you can interpret the sign of the estimate). This boils down to the question: was the sample size large enough to conclude the sign of the parameter from the sample estimate?

Jochen Wilhelm That's an interesting point that p-values can be used as a sort of check on the data. I was speaking more to the (still common) practice of using strict p-values as decision criteria of significance. As you've mentioned elsewhere, a null hypothesis is basically false by definition and researchers are nearly guaranteed to reject it given an enormous sample size, as discussed in the attached paper.

Blaine Tomkins great help, the article you shared on "sample size and p-Value Problem" clears my misconception on sample size and p value contemporary belief. Thanks

The first step in determining sample size is to know the answer to the question asked. You cannot sample for an unknown answer.

A question and answer assumes you know the population. A question and answer require prior knowledge. The question is formed within the prior knowledge and the answer is what you deem important to the population by answering the question.

Importance leads to an 'effect size'. An important effect size is one that makes a difference and is reliably predictable. The usual p-value is that difference that is enough to show a possible direction of the difference. A p-vlaue can be used to determine the number of samples needed to show the direction. The number of samples will depend upon your prior knowledge of the population distribution and the distribution of the effect.

No effect can be quantified by a p-value. A p-value shows a possible direction, not a qualified effect. The sample sized determined by a p-value calculation is the minimum sample size to show the direction. The sample size to achieve a reliable prediction is necessarily larger than the minimum. The sample size is based on the uncertainty of the prediction.

Rainer Duesing I'll confess to you that I have a very limited knowledge about and even fewer experience with Bayesian analysis but I will agree with you on the bases of my experience with different data sets. We have recently finished an experiment and I was astonished by finding an statistically significant therm in a model that would translate to a completely negligible effect size. It was statistically significant alright but was completely meaningless in the biological system. The significance was surely a fruit from the sample size (nearly 1300 observations).

A less experienced person could easily fall into that trap and even stamp it in the article title, surely proud of the yet non described effect, but in reality merely misled by the "culture" of P value.

I use PASS software. It calculates sample size based on your statistical test and give you the reference of each formula.

Igor Eloi The book "Statistical Rethinking: A Bayesian Course with Examples in R and Stan (2nd ed)" by Richard McElreath is a TERRIFIC resource for anyone wanting to learn how to conduct Bayesian analysis. It's more of a course than a book and has helped me tremendously with my research!

Blaine Tomkins how do you think about Kruschke, J. (2014). Doing Bayesian data analysis: A tutorial with R, JAGS, and Stan. Academic Press. ? I really liked the book and it has also lots of code to follow all analyses. I just started with the new Gelman book, Gelman, A., Hill, J., & Vehtari, A. (2020). Regression and other stories. Cambridge University Press. which also focuses on bayesian analyses, although not mentioned in the title.

Rainer Duesing Hmm..I haven't read that one yet. I'll have to check it out!