# How to justify the sample size? [closed]

I'm wondering how can I justify my sample size! I have 45 observations and 6 independent variables from which one is control variable. Is there any rule of thumb or specific test in this regard?

Many thanks,

• There is not enough information disclosed in order to provide an answer. You need to explain your data and what your research question is. Further, sample-size estimates should be made a priori and not a posteriori. Have you researched publications in your field to review how others have set sample size? Commented Apr 25, 2013 at 0:59
• +1 for @doug.numbers' comment. For example, you certainly need to tell us what analysis you are intending to do, where the data come from, and if (for example) there is a response variable you are seeking to model and what type it is (it makes a big difference if it is continuous or categorical). Guessing that you want to fit a model with six explanatory variables and a response variable, most rules of thumb out there suggest you don't have enough to do this. Commented Apr 25, 2013 at 2:30
• Previously asked on stackoverflow.com/questions/16174959/… That thread signalled that the question was too vague to answer easily. Commented Apr 25, 2013 at 7:47

You need to study (or search for) "power calculations" which allows you to determine your sample size and your test power. You can calculate power for your running test from your sample size and some other factors such as variance and the type of the test used and sometimes other factors. A power > 0.8 is usually considered as appropriate.

If your test power sufficed, then it is fine, although you should still state in your limitations that your sample size and power were not pre-determined before the experiments. It is strongly advised to calculate power and sample size Before the experiment (a priori), however many studies still ignore this and calculate their power on journal request (after everything is finished and even the article is written!); but many journals still publish them. So it is still a possibility, although not the best choice.

However, if your sample size did not suffice to obtain a good power, you should consider your current study as merely a pilot study and calculate a proper power based on your current pilot study, and according to the proper power, determine and hit a new sample size (and run new experiments until reaching the pre-determined sample size). Now you have a "a priori" power and sample size calculation.

And I agree, for being able to clearly answer, the responders need to know about the study design, its goals, the details about the variables and their nature (type), and extra details such as statistical analyses determined etc., in an organized way.

• Thanks a lot Vic. The response variable is the number of books written in a given period and the independent variables are some important factors that may affect the response variable like past productivity of the author, the amount of money that he/she had etc. Commented Apr 27, 2013 at 15:42
• I'm doing a poisson regression. The point that I cannot get in Power Analysis is that it works with mean and st. dev., right? In my case, since I'm dealing with the number of books in different periods the standard deviation is huge. That's why the power analysis is proposing me a huge sample size to be in the safe side which is not possible since at most I can go back and collect data from 1950s and it is not possible to go back 1000 years! Here is where I got lost in this analysis. Commented Apr 27, 2013 at 15:44
• I see. Maybe you could add more recent authors? Isn't it possible to collect information regarding 1000 authors between 213 and 1950, instead of 100 authors currently collected? Do you certainly need to go beyond 1950 for collecting the extra 900 authors? Your design is not still clear to me... For example how many authors do you have and how many the sample size calculation methods suggest you need?
– Vic
Commented Apr 27, 2013 at 15:52
• But even if it was not possible to collect more authors, and you have not started your experiments, you can do another thing: you can configure your alpha to compensate your lack of power. It would fix your power problem, but itself would increase the chance of obtaining false positive errors. And remember that you can do it, ONLY and only if you have not started any experiments (not after that). If your experiments are done, this method is totally incorrect and useless.
– Vic
Commented Apr 27, 2013 at 15:54
• Many thanks Vic. The reason I am not able to collect more data is that I'm not analysing the effect at the individual level (for each single book), instead I have 45 periods (for each year) representing the total number of books in that year. Commented Apr 27, 2013 at 20:03