Since this is a masters-level thesis work, I strongly suggest that you include considerations in capturing patients with PCOS who are not in Facebook. Furthermore, you can also delimit your coverage to include only patients with PCOS in a particular country (such as Denmark) or in that Facebook group (which I perceive will be an issue to your adviser and in your desire to get a statistically-sound estimate).

"Is it possible to find the prevalence (of anxiety and depression among Danish women with PCOS), when the requited women on Facebook are not representative of the general population?" - Answer: Technically speaking, it is possible to get an estimate of the prevalence even in this scenario, but it will be challenging to convince the reader or yourself or your adviser that this estimate is close to the parameter given the issue of representativeness. You have to contend with issues such as whether there is expected or real differences between patients with PCOS who are in and not in that group.

"Furthermore, is it possible to randomize the sample?" - Answer: Randomization is possible, but it will still not address the fact the Facebook group where you'll do it is likely not representative of the population you want to study in conceptual terms. In this regard, assuming that you'll stick to the plan that you mentioned, I suggest that you aim for law of large numbers and strive to invite as many members from that group as possible, rather than randomizing in a sample that is "flawed" to begin with, given the relative convenience.

"If not, should I just use the word “proportion” instead?" - Answer: Proportion may be a safer word compared to prevalence, but there is no doubt that you are aiming to estimate prevalence anyway.

Regarding your final paragraph, remember that, in more cases than not, standard sample size equations assume that the population ("N") you are working on is appropriate, and you will obtain the sample ("n") through means that will lead to a representative group. The number you will get from any equation is usually the minimum number that will be sound given the conditions/scenarios/values you plugged in from the equation that you used (hence, that minimum sample size estimate is only as good as the values you plugged in the equation), so you can theoretically exceed the number (with approval of course from your ethical board).

Aedrian Abrilla explained it very well.

I just want to add something in it, If you study objective is to calculate prevalence then you can calculate it as prevalence is simply a proportion so if you calculate proportion its still gives you prevalence. But as stated by Aedrian Abrilla "proportion may be a safer word than prevalence.

Secondly, if you are conducting your study by means of convenient sampling technique, you can proceed without calculating sample size. You can take any number of samples based on your convenience but have to decide it first before start of study. Convenient sampling is totally based on your convenience but if you are interested in other sampling methodologies you have to calculate sample size. As far as randomization is concerned, you can do it but its very unlikely that your sample frame is representative of target population. The main problem with digital epidemiology is that it is not representative of target population or whole population so you can calculate prevalence but it will be difficult to generalize it.

Dear Vian,

I would tend to believe that the facebook PCOS support group of >5,000 members would be fairly representative of the general population of Danish women with PCOS - unless there's contrary evidence.

On randomization, I think this would be possible. However, a simple random sample seems less ideal....perhaps if the Danish town, or other relevant variable can e identified, a stratified random sample may be best.

Your sample size calculation would be based on the prevalence of your outcome of interest in your target population. Using a larger sample enhances the accuracy of your results.

I hope you find this useful.

Godfrey.

You could calculate sample size based on a previous study using cochran. I think getting respondents outside of Facebook and online( hospitals) will be good and then combine to make up the total size N. Prevalence is the proportion who from your research questions were found to be depressed out of the total number of respondents.

Anita E. Asamoah Unfortunately, the Corona pandemic has resulted in many limitations in Denmark including lock downs, which make it really inconvenient to have an institutional data collection in the months I am supposed to recruit participants.

Hence, it doesn't seem possible to reach the general population of women with PCOS in Denmark as I don't have any other option than using Facebook as data collection platform.

Thank you everyone for your comments, they have been useful and I have taken them all into consideration.

If anyone is interesting in reading the synopsis of the thesis, to share some knowledge or provide with some comments, please send me a private message, and I will send you the file. It contains: introduction (statement of problem, significance of study, variables, objectives, research questions), literature review and methodology. This is a summary of the main important parts of the study, and doesn't contain details like inclusion and exclusion criteria on purpose (there is page limit on the synopsis).

I totally agree with Aedrian Abrilla