Earlier quoted context omitted.
You can absolutely draw conclusions about the statistical power of the test. That’s what statistics is for. If this sample data is randomly sampled it looks like it will be a fairly high precision test for invasive cancers, with room for false negatives. You would have had to have gotten very unlucky to see such a difference in distributions even on a small sample like this. But sure, let’s get more samples.
Thank you for this! I get frustrated with the "N of only 21? Might as well flip a coin!" responses. Like you say, the whole purpose of statistical testing is to give an accurate, numeric value that says how likely the results are due to chance. One thing I'd note, though, is that the paper's title is "High sensitivity saliva-based biosensor in detection of breast cancer biomarkers: HER2 and CA15-3". My understanding…
To all who criticize and ridicule someone who would like to have more samples, why do you think 21 is such a perfect number in this case? Wouldn't 15 be enough, if statistics and all applies? 10? 1? Would 30 be too much?