Many of us deal with physical parameters to be constraint... that is performing theory, but in which way I can make sure that my experimental sample is a representative sample?
Imagining that my data base is formed by N stars of certain type, these are the only ones that have hitherto been observed. One may say okay if N=1000 that is big enough, how could I be certain about it?
One possibility is to wait maybe 10 years more to collect more observational database and corroborate theory with the new bigger group...but again how can I be certain again? Our Galaxy contains millions millions of stars of these group, how could I validate my theory? That is to extend what happens in one sample to the whole sample that is a whole galaxy
Hi Judit,
This is a really good question, that, unfortunately, can be really complex depending on what effect you are studying. I come from the public health perspective, where epidemiologists and biostatisticians work on designing experiments with an appropriate sample size. This depends on the size of the effect that you are studying, and the statistical power with which you want to observe your effect. Of course, because you don't know exactly how big your effect is (that is, how frequently it occurs) before you study it, you have to make some assumptions from previous research.
Also, you need to make sure that your sample is representative of the population that you are trying to generalize your studied effect for... so this is where selection methods come into play. If you can get a hold of it, Kenneth Rothman's Modern Epidemiology is a really good introduction to these study design issues. Also, these links may help you out.
http://smm.sagepub.com/content/4/4/311.abstract
http://en.wikipedia.org/wiki/Sample_size_determination
Good luck
Marianna
It does not sound like you can call your sample of stars a "true" representative sample of stars of type X. To have a true representative sample, you would need to take a random sampling of all the stars of type X in the universe. By definition, your sample is non-random. If you knew the characteristics of all the stars of type X, you could compare your sample to the known characteristics of all stars of type X and make a confident assertion that your sample is representative. You cannot do this, however, because you do not know what the characteristics are for all stars of type X.
What you might consider doing to help you in testing your theory is segmenting your data set by when the star was discovered (150 years ago, 100 years ago, 50 years ago - whatever is appropriate for your analysis) and testing your hypotheses on the smallest subset (that is, the group of stars that was discovered earliest), then testing your hypotheses on the second smallest subset (the earliest and second earliest discovered stars), and so on, finally running your analysis on your entire data set. This is essentially your idea of waiting for a large dataset, but in reverse. If your theory holds as you add more observations, it strengthens the assertions of the theory.
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