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Suppose that sample size of both group is not 1,000 but 100, and 5 lung cancer cases in smokers and 1 in not smokers group were observed.
In this case ratio of smokers/not smokers=5%/1%=5 stays same. However, if statistical test was conducted, p-value became 0.212.
From this study, you can not conclude that there are significant relationship between smokers and lung cancer.
How did it happen?
In epidemilogic study, to detect certain level in difference of outcome, relatively large sample size are required. If the study was conducted in small sample size like this, sometimes true results were not drawn. In such a case, it is nothing more than waste of time and money.
We have to be careful about sample size when we conduct