In statistics, why is a sample not allowed to be more than 10% of the population. It seems intuitive that the closer you can survey the whole population, the more accurate the results would be.
In: Mathematics
I’ve never heard of this “rule”. As long as the sample isn’t biased in some way (it needs to be as random as possible) then there’s no reason it can’t be 10%. In fact the percentage is mostly irrelevant; it’s the sample size that matters.
I also never heard of that 10% rule but it indeed exists. To summarize, the 10% value (or 5%) is a rule of thumbs that mostly applies when you make a sampling **without** replacement (like in a survey for example, where each person is questionned only once). In this case you will create a bias in the estimation of the variability of the measure (see source 3)
There could also be an issue in experiments where observations are not independent. A small sample size will limit the fact that your observations are linked together.
Source : [http://www.tools4dev.org/resources/how-to-choose-a-sample-size/](http://www.tools4dev.org/resources/how-to-choose-a-sample-size/)
[https://www.statisticshowto.com/10-condition/](https://www.statisticshowto.com/10-condition/)
University of Texas explanation : [https://web.ma.utexas.edu/users/mks/M358KInstr/TenPctCond.pdf](https://web.ma.utexas.edu/users/mks/M358KInstr/TenPctCond.pdf)
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