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I want to know that how do deal with the data that has some measurement uncertainties in it. So for example, Let's say I have a set of population densities data for different counties and I want to calculate the average population density. Then I look at three scenarios- 1) I take the weight as area of counties and 2) I take the weight as population of the counties and 3) Simply take the average. Which one of these two choices will handle the census errors more clearly? So, I have no way of knowing what kind of uncertainties were involved in the experiment. In that case what is the best case scenario for handling the data for statistical tests? Also I don't know how many (if there are any) uncertainties are present in the data. So, if I want to tackle this situation mathematically then what should I do? I mean like calculating weighted averages of the values that my variable/s of interest can take or removing the outliers and studying them separately or some other procedure like that!

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    $\begingroup$ I flagged this as too broad. I read this question as effectively saying "I have some data which may, or may not, have a wide range of different errors. What steps might I take to deal with these errors?" Answering the question seems to involve anticipating potential errors (which may or may not be present) and then presenting one (of a possible range) of solutions. Could it be made any more specific? $\endgroup$ – Ian_Fin Oct 6 '16 at 12:58
  • $\begingroup$ @Ian_Fin I edited my question! $\endgroup$ – Dark_Knight Oct 6 '16 at 13:29
  • $\begingroup$ There is still too little information to give a somewhat right answer. In general if you want a correct answer, you have to have sufficient information on your data. You can make assumptions, which will limit the value of the analysis. But anyway, the question is still basically the subject of a lot of books and publications. $\endgroup$ – cherub Oct 6 '16 at 13:54
  • $\begingroup$ I know.. it's a subjective issue like choosing a confidence level ($\alpha$) but still I hope someone can give me some insight on it! $\endgroup$ – Dark_Knight Oct 6 '16 at 14:36

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