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I want to do some tests based on all historical data of a product updated on a daily basis. These data are not supposed to have any time trend associated with them just be pulled on different days.

I am just wondering if I want to do some statistical inference of this kind of data, do I have to randomly sample it again within this data or I can treat this data as a sample of the whole population (which includes the future data points) if I want to conduct some hypothesis tests?

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  • $\begingroup$ What inference do you want to do exactly? $\endgroup$ – gung Mar 2 '15 at 23:57
  • $\begingroup$ I actually want to compare proportions across different groups $\endgroup$ – MYjx Mar 3 '15 at 17:47
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The population/sample paradigm is one way to understand statistical inference, but it is not the only one. Since it is fairly easy to understand it is the way that many introductory stats classes discuss inference. Your description is a random process that will generate a meaningful sample as long as your assumptions hold (the mean is not changing over time, etc.) and you can use the standard tools without worrying about defining what your population is.

Think about flipping a coin, another common introductory example, we don't make a list of every time that coin will be flipped and then randomly choose among them, we just use the next $n$ flips as our sample. Your case is similar.

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