When using statistical evidence, why is it important that it was compiled by a disinterested source?

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The reason for this is that statistics can easily be manipulated to tell a story that a particular source wants them to tell.  Therefore, you need to have evidence from a source that is not trying to prove a particular point.

To use a hypothetical example, let us imagine you are looking at the rate at which students drop out of school.  A source that wants to dramatize the problem might look at a cohort of kindergartners in a given school district and then ask how many of those students graduated from high school in the same district thirteen years later.  A source that wants to play down the situation might look only at students who started high school in a given school.  They would then not count those who transferred to another school.  The first method would yield a much greater dropout rate than the second.  

If you do not use evidence from a disinterested source, you run the risk of getting biased data.

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