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I don't understand. If you can't control the variables, how can you get
statistically "valid" results?
My expeerimentalizt friends (in particle physics) now divide uncertainties
into a +statistical" part and a "systematic" part. These two parts must
be combined somehow (how to combine is still IMO an unsolved problem) in
order to arrive at a meaningful statement of uncertainty. When several
experiments measure the same quantity, then a comparison of quoted
uncertainties gives one an intuitive feeling for the uncertainty of our
knowledge of the quantity being measured.
I have seen nothing in the field of measuring teaching techniques the
tells me that we have much insight into how to make "statistically valid"
comparisons.
Regards,
Jack