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As my question title implies, I'd like a brief explanation of the significance of measures of variation in hypothesis testing.

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    I disagree with the vote to close as "too broad" because the question admits a simple answer, as demonstrated by the one I posted. ${}\qquad{}$ – Michael Hardy Feb 11 '15 at 23:23

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I shall assume you intended no pun and I won't even mention it.

If the observed mean is far from the hypothetical mean by comparison to what you would expect given its normal range of variation, then one rejects the hypothesis. But you can't know how far is far by comparison unless you know what you're comparing it with. The latter is the measure of variation.

  • Thank you very much. Just what I needed. No pun. Maths is serious business! –  Feb 11 '15 at 23:27