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Column: Technical Aids: Single Test that Two Samples Came from the Same Normal Population

Summary: When two normal populations are compared with respect to a single characteristic, it is possible to test separately for a difference between the means and between the standard deviations. However, it was suggested by Pearson and Neyman (1930) that a single and more powerful test could be based on the principle of likelihood. The test they developed is given here with two changes. First, the standard deviation calculations follow the present-day common practice of using N - 1 in the denominator (Pearson and Neyman used N). Second, the critical values have been inverted to correspond to the more intuitive interpretation where larger sample statistics correspond to more significant results.

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  • Topics:
  • Keywords: Approximation,Monte Carlo methods,Critical values
  • Author: Nelson, Lloyd S.
  • Journal: Journal of Quality Technology