Scheffe's Method

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A Scheffe's Method is a post-hoc multiple comparison procedure for estimating of all possible contrasts.



References

2016

Scheffé's method is a single-step multiple comparison procedure which applies to the set of estimates of all possible contrasts among the factor level means, not just the pairwise differences considered by the Tukey–Kramer method.

2016

  • (PSU online courses, 2016) ⇒ 3.3 - Multiple Comparisons. (n.d.). Retrieved August 28, 2016, from https://onlinecourses.science.psu.edu/stat503/node/15 Copyright: 2016, The Pennsylvania State University.
    • Scheffé's method for investigating all possible contrasts of the means corresponds exactly to the F-test in the following sense. If the F-test rejects the null hypothesis at level α, then there exists at least one contrast which would be rejected using the Scheffé procedure at level α . Therefore, Scheffé provides α level protection against rejecting the null hypothesis when it is true, regardless of how many contrasts of the means are tested.

2015

1985

  • (Kennedy & Bush, 1985) ⇒ Kennedy, J. J., & Bush, A. J. (1985). An introduction to the design and analysis of experiments in behavioral research. University Press of America. ISBN: 0-8191-4806-7
    • [...] The statistical reasoning underlying the Scheffe method appears rather complex. Approached intuitively, however, the Scheffe can be viewed as a method which: a) converts a t-ratio approach to individual comparisons to an F-test approach and b) reduces the rejection region of the F-distribution, with a concomitant loss of power, to accommodate all conceivable comparisons without exceeding the desired hypothesiswise error rate.