However, this calculator is hard-coded for contrasts that are pairs, and hence does not pester the user for additional input that defines generalized contrast structures.The post-hoc Scheffé multiple comparison of treatment pairs by this calculator is based on the formulae and procedures at the NIST Engineering Statistics Handbook page on Scheffé's method that was published by Scheffé in 1953.The recommendation on the relative merits and advantages of each of these methods in the NIST Engineering Statistics Handbook page on comparison of these methods are reproduced below: When the number of contrasts to be estimated is small, (about as many as there are factors) Bonferroni is better than Scheffé.
On the other hand, Scheffé's method is independent of the number of contrasts under consideration.
The post-hoc Bonferroni simultaneous multiple comparison of treatment pairs by this calculator is based on the formulae and procedures at the NIST Engineering Statistics Handbook page on Bonferroni's method.
Among the many reviews of the merits of the Holm method and its uniform superiority over the Bonferroni method, that of Aickin and Gensler (1996) is notable.
This paper is the also source of our algorithm to make comparisons according to the Holm method.
The Bonferroni and Holm methods of multiple comparison depends on the number of relevant pairs being compared simultaneously.
This calculator is hard-coded for Bonferroni and Holm simultaneous multiple comparison of (1) all pairs and (2) only a subset of pairs relative to one treatment, the first column, deemed to be the control.
In contrast, when spouting out Tukey HSD, Scheffé, Bonferroni and Holm multiple comparison results, this calculator also tells you how to verify and reproduce their output and results manually in Excel, by teaching you how to take the output of Anova (from Excel or other package), enabling you to conduct post-hoc Tukey HSD, Scheffé, Bonferroni and Holm multiple comparison by hand in Excel.
Your automatic A grade results from wizardry in producing post-hoc Tukey HSD, Scheffé, Bonferroni and Holm pairwise multiple comparison yourself manually in Excel, in which case you would no longer need this calculator, nor have to struggle with harnessing the old school statistical packages.
This calculator is designed to relieve biomedical scientists from the travails of coding heavy-duty statistical packages: Are you a biomedical or social scientist, who has narrow interest in one-way ANOVA followed automatically by post-hoc Tukey HSD, Scheffé, Bonferroni and Holm methods, but do not have the patience and perseverence to hack code to harness R, Stata, SPSS, SAS or Matlab? It was inspired by the frustration of several biomedical scientists with learning the software setup and coding of these serious statistical packages, almost like operating heavy bulldozer machinery to swat an irritating mosquito.
For code grandmasters, fully working code and setup instructions are provided for replication of the results in the serious academic-research-grade open-source (and hence free) R statistical package.
Tukey originated his HSD test, constructed for pairs with equal number of samples in each treatment, way back in 1949.