Simultaneous CI Formulas for a CRD with

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Simultaneous CI Formulas for a CRD with k
Treatments and n Replications per Treatment
Bonferroni
vs.
Scheffe for all linear combinations
or
Scheffe for all contrasts
The question of which simultaneous intervals are
best (narrowest) does not depend on the data.
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Hybrid Methods

• Suppose we want simultaneous 95 CIs for all
  means and all pairwise differences among means.
• We could construct simultaneous 97.5 CIs for
  all means using Bonferronis method and
  simultaneous 97.5 CIs for all pairwise
  differences among means using Tukeys method.
• The combined set of intervals gives simultaneous
  coverage at least 95 using Bonferronis
  inequality.

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R Commands for Distribution of the Studentized
Range

• ptukey(u, nmeansk, dfnk-k)
• gives PUltu.
• qtukey(p, nmeansk, dfnk-k)
• gives value of u such that PUltup.