ANOVA POST HOC Testing

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STAT 3130Statistical Methods I

• Session 3
• ANOVA POST HOC Testing

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ANOVA Post Hoc Testing

• From the previous notes, we found an F-statistic
  of 24.33. This equated to a very low p-value
  (lt.001), allowing us to reject the Null
  Hypothesis and conclude that a difference amongst
  the means was present
• This does not really guide our decision making
  although we concluded that at least one of the
  plans is different, at this point we have no
  information regarding WHICH plan(s) is (are)
  different.
• To determine this, we need to execute a Post Hoc
  test.

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ANOVA Post Hoc Testing

• Post Hoc tests are a critical step in the ANOVA
  process because they allow us to determine WHICH
  plans are different from the others.
• There are several possible Post Hoc tests to
  choose from based upon the specifics of your
  analysis. We will look at the two most common
  Fishers LSD and Tukey.
• ltOther post hoc tests which you may hear about
  include Duncan, Scheffe, Bonferroni, Dunnett,
  Sidak, Waller, Welchgt

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ANOVA Post Hoc Testing

• Both Fishers LSD test and Tukeys test are
  commonly accepted tests amongst statisticians.
  You really cannot go too far wrong with either.
  Here are a few general points of comparison
• Fishers LSD (least significant difference) is
  less conservative than Tukeys HSD (honestly
  significant difference).
• Fishers LSD executes a series of ttests amongst
  the pairs, resulting in a higher Type 1 error
  rate, while Tukeys HSD specifies a family error
  rate across all comparisons
• Tukeys HSD calculates Tukeys Yardstick any
  mean differences which are at least as large as
  the Yardstick are considered to be different.

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ANOVA Post Hoc Testing

• Additional sources for detailed information
  regarding Post Hoc tests
• http//support.sas.com/documentation/cdl/en/statug
  /63347/HTML/default/viewer.htmstatug_glm_a0000000
  867.htm
• http//www.uwsp.edu/psych/cw/statmanual/posthocs.h
  tml
• http//pages.uoregon.edu/stevensj/posthoc.pdf
• http//practicalstats.labanca.net/index.php?title
  Selecting_a_Post_Hoc_test