Dunnett's test

Finally, instead of comparing all possible combinations, you might instead want to just compare each group to a reference. In this case, you might want to use the "Background" group as a reference. Dunnett’s test will do this, and can be implemented in the multcomp library. The main function in multcomp for doing post hoc tests is glht (which stands for ’general linear hypothesis tests’). At this point, the syntax may seem a little strange, but the multcomp library is extremely powerful. We will only scratch the surface by using it to conduct the Dunnett’s test. (Also, be aware that when you install multcomp, there are a large number of other libraries it depends on.)

     >  library(multcomp)
     >  test.out = glht(out, linfct = mcp(ZNGROUP = "Dunnett"))
     >  summary(test.out)

         Simultaneous Tests for General Linear Hypotheses

    Multiple Comparisons of Means: Dunnett Contrasts


    Fit: aov(formula = DIVERSTY ~ ZNGROUP, data = d)

    Linear Hypotheses:
     Estimate Std. Error t value Pr( > |t|)
    2 - 1 == 0 0.23500 0.23303 1.008 0.6195
    3 - 1 == 0 -0.07972 0.22647 -0.352 0.9701
    4 - 1 == 0 -0.51972 0.22647 -2.295 0.0725 .
    ---
    Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
    (Adjusted p values reported -- single-step method)

Notice that the first group (whatever that happens to be) is considered the reference group. Be careful to make sure this is what you want!

Key Point to Remember: The steps to analyzing the data using ANOVA were:

  • plot the response as a function of the grouping variable,

  • fit the linear model using lm(),

  • consider the assumptions (e.g., by examining the residuals of the linear model),

  • interpret the ANOVA results, which were obtained using anova(),

  • consider post-hoc comparisons.