After performing an ANOVA test, an analyst has determined that a significant effect exists due to income. The analyst wants to compare each income to all others and wants to control for…

Question

Options

• Alsmeans income / pdiff=control adjust=dunnett;
• Blsmeans income / pdiff=control adjust=t;
• Clsmeans income / pdiff=all adjust=tukey;
• Dlsmeans income / pdiff=all adjust=t;

• A
  79% (52)
• B
  6% (4)
• C
  12% (8)
• D
  3% (2)

Explanation

Option A correctly pairs pdiff=control with adjust=dunnett - Dunnett's method is specifically engineered to control the experimentwise (familywise) error rate when comparing each treatment group against a designated reference/control group, making it the most powerful and targeted approach for this design. The pdiff=control option limits comparisons to each income level vs. the reference, which aligns with the analyst's goal and reduces unnecessary Type I error inflation.

Option B (pdiff=control, adjust=t) is wrong because adjust=t applies unadjusted t-tests, controlling only the comparisonwise error rate - the experimentwise error rate balloons as comparisons accumulate, directly violating the analyst's requirement.

Option C (pdiff=all, adjust=tukey) is tempting since Tukey's HSD does control experimentwise error, but pdiff=all performs every pairwise combination rather than comparisons against a reference group; when a control exists, Dunnett's is more statistically powerful because it makes fewer comparisons.

Option D (pdiff=all, adjust=t) is doubly wrong: it does all pairwise comparisons AND uses no experimentwise error correction.

Memory tip: Think "Dunnett = Designated control" - Dunnett's is your go-to when each group is compared to one reference. Tukey is for free-for-all pairwise battles with no reference group.

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