An analyst compares the mean salaries of men and women working at a company. Source DF Type III SS Mean Square F Value Pr > F School 3 17905.24929 5968.41643 4.14 0.0073 Gender 1 1578.63006…

Question

Options

• ASchool*Gender should be removed because it is non-significant.
• BGender should be removed because it is non-significant.
• CSchool should be removed because it is significant.
• DGender should not be removed due to its involvement in the significant interaction.

• A
  11% (5)
• B
  4% (2)
• C
  20% (9)
• D
  65% (30)

Explanation

Option D is correct because when an interaction term (School*Gender) is statistically significant (p = 0.0091 < 0.05), the hierarchical principle of model building requires that all lower-order terms involved in that interaction remain in the model - regardless of their individual significance. Gender's p-value of 0.2971 is irrelevant here; removing it would produce an uninterpretable, non-hierarchical model.

Why the distractors fail:

• A is wrong because School*Gender is significant (p = 0.0091 < 0.05) - the premise is false.
• B is wrong because it ignores the interaction: you cannot remove a main effect that participates in a significant interaction, even if that main effect alone is non-significant.
• C is doubly wrong - significant terms are retained, not removed, and School is also part of the significant interaction so it must stay for that reason too.

Memory tip: Think of the interaction as a "contract" between its main effects. If the interaction is significant, both parties (School and Gender) are bound to stay in the model. A significant interaction always takes precedence over a non-significant main effect.

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