PYB350 Chap.7 Simple Effects and Follow-Up Tests
Simple Effects and Follow-Up Tests
Once the omnibus two-way ANOVA is run, the interaction decides what happens next.
This chapter follows the unit's decision tree: with no interaction, interpret main effects and follow up any with more than two levels using planned contrasts or Tukey tests on the marginal means; with a significant interaction, test simple effects of the focal factor at each level of the other using the pooled error term, then follow up significant simple effects with contrasts or post hoc comparisons on the cell means.
It also covers omega-squared, JASP and bootstrapped follow-ups.
Two worked examples cover both branches: planned contrasts on marginal means after a clean main effect, and simple effects with simple comparisons after a significant interaction, each computed with the pooled error term.
What this chapter covers
- 01
Interpreting main effects when there is no interaction
- 02
Contrasts and Tukey tests on marginal means
- 03
Omega-squared beside eta-squared
- 04
Simple effects with the pooled error term
- 05
Simple comparisons within a significant simple effect
- 06
Type I error control and bootstrapped follow-ups
- 07
Writing up a sliced interaction in the order the analysis ran
Worked example · free
Simple effects of message source in the framing study
- 2Loss frame: mean of cells 4.2; SS = 5 times (1.44 + 4.00 + 0.64) = 30.4; MS = 15.2; F(2, 24) = 10.13, above the critical 3.40.
- 1Gain frame: SS = 0.93; MS = 0.47; F(2, 24) = 0.31, p = .736, not significant and not followed up.
- 2Within the loss frame, expert against the others (weights minus 1, 2, minus 1): contrast 6.0, SE 1.342, t(24) = 4.47, p below .001.
- 1Peer against anonymous (1, 0, minus 1): contrast minus 0.4, SE 0.775, t(24) = minus 0.52, p = .610.
Key terms
- Simple comparison
- A contrast or pairwise test among cell means inside one significant simple effect.
- Focal variable
- The factor whose simple effects are tested, chosen because the hypothesis is about it.
- Pooled error term
- The within-cells mean square from the whole factorial design, used as the denominator for every simple effect.
- Decision tree
- The unit's yes or no route from the omnibus results to the right follow-up test.
Simple Effects and Follow-Up Tests FAQ
Do I follow up a significant main effect when the interaction is significant?
No. The tutorial reports the main effects but does not follow them up, because a significant interaction means each main effect averages over effects that differ across the levels of the other factor. The follow-up work moves to simple effects of the focal factor, tested on cell means with the pooled error term.
Why use the pooled error term for simple effects?
Simple effect analyses are like separate one-way ANOVAs on slices of the design, but the tutorial uses the mean square within from the whole two-way design as the error term, the variance pooled across all cells, rather than a separate error for each slice. That keeps the error estimate stable and uses every participant.
Does a significant two-level simple effect need more tests?
No. With only two levels, a significant simple effect already locates the difference, so you interpret it from the two cell means. Further contrasts or post hoc tests are only needed when the factor being tested has three or more levels and its simple effect is significant.
How do I know which simple-effects table I am reading?
Check the label for the factor being tested and the factor it is tested at. A table of the simple effects of deviant at each confederate reaction looks almost identical to one of confederate at each level of deviant, and the lecture warns students about misreading them. Write the factor names into your sentence before quoting any F, so the direction is explicit.
Exam move
Copy the decision tree onto one page and walk every practice output through it aloud, naming the branch you take and the means, marginal or cell, that the next test uses. Then rehearse the write-up order aloud: interaction, simple effects, comparisons inside the significant slice, and the closing sentence in the words of the study.
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