PYB350 Chap.3 Checking ANOVA Assumptions
Checking ANOVA Assumptions
Every between-groups F test rests on three assumptions: independent observations, a normal sampling distribution within each cell, and similar variances across cells.
This chapter shows how the unit checks each one in SPSS, from histograms and skewness z-scores to the four rows of Levene's test, and what to do when one fails: rely on ANOVA's robustness with equal and adequate cell sizes, lower alpha, switch to Welch's test and Games-Howell or Dunnett T3 comparisons, transform the scores, or bootstrap the follow-up comparisons.
The worked example reads a block of normality and homogeneity output and turns it into a decision and a reporting sentence, which is exactly the move short-answer questions reward.
What this chapter covers
- 01
Independence of observations as a design feature
- 02
Normality of the sampling distribution in each cell
- 03
Skewness and kurtosis z-scores against 1.96 and 3.29
- 04
Homogeneity of variance and the four Levene rows
- 05
Welch's F, Games-Howell and Dunnett T3
- 06
Transformations, outliers and bootstrapped follow-ups
- 07
Reading the Levene, skewness and kurtosis output in a short-answer question
Worked example · free
From Levene's test to the analysis you report
- 1Skewness z = 1.10 / 0.51 = 2.16, beyond 1.96 so significant at .05, but below 3.29 so not at .001.
- 1Levene p = .028 is below .05, so the group variances cannot be treated as equal.
- 2Equal cells of ten make the mild skew tolerable, but the homogeneity breach changes the analysis: report Welch's F for the omnibus test.
- 1With 27 error degrees of freedom, follow up with Games-Howell or Dunnett T3 comparisons.
Key terms
- Welch's test
- A version of the F or t test that adjusts the error degrees of freedom so it does not assume equal group variances.
- Games-Howell test
- A post hoc comparison procedure for pairwise tests that does not assume equal variances.
- Outlier
- An extreme score that inflates variance estimates because variances are built from squared deviations.
Checking ANOVA Assumptions FAQ
How large do cells need to be for ANOVA to be robust?
The factorial lecture lists three conditions under which departures from normality matter little: roughly equal cell sizes, at least ten people per cell, and departures from normality that run in the same direction in every condition. Outliers are the bigger risk, because one extreme score can inflate the variance and distort the F ratio.
Why are formal normality tests not enough on their own?
With small samples they have very little power, so a non-significant result says little; with large samples they have so much power that they flag trivial departures. The tutorial puts visual inspection of histograms first, then skewness and kurtosis divided by their standard errors, and treats the tests as supporting information.
Can I bootstrap the ANOVA if assumptions fail?
Not the omnibus F: neither SPSS nor JASP provides a bootstrap version of it. What you can bootstrap are the follow-up comparisons and post hoc tests, which is especially useful with small samples. The other options are Welch's test, a rank-based test, a transformation, or keeping the standard analysis with a lower alpha when cells are equal and large.
What should I do about an outlier?
First check whether it is an error in data entry. If it is a genuine but extreme score, remember that it inflates the variance estimate because variances use squared deviations, which can distort the F ratio. The lecture suggests considering removal of extreme outliers, and a transformation can also reduce their pull. Whatever you choose, report it and the reason.
Exam move
Write the remedy route as a short checklist: explore each group, read Levene based on the mean, then choose standard F or Welch with Games-Howell or Dunnett T3, and practise saying each decision in one sentence. For each practice output, name the Levene row you read and the remedy you would choose before you look at any F, so the decision becomes automatic.
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