Lesson 06.03 · ANCOVA assumption checks

Equal spread. Equal rule.

Before ANCOVA adjusts group means, two questions matter: Are the outcome scores similarly spread across groups? And does the covariate relate to the outcome in the same way for every group?

By the end, you can:

read the workbook's Levene's Test decision using the Based on Mean row;
explain what a significant Levene's result signals;
recognize parallel versus different regression slopes; and
decide whether the ANCOVA assumptions are supported.

Assumption 3

Homogeneity of variance

The dependent variable should have a reasonably similar spread in each program group. One group should not be extremely scattered while another is tightly packed.

Plain-language memory cue: Means tell you where groups center. Variance tells you how widely scores spread around those centers. Levene's Test checks whether those spreads are similar enough for the comparison.

Concept illustration comparing three groups with similar score spread to three groups where one group has a much wider spread.

Concept illustration only. The workbook decision is made with Levene's Test, not by this invented example.

p > .05Levene's is not significant. The assumption is met.

p ≤ .05Levene's is significant. The assumption is not met.

Workbook scenario

Read Levene's in three moves

The study compares PostTest scores across After-School Tutoring, Saturday Academy, and Summer Bridge. For this workbook, interpret the row labeled Based on Mean.

Tests of Homogeneity of Variances

The source supplies the interpretation row and its significance value. Other SPSS statistics are intentionally not added here.

Workbook interpretation extract
Row to read	Dependent variable	Sig. (p-value)	Decision
Based on Mean	PostTest	.958	Assumption met

1. Find the rowUse Based on Mean for this workbook.

2. Read Sig.The p-value is .958.

3. Compare with .05.958 is greater than .05, so the test is not significant.

Decision anchor

Levene's Test was not significant, p = .958, indicating that the homogeneity of variance assumption was met.

When the result is significant

A warning is not the same as an automatic stop

A practice output gives Based on Mean p = .012. Because .012 is less than .05, Levene's is significant and the homogeneity of variance assumption is not met.

Check group sizesAsk whether the groups are similarly sized or strongly unbalanced.

Inspect severityDecide whether the spread difference is mild or extreme.

Look for causesCheck outliers and possible data problems before deciding what to do.

Careful conclusion

A significant Levene's result means pause, investigate, and report transparently. The workbook does not treat it as an automatic command to abandon the analysis.

Assumption 4

Homogeneity of regression slopes

This is the ANCOVA-specific check. Pretest must predict PostTest in a similar way across the three program groups. In plain language, the covariate must use the same rule for everyone.

X → Y

The question: Does the relationship between Pretest and PostTest differ by program? Statistically, this is tested with the Program × Pretest interaction. If the interaction is not significant, the assumption is met.

Concept illustration showing three parallel regression lines when the slopes assumption is supported and three differently tilted lines when it is violated.

Parallel lines may start at different heights, but they tilt at about the same rate. Crossing or differently tilted lines mean the covariate does not work the same way across groups.

Interaction not significant

Program × Pretest is not significant. The relationship is similar across groups, so the slopes assumption is met.

Interaction significant

Program × Pretest is significant. The covariate behaves differently by group, so a standard ANCOVA adjustment cannot be interpreted as intended.

Bring both checks together

Is the model ready for the next step?

A novice-friendly assumption summary names the evidence, applies the rule, and states whether the analysis may continue.

Lesson 06.03 | Source boundary: printed workbook pages 610–615. The lesson ends before “Running the ANCOVA in SPSS.”

Equal spread. Equal rule.

By the end, you can:

Homogeneity of variance

Read Levene's in three moves

Tests of Homogeneity of Variances

What does p = .958 mean here?

A warning is not the same as an automatic stop

Homogeneity of regression slopes

Which pattern supports ANCOVA?

Is the model ready for the next step?

Complete the two-assumption summary