05.05 | Chapter 5 ANCOVA
A beginner-friendly guide to the five checks that make an adjusted group comparison believable. Use this page as a map: learn what each assumption asks, how it is checked, and what a warning sign means.
Start here
ANCOVA adjusts group means using a covariate. These five assumptions check whether that adjustment is sensible, consistent, and fair across groups.
Beginner rule: do not memorize five isolated terms. Pair each term with one simple question and one common check. That turns the list into a usable decision tool.
| Assumption | Plain-language question | Common check | Warning sign |
|---|---|---|---|
| Normality | Are outcome scores reasonably shaped within each group? | Histogram, Q-Q plot, or Shapiro-Wilk | Strong skew, heavy tails, or extreme outliers |
| Homogeneity of variance | Do groups have similar amounts of spread? | Levene's test | A very small Levene p-value, such as p = .001 |
| Linearity | Does the covariate relate to the outcome in a roughly straight-line way? | Scatterplot within groups | Curves, bends, or no clear relationship |
| Independence | Is each participant's observation separate from the others? | Study design | Repeated, shared, clustered, or influenced responses |
| Homogeneity of regression slopes | Does the covariate predict the outcome similarly in every group? | Grouping factor × covariate interaction | Different slopes or a significant interaction |
Five fairness checks
Each card gives you the same three pieces: what the assumption protects, how you check it, and what a problem would look like.
Are outcome scores reasonably bell-shaped within each group?
ANCOVA uses group means, so extremely distorted outcome distributions can make those means less representative.
Do all groups have a similar spread of outcome scores?
One group should not be dramatically more variable than the others. Unequal spread can make the comparison less stable.
Does the covariate relate to the outcome in a roughly straight-line way?
ANCOVA uses a regression relationship to adjust group means. A strongly curved relationship cannot be represented well by one straight line.
Is each participant's observation separate from everyone else's?
Independence comes from the research design. Standard ANCOVA assumes one separate outcome and covariate value for each independent case.
Does the covariate predict the outcome similarly in every group?
This is the signature ANCOVA assumption. ANCOVA applies one shared adjustment logic across groups. If the covariate has a different effect in each group, one common adjustment can misrepresent the pattern.
Important distinction
Parallel lines support a common adjustment. Crossing or clearly diverging lines suggest the covariate does not behave the same way in every group.
Visual index
The graphics below are diagrams, not real data. Their purpose is to make the slope assumption visible.
The covariate has a similar relationship with the outcome in both groups.
The covariate-outcome relationship changes by group, so one shared adjustment may not fit.
Novice decision map
Most assumption questions contain a clue. Learn to match the clue with the correct assumption.
Quick check
Choose the best answer for each scenario. The answer bubbles match the format used throughout the course.
Apply the index
Use the five-check index to name your variables and identify the assumption most likely to need attention.
Final novice takeaway
Normality checks shape. Variance checks spread. Linearity checks the form of the relationship. Independence checks the design. Homogeneity of regression slopes checks whether the covariate works the same way across groups.
Source boundary: printed workbook pages 588-596. The next lesson begins Chapter 6 with “Making Sure ANCOVA Is a Fair Test.”