06.01 | Chapter 6: Assumption Checks

Start with a Fair Test

Before ANCOVA adjusts group means, you must confirm that the study design and outcome distributions support that adjustment. This lesson begins with the first two checks: independence and normality.

By the end of this lesson, you can

explain why assumptions protect the meaning of ANCOVA;
verify independence through study design and coding;
apply the Shapiro-Wilk decision rule within each group; and
recognize when a normality result calls for investigation rather than rejection.

Assumption 1

Independence is a design check

SPSS cannot repair or prove independence with a p-value. You establish it through the way the study was conducted and the way each case appears in the dataset.

What independence means

Each participant contributes one observation, belongs to one group, and is not influenced by another participant's score.

One participant. One row. One group.

Row 27

Student 27

Program = 2

Why it matters

If participants overlap across groups or contribute dependent scores, group means and standard errors may be distorted. The resulting p-values no longer answer the intended question.

Stop signal: If independence is violated, standard ANCOVA is not the right analysis for that dataset. The design or analysis must be reconsidered.

One row per participantScan Data View for duplicate cases or repeated records.

One group per participantUse clear, non-overlapping codes such as 1, 2, and 3.

Separate observationsParticipants should not share, copy, or jointly produce the measured outcome.

Sample study

Students participate in one enrichment program: After-School Tutoring, Saturday Academy, or Summer Bridge. Each student should appear once and have exactly one program code. Participation in two programs would break the one-group structure.

Assumption 2

Normality belongs to the outcome within groups

ANCOVA compares adjusted means. The dependent variable should therefore be approximately normally distributed within each group. The goal is not perfect symmetry, but a distribution that is not so skewed or extreme that the mean becomes misleading.

Shapiro-Wilk p > .05No statistical evidence of serious non-normality. Continue to the next check.

Shapiro-Wilk p ≤ .05Possible concern. Pause and investigate severity, sample size, outliers, or data errors.

Do not test the entire dataset onceNormality is evaluated separately within every group created by the independent variable.

Do not treat significance as automatic failureA significant Shapiro-Wilk result is a warning flag that requires closer inspection, not an instant ban on ANCOVA.

Worked example

Three programs, three checks

The sample study reports one Shapiro-Wilk result for each enrichment program. All three p-values are above .05, so the normality assumption is supported for this first pass.

Program group	Reported result	Beginner interpretation
After-School Tutoring	p > .05	No normality flag
Saturday Academy	p > .05	No normality flag
Summer Bridge	p > .05	No normality flag

Guided practice

Read a second normality output

A therapy study compares post-intervention anxiety across three formats while controlling for baseline anxiety.

Quick check

Which conclusion is best supported?

Group	Shapiro-Wilk p
Group A	.041
Group B	.118
Group C	.089

Select one answer.

AAll groups clearly violate normality, so ANCOVA must be abandoned. BGroups B and C are above .05, while Group A raises a possible concern that should be investigated. COnly Group A is normal because its p-value is the smallest. DNormality is tested once across all three groups, so the separate values are irrelevant.

Apply it

Check your own study

Use one short response to connect the two assumptions to your design.

Lesson 06.01 | Source boundary: printed workbook pages 597–604. The next lesson begins with visual normality checks using histograms.