Descriptive Statistics
Dependent variable: PostTest
| Program | Mean | Std. Deviation | N |
|---|---|---|---|
| After School | 80.50 | 5.287 | 20 |
| Saturday Academy | 82.40 | 5.679 | 20 |
| Summer Bridge | 86.45 | 5.539 | 20 |
| Total | 83.12 | 5.961 | 60 |
Lesson 06.05 · Workbook pages 623–632
Read the core ANCOVA output
This lesson moves from the raw group averages to the table that answers the research question. You will learn what can be described before adjustment, then read the covariate, adjusted group effect, effect size, and model fit in the correct order.
The novice rule
Raw means show what happened as-is. The Tests of Between-Subjects Effects table shows what still matters after the covariate is controlled.
Output 2
Start with the raw means
The Descriptive Statistics table shows the unadjusted PostTest scores. It gives you a starting picture, not the final ANCOVA conclusion.
Summer Bridge has the highest raw mean, and After School has the lowest.
Each group has 20 students, and the standard deviations are fairly similar.
Do not say Summer Bridge is the most effective program.
Do not say the groups differ significantly. This table contains no hypothesis test.
Raw means
What each group scored as-is, before controlling for Pretest.
Adjusted means
What the group averages would look like if everyone started at the same covariate level.
Common misstep
The highest raw mean is not automatically the best program. A group may start higher on Pretest, so ANCOVA waits to see what remains after adjustment.
Output 3
Use the table that answers the ANCOVA question
The Tests of Between-Subjects Effects table asks whether the covariate predicts the outcome and whether program differences remain after adjustment.
Do not read this like a standard ANOVA table. ANCOVA has a specific reading order that keeps the covariate and adjusted group effect separate.
The ANCOVA reading order
1Covariate line first: Pretest
Does the starting score relate to the ending score?
2Group line second: Program
Do program differences remain after controlling for Pretest?
3Effect size: partial eta squared
How strong is each effect?
4Model strength: R²
How much PostTest variation does the full model explain?
5Skip the Intercept
It usually does not answer the applied research question.
Worked example
Interpret Program and Pretest
The study compares three academic enrichment programs on PostTest while controlling for Pretest.
Tests of Between-Subjects Effects
Dependent variable: PostTest
| Source | Type III Sum of Squares | df | Mean Square | F | Sig. | Partial Eta Squared |
|---|---|---|---|---|---|---|
| Corrected Model | 1994.381 | 3 | 664.794 | 365.694 | < .001 | .951 |
| Intercept | 796.169 | 1 | 796.169 | 437.962 | < .001 | .887 |
| Pretest | 1624.948 | 1 | 1624.948 | 893.863 | < .001 | .941 |
| Program | 145.640 | 2 | 72.820 | 40.057 | < .001 | .589 |
| Error | 101.802 | 56 | 1.818 | — | — | — |
| Corrected Total | 2096.183 | 59 | — | — | — | — |
Model note: R² = .951; Adjusted R² = .949.
1. Covariate: Pretest
F(1, 56) = 893.863, p < .001, partial η² = .941Pretest strongly predicts PostTest. Students’ starting scores are closely related to their ending scores, so controlling for Pretest is justified.
2. Group effect: Program
F(2, 56) = 40.057, p < .001, partial η² = .589Program differences remain after controlling for Pretest. This is the main ANCOVA conclusion.
3. Effect size
Pretest = .941 · Program = .589Pretest has a very large effect, and Program still has a large, meaningful effect after adjustment.
4. Model fit
R² = .951Pretest and Program together explain about 95% of the variation in PostTest scores in this sample.
5. What this table does not tell you
It does not identify which programs differ or show the adjusted group means. Those answers require estimated marginal means and pairwise comparisons.
ANCOVA conclusions depend on adjusted results.
Pretest is part of the result, not background noise.
It does not answer the study’s applied question.
Causal language depends on the research design, not ANCOVA alone.
Transfer practice
Use the same order in a new study
A hospital compares three discharge plans on RecoveryScore while controlling for baseline symptom severity.
Open the hospital practice output
DV: RecoveryScore · IV: DischargePlan · Covariate: SeverityBaseline
| Source | df | F | Sig. | Partial η² |
|---|---|---|---|---|
| Corrected Model | 3 | 18.42 | < .001 | .434 |
| Intercept | 1 | 2.11 | .151 | .028 |
| SeverityBaseline | 1 | 39.70 | < .001 | .355 |
| DischargePlan | 2 | 3.62 | .032 | .091 |
| Error | 86 | — | — | — |
Model note: R² = .434; Adjusted R² = .414.
End-of-lesson checkpoint
You can now separate the starting picture from the adjusted conclusion. Next, you will examine the adjusted means themselves.