Lesson 06.06 · Workbook pages 633–643

Compare adjusted means fairly

ANCOVA has already answered whether program differences remain after controlling for Pretest. Now you will learn what the adjusted means are, which program pairs differ, and how the sign of a mean difference tells you who is higher.

The novice rule

Adjusted means show the fair comparison. Pairwise comparisons tell you exactly where the significant differences are.

Output 4

Estimated marginal means

Estimated marginal means are adjusted means. They show the expected PostTest score for each program after SPSS places every group at the same Pretest value.

Read the footnote before the means. SPSS evaluated every program at Pretest = 70.23. That shared starting point is what makes the comparison fair.

Estimated Marginal Means · Dependent Variable: PostTest
Program	Adjusted mean	Std. error	95% CI lower	95% CI upper
After School	81.183	0.302	80.577	81.789
Saturday Academy	83.118	0.302	82.512	83.724
Summer Bridge	85.049	0.305	84.438	85.661

SPSS footnote translated

These are the expected PostTest means when every program is compared at the same Pretest score of 70.23.

After School

81.18

Saturday Academy

83.12

Summer Bridge

85.05

Safe conclusion: After controlling for Pretest, Summer Bridge has the highest adjusted mean, Saturday Academy is next, and After School is lowest.

Wait before declaring pairwise significance. This table shows the pattern. The Pairwise Comparisons table determines which specific differences are statistically significant.

Quick check 1

What do these means represent?

Choose the best interpretation.

AThe original PostTest averages before controlling for Pretest. BThe expected PostTest means after all programs are compared at Pretest = 70.23. CThe number of students predicted to pass in each program.

Output 5

Pairwise comparisons

Once the overall ANCOVA shows that adjusted group differences exist, pairwise comparisons locate those differences. These comparisons use adjusted means and a Bonferroni correction.

Read every row in the same order

1Name the two groups.

Identify Group I and Group J.

2Check Sig.

p ≤ .05 means the adjusted means differ significantly.

3Read the sign of I − J.

Positive means I is higher. Negative means J is higher.

4Confirm with the confidence interval.

An interval that does not include 0 supports significance and direction.

Unique Bonferroni Pairwise Comparisons · Adjusted PostTest Means
Group I	Group J	Mean difference (I − J)	Sig.	95% confidence interval
After School	Saturday Academy	−1.935	< .001	[−2.987, −0.882]
After School	Summer Bridge	−3.866	< .001	[−4.933, −2.800]
Saturday Academy	Summer Bridge	−1.932	< .001	[−2.998, −0.865]

After vs. Saturday

Significant, negative difference. Saturday Academy is higher.

After vs. Summer

Significant, negative difference. Summer Bridge is higher.

Saturday vs. Summer

Significant, negative difference. Summer Bridge is higher.

Overall pairwise story: All three programs differ significantly after controlling for Pretest. The adjusted ordering is Summer Bridge, Saturday Academy, then After School.

Direction without guessing

Use the sign, then check the interval

The p-value answers whether a difference exists. It does not tell you which group is higher. Direction comes from the mean difference, calculated as Group I minus Group J.

Positive mean difference

Group I is higher than Group J.

−

Negative mean difference

Group J is higher than Group I.

Worked comparison

After School vs. Saturday Academy

1. Significant?

Yes. p < .001.

2. Who is higher?

Mean difference = −1.935, so Group J, Saturday Academy, is higher.

3. CI support?

Yes. [−2.987, −0.882] stays below 0.

Plain-language sentence: After controlling for Pretest scores, Saturday Academy students had a significantly higher adjusted PostTest mean than After School students.

Mistake: using only the p-value

A small p-value shows significance, but the sign tells you who is higher.

Mistake: using CI overlap as the pairwise test

Use the reported pairwise Sig. value and the CI for the mean difference.

Mistake: forgetting I − J

Always read the calculation order before interpreting a positive or negative value.

Mistake: claiming causation

Adjusted differences do not prove a program caused the outcome unless the design supports causation.

Quick check 2

Interpret one pair correctly

Saturday Academy vs. Summer Bridge has I − J = −1.932, p < .001, CI [−2.998, −0.865]. What is correct?

ASaturday Academy is significantly higher because the result is significant. BSummer Bridge is significantly higher because the difference is negative and the interval stays below 0. CThe programs do not differ because the mean difference is close to 0.

Transfer the skill

New table, same routine

A workplace study compares productivity across In-Person, Hybrid, and Online training while controlling for years of experience.

Open the workplace pairwise table

Practice Pairwise Comparisons · Adjusted Productivity Means
Group I	Group J	Mean difference (I − J)	Sig.	95% confidence interval
In-Person	Hybrid	1.4	.021	[0.22, 2.58]
In-Person	Online	3.1	.001	[1.95, 4.25]
Hybrid	Online	1.7	.083	[−0.22, 3.62]

Quick check 3

What does the practice table say?

Choose the complete interpretation.

AAll three formats differ significantly. BIn-Person is higher than Hybrid and Online; Hybrid and Online do not differ significantly because p = .083 and the CI includes 0. COnline is higher than both other formats because its name appears in Group J.

Your interpretation

Write the adjusted comparison in plain language

Use significance, direction, and the confidence interval. Keep the covariate in the sentence.

Sentence frame

After controlling for __________, __________ had a significantly higher/lower adjusted __________ mean than __________.

For a non-significant pair: After controlling for __________, __________ and __________ did not differ significantly on __________.

Write one sentence about the workplace table

0 words