Lab 3: Mixed Factorial ANOVA

Comparing Strength Change Across Time in Training and Control Groups

TipLab Materials
  1. Download the Word version of this lab.
  2. Import the Word file into Google Docs.
  3. Complete the assignment in Google Docs.
  4. Download the completed file as Markdown.
  5. Submit the .md file.

Download the dataset lab03_strength_wide.csv and import it into SPSS.

When reading SPSS output, use the left navigation panel and look for these table names: Frequencies, Report, Descriptive Statistics, Mauchly’s Test of Sphericity, Levene’s Test of Equality of Error Variances, Tests of Within-Subjects Effects, Tests of Between-Subjects Effects, Estimates, and Pairwise Comparisons.

ImportantNo SPSS Output Required

No need to upload your SPSS output nor add images of SPSS output to your lab report. Just report the relevant values in the tables and write your interpretations in your own words.

WarningQ2.5 Clarification

For Q2.5, do not use a Univariate Tests table that says it is testing the effect of group. That is the wrong table for the follow-up simple effects.

After you split the file by group, rerun the repeated-measures ANOVA with only time in the model. Leave Between-Subjects Factor(s) empty. SPSS will organize the output into separate sections for Training and Control.

For each group, use the time row in Tests of Within-Subjects Effects to get the F, df, p-value, and partial eta squared. There will not be one combined table with both groups; create the two-row Q2.5 table by taking the Time result from the Training section and the Time result from the Control section.

PART 1: Instructions

Lab Overview

In this lab you will run a 2 × 3 Mixed Factorial ANOVA in SPSS.

  • The between-subjects factor is Group: Training vs. Control.
  • The within-subjects factor is Time: Pre, Mid, and Post.

Your main job is to decide whether the two groups changed differently over time.

Learning Objectives

By the end of this lab, you should be able to:

  1. Recognize the wide-format data structure needed for repeated-measures analysis in SPSS.
  2. Run and interpret a mixed factorial ANOVA.
  3. Identify and interpret the Group × Time interaction.
  4. Write a short APA-style results paragraph.

Scenario

Sixty participants completed a 12-week study. Half were assigned to a Training group and half to a Control group. Leg-press strength (kg) was measured at:

  • Pre (Week 0)
  • Mid (Week 6)
  • Post (Week 12)

Research question:

Did strength change differently over time for the Training group than for the Control group?

Dataset

The dataset is already in wide format, meaning each participant appears once.

Variable Description
id Participant ID
group 1 = Training, 2 = Control
strength_pre Pre-program strength
strength_mid Mid-program strength
strength_post Post-program strength

Section 1: Setup and Quick Check (20 points)

Q1.1 — Import and Label the Groups (5 points)

Import lab03_strength_wide.csv into SPSS.

Then:

  1. Go to Variable View.
  2. Find the variable group.
  3. In the Values cell, enter:
    • Value: 1; Label: Training
    • Value: 2; Label: Control
  4. Click OK.

Q1.2 — Check the File Structure (5 points)

Use Data View and Variable View to confirm that:

  • the file has 60 rows
  • each row is one participant
  • the file includes id, group, strength_pre, strength_mid, and strength_post

Then go to Analyze → Descriptive Statistics → Frequencies, move group into the variable box, and run the output.

Report:

  1. How many total participants are in the dataset?
  2. How many are in each group?
  3. Why is this file already in the correct format for SPSS Repeated Measures?

Q1.3 — Descriptive Statistics (10 points)

Go to Analyze → Compare Means & Proportions → Means.

  1. Move strength_pre, strength_mid, and strength_post to the Dependent List.
  2. Move group to Layer 1 of 1.
  3. In Options, ensure Mean, N, and Std. Deviation are under Cell Statistics.
  4. Click Continue and then OK.

Use the Report table to complete the table below.

Pre Mid Post
Training M (SD)
Control M (SD)

In 1-2 sentences, describe the pattern.

Section 2: Mixed Factorial ANOVA (55 points)

Q2.1 — Run the Analysis in SPSS (10 points)

Go to Analyze → General Linear Model → Repeated Measures.

  1. Name the within-subjects factor time.
  2. Set the number of levels to 3.
  3. Click Add, then Define.
  4. Assign:
    • strength_pre to time 1
    • strength_mid to time 2
    • strength_post to time 3
  5. Move group to Between-Subjects Factor(s).

Then request the following:

  • Plots:
    • Horizontal Axis = time
    • Separate Lines = group
  • EM Means:
    • Move group, time, and group*time into Display Means for
    • Check Compare main effects
    • Use Bonferroni
  • Options:
    • Check Descriptive statistics
    • Check Estimates of effect size
    • Check Homogeneity tests

Click OK.

Q2.2 — Means and Plot from the ANOVA Output (10 points)

Use:

  • the Estimates table for means
  • the Descriptive Statistics table for SD values

Complete this table:

Pre Mid Post
Training M (SD)
Control M (SD)

Paste the Profile Plots graph below your answer and briefly describe what it shows.

Q2.3 — Assumptions (10 points)

Use the following SPSS tables:

  • Levene’s Test of Equality of Error Variances
  • Mauchly’s Test of Sphericity

Part A: Levene’s test

Fill in:

Time Point F p Assumption Met?
Pre
Mid
Post

Part B: Mauchly’s test

W Approx. χ² df p

Then answer:

  1. Was sphericity violated?
  2. Which row should you use in Tests of Within-Subjects Effects?

Use this rule:

  • If p > .05, use Sphericity Assumed
  • If p ≤ .05, use Greenhouse-Geisser

Q2.4 — Main ANOVA Results (15 points)

Use:

  • Tests of Within-Subjects Effects for time and time * group
  • Tests of Between-Subjects Effects for group

Fill in:

Effect F df p η²_p
Group × Time
Time
Group

Then answer in a few sentences:

  1. Was the Group × Time interaction significant?
  2. What does that mean in plain language?
  3. Given the interaction, how should you interpret the main effects?

Q2.5 — Follow-Up Simple Effects (10 points)

Only complete this step if the Group × Time interaction in Q2.4 is significant.

Run a separate follow-up analysis to test the simple main effect of Time within each group.

Step 1 — Split the file by group

  1. Go to Data → Split File.
  2. Select Organize output by groups.
  3. Move group into the grouping box.
  4. Click OK.

Step 2 — Run a one-way repeated-measures ANOVA for Time

  1. Go to Analyze → General Linear Model → Repeated Measures and click Reset (DO NOT FORGET THIS STEP).
  2. Name the within-subjects factor time.
  3. Set the number of levels to 3.
  4. Click Add, then Define.
  5. Assign:
    • strength_pre to time 1
    • strength_mid to time 2
    • strength_post to time 3
  6. Leave Between-Subjects Factor(s) empty. Because the file is split by group, SPSS will run the same repeated-measures ANOVA separately for the Training group and the Control group.
  7. In EM Means:
    • Move time into Display Means for
    • Check Compare main effects
    • Use Bonferroni
  8. In Options:
    • Check Descriptive statistics
    • Check Estimates of effect size
  9. Click OK.

Step 3 — Turn Split File off when finished

  1. Go to Data → Split File.
  2. Select Analyze all cases, do not create groups.
  3. Click OK.

Use:

  • the Tests of Within-Subjects Effects table inside each split-file output section for the simple main effect of Time within that group
  • the Pairwise Comparisons table for the Training-group follow-up comparisons

SPSS will not give one combined table with both groups. Instead, the output should be organized into separate sections, one for Training and one for Control. In each group section, use the time row from Tests of Within-Subjects Effects. Use the same sphericity rule as before:

  • If that group’s Mauchly’s test has p > .05, use the Sphericity Assumed row.
  • If that group’s Mauchly’s test has p ≤ .05, use the Greenhouse-Geisser row.
Warning

If you see a Univariate Tests table that says “The F tests the effect of group” or shows df = 1, 58, that is not the Q2.5 follow-up test. That table is testing the overall Group effect from the original mixed ANOVA. Return to Data → Split File, make sure the file is split by group, click Reset in Repeated Measures, and leave Between-Subjects Factor(s) empty.

Report the simple main effect of Time within each group:

Group F df p η²_p
Training
Control

For the Training group, report the Bonferroni pairwise comparisons:

Comparison Mean Difference p
Pre vs. Mid
Pre vs. Post
Mid vs. Post

In 2-3 sentences, explain what these follow-up results tell you.

Section 3: APA Results Paragraph (25 points)

Q3.1 — Write the Results Paragraph (25 points)

Write one clear APA-style paragraph that includes:

  1. The design: 2 × 3 mixed factorial ANOVA
  2. The assumption check for sphericity and which row you used
  3. The Group × Time interaction
  4. The main effects of Time and Group
  5. The simple main effects of Time within each group
  6. The Training group pairwise comparisons
  7. A practical conclusion about whether the training program worked

Use APA style:

  • F(df1, df2) = XX.XX, p = .XXX, η²_p = .XX
  • If p < .001, write p < .001

Evaluation Rubric

Section Points
Section 1: Setup and Quick Check 20
Section 2: Mixed Factorial ANOVA 55
Section 3: APA Results Paragraph 25
Total 100
Question Criteria Points
Q1.1 Group labels entered correctly 5
Q1.2 Correct counts and correct explanation of wide format 5
Q1.3 Descriptive table completed and pattern described accurately 10
Q2.1 Mixed ANOVA set up correctly in SPSS 10
Q2.2 Means table and profile plot interpreted correctly 10
Q2.3 Assumptions reported and correct row selected 10
Q2.4 Main ANOVA effects reported and interpreted correctly 15
Q2.5 Simple effects and pairwise comparisons reported correctly 10
Q3.1 Clear APA-style paragraph with all major findings 25

PART 2: Your Answers

Important

Type all answers below. Do not delete the question headers. Complete the lab in Google Docs using the Word version, then download it as Markdown and submit the .md file.

  • Download the Word version of this lab - > lab03.docx
  • Import the Word file into Google Docs.
  • Complete the assignment in Google Docs.
  • Download the completed file as Markdown.
  • Submit the .md file.

Section 1: Setup and Quick Check

Q1.1 — Import and Label the Groups

Type text here…

Q1.2 — Check the File Structure

Total participants: Type text here…

Participants in Training: Type text here…

Participants in Control: Type text here…

Why is this file already in the correct format for SPSS Repeated Measures? Type text here…

Q1.3 — Descriptive Statistics

Group Pre Mid Post
Training M (SD) Type here… Type here… Type here…
Control M (SD) Type here… Type here… Type here…

Pattern description: Type text here…

Section 2: Mixed Factorial ANOVA

Q2.1 — Run the Analysis in SPSS

Type text here…

Q2.2 — Means and Plot from the ANOVA Output

Group Pre Mid Post
Training M (SD) Type here… Type here… Type here…
Control M (SD) Type here… Type here… Type here…

Profile plot interpretation: Type text here…

Q2.3 — Assumptions

Part A: Levene’s test

Time Point F p Assumption Met?
Pre Type here… Type here… Type here…
Mid Type here… Type here… Type here…
Post Type here… Type here… Type here…

Part B: Mauchly’s test

W Approx. χ² df p
Type here… Type here… Type here… Type here…

Was sphericity violated? Type text here…

Which row did you use in Tests of Within-Subjects Effects? Type text here…

Q2.4 — Main ANOVA Results

Effect F df p η²_p
Group × Time Type here… Type here… Type here… Type here…
Time Type here… Type here… Type here… Type here…
Group Type here… Type here… Type here… Type here…

Interpretation: Type text here…

Q2.5 — Follow-Up Simple Effects

Group F df p η²_p
Training Type here… Type here… Type here… Type here…
Control Type here… Type here… Type here… Type here…
Comparison Mean Difference p
Pre vs. Mid Type here… Type here…
Pre vs. Post Type here… Type here…
Mid vs. Post Type here… Type here…

Follow-up interpretation: Type text here…

Section 3: APA Results Paragraph

Q3.1 — Write the Results Paragraph

Type text here…