Lab 2: Repeated Measures ANOVA

Analyzing Strength Changes Across a 12-Week Training Program

TipHow to Use This Lab Document

For Students:

  1. 📥 Download Lab 2 (Word Format) - Click to download the editable version
  2. Add your name and date in the document header
  3. Complete all questions in Part 2: Your Answers
  4. Include SPSS output where requested
  5. DELETE Part 1 (Instructions) before submitting
  6. Submit only Part 2 (Your Answers) via Canvas

File Naming: Save as LastName_FirstName_Lab02.pdf

PART 1: INSTRUCTIONS

WarningImportant: Delete This Section Before Submission

Part 1 contains the lab instructions and background information. After reading the instructions and completing your work in Part 2, DELETE this entire Part 1 section before submitting your lab.

Due Date & Submission Requirements

Due: One week from assignment date (see Course Schedule for specific deadline)

Submission: Submit your completed lab via Canvas as a single Word document containing only Part 2 (Your Answers)

Deliverables

Your lab submission must include:

  1. Cover Page with:
    • Your name
    • Course number and section
    • Lab title: “Lab 2: Repeated Measures ANOVA”
    • Date of submission
  2. Responses to All Questions (Sections 1–5):
    • Section 1: Questions 1.1, 1.2, 1.3
    • Section 2: Questions 2.1, 2.2
    • Section 3: Questions 3.1, 3.2, 3.3, 3.4
    • Section 4: Questions 4.1, 4.2
    • Section 5: Question 5.1 (results paragraph)
  3. SPSS Output Tables - Include all relevant output:
    • Descriptive statistics table
    • Mauchly’s test of sphericity table
    • Tests of within-subjects effects table
    • Pairwise comparisons table
    • Means plot (profile plot)
  4. Written Interpretations in complete sentences for all questions
  • File Type: PDF only (.pdf) - Word documents will not be accepted
  • Font: 12-point, readable font (Times New Roman, Arial, Calibri)
  • SPSS Output: Can be pasted as images or tables (ensure readability)

Before submitting, verify you have:

WarningIncomplete Submissions

Labs missing required components (SPSS output, unanswered questions, or missing interpretations) will receive deductions as specified in the evaluation rubric. Ensure your submission is complete before uploading.

Lab Overview

Learning Objectives

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

  1. Explain why repeated measures designs offer greater statistical power than equivalent between-subjects designs
  2. Restructure data from long to wide format in SPSS for repeated measures analysis
  3. Check the normality and sphericity assumptions of one-way repeated measures ANOVA
  4. Run a one-way repeated measures ANOVA in SPSS and select the correct F-row based on Mauchly’s test
  5. Conduct and interpret Bonferroni-corrected pairwise comparisons following a significant within-subjects effect
  6. Compute and interpret partial eta-squared (η²_p) and partial omega-squared (ω²_p) as effect size measures
  7. Report a complete one-way repeated measures ANOVA result in APA format

Scenario

You are a strength and conditioning researcher working with a university athletic department. A cohort of 30 student-athletes completed a 12-week progressive resistance training program. Muscular strength (kg) was assessed at three time points: before the program began (pre), at the six-week midpoint (mid), and at the completion of the program (post). Each athlete was measured at all three time points — the same individuals appear in every condition.

Your task is to determine whether strength changed significantly across the 12-week program, whether the change was consistent across all pairs of time points, and how large the training-induced effect was.

Dataset

You will use the Core Dataset for this lab — specifically, the strength_kg variable (muscular strength in kilograms) filtered to the training group.

Accessing the Dataset

TipDataset File

For this lab, you will need the core_session.csv file from the Core Dataset.

Download: Get the file from the SMS book repository at https://github.com/drfurtado/sms/tree/main/data

Dataset Information: For full details about variables and the study background, see the Core Dataset Overview and Core Dataset Codebook in the SMS textbook.

Download the file and save it to your computer, then import it into SPSS from your local folder.

SPSS Access

On Campus: Use SPSS installed in the computer labs
Remote Access: Use Virtual SPSS via Apporto (link available in Canvas)

Section 1: Data Preparation (10 points)

Task 1.1: Import the Data into SPSS

  1. Open SPSS (either on campus or via Apporto)
  2. Import the core_session.csv file into SPSS
NoteNeed Help?

If you’re not sure how to import CSV files into SPSS, refer to the SPSS tutorials on Canvas or ask your instructor for guidance.

Question 1.1 (2 points): How many total observations (rows) are in the full dataset? Then, how many observations belong to the training group? Report both numbers.

Task 1.2: Filter to the Training Group

Because our research question focuses on the individuals who completed the training program, you need to restrict the dataset to training-group participants only.

  1. Go to Data → Select Cases
  2. Choose If condition is satisfied, then click If…
  3. Enter the condition: group = "training"
  4. Click Continue → OK

SPSS will mark non-training cases with a diagonal line through the row number; they will be excluded from subsequent analyses.

TipTip: Keep the filter active throughout this lab

Leave the Select Cases filter active for the entire lab. You will need training-group data only for the repeated measures ANOVA.

Question 1.2 (3 points): After applying the filter, run Analyze → Descriptive Statistics → Descriptives on the strength_kg variable. From the SPSS output, report:

  1. What is the overall mean strength (kg) across all time points for the training group?
  2. What is the overall standard deviation?
  3. What is the minimum and maximum strength value in the training group?

Task 1.3: Restructure to Wide Format

SPSS’s repeated measures ANOVA procedure requires one row per participant with separate columns for each time point (wide format). Currently, the dataset is in long format (one row per participant per time point). You must restructure it before proceeding.

  1. Go to Data → Restructure
  2. Select Restructure selected cases into variables (this converts long → wide)
  3. Click Next
  4. Set the Identifier variable to id
  5. Set the Index variable to time
  6. Move strength_kg to the Variables to be transposed list (this step is not needed)
  7. Click Next through the remaining steps, then click Finish

SPSS will create a new dataset with one row per participant and three new variables: strength_kg.1, strength_kg.2, and strength_kg.3. Rename these to strength_pre, strength_mid, and strength_post using Variable View (double-click the variable name to edit it).

TipSave the wide-format file

After restructuring, save the new wide-format dataset (File → Save As) with a descriptive name such as core_session_wide.sav. Keep both files — you will work from the wide-format file for the ANOVA.

NoteNeed Help?

For a detailed walkthrough of reshaping data in SPSS, refer to the SPSS Tutorial: Repeated Measures ANOVA in the textbook appendix.

Question 1.3 (5 points):

  1. After restructuring, how many rows does the wide-format dataset have? Does this match the number of training-group participants you identified in Question 1.1?
  2. List the three new variable names you created (e.g., strength_pre, strength_mid, strength_post) in the correct chronological order.
  3. In 1–2 complete sentences, explain why repeated measures ANOVA requires wide-format data (one row per participant) rather than long-format data (one row per observation).

Section 2: Checking Assumptions (20 points)

Before running the ANOVA, you must verify two key assumptions: (1) normality of the difference scores, and (2) sphericity.

Task 2.1: Check Normality of Difference Scores

Repeated measures ANOVA assumes that the differences between each pair of time points are approximately normally distributed. You will examine the difference between pre and mid, and between mid and post.

Step 1: Compute difference scores

  1. Go to Transform → Compute Variable
  2. Create a new variable diff_pre_mid with the formula: strength_mid - strength_pre
  3. Repeat to create diff_mid_post with the formula: strength_post - strength_mid

Step 2: Assess normality

For each difference variable:

  1. Go to Analyze → Descriptive Statistics → Explore
  2. Move the difference variable to the Dependent List
  3. Click Plots, check Normality plots with tests, click Continue, then OK
  4. From the output, examine the Shapiro-Wilk statistic (prefer this over Kolmogorov-Smirnov for n < 50)
NoteNeed Help with Normality Assessment?

Review Chapter 7: The Normal Distribution in the SMS textbook for guidance on interpreting normality tests and Q-Q plots.

Question 2.1 (10 points):

  1. Report the Shapiro-Wilk statistic and p-value for both difference variables (diff_pre_mid and diff_mid_post). Use the table format below:
Difference Variable Shapiro-Wilk W p-value Normal? (Yes/No)
diff_pre_mid
diff_mid_post
  1. Include the Q-Q plot for diff_pre_mid in your report. Do the points closely follow the diagonal reference line, or do you see systematic departures?
  2. Based on your Shapiro-Wilk results and Q-Q plots, is the normality assumption reasonably met? Justify your answer in 2–3 sentences.

Task 2.2: Mauchly’s Test of Sphericity

Sphericity is the assumption unique to repeated measures designs: it requires that the variances of the differences between all pairs of time points are approximately equal. You do not need to run Mauchly’s test separately — SPSS will produce it automatically when you run the repeated measures ANOVA (Section 3). For now, read the background below so you can interpret it correctly when you encounter it.

NoteWhat Is Sphericity?

Sphericity requires that the variance of (pre − mid), the variance of (mid − post), and the variance of (pre − post) are all approximately equal. When this assumption is violated, the F-ratio is positively biased — it is larger than it should be, and Type I error rates are inflated. The Greenhouse-Geisser and Huynh-Feldt corrections adjust the degrees of freedom downward to compensate.

For a full explanation, see Chapter 15: Repeated Measures Designs in the SMS textbook.

Question 2.2 (10 points): After running your ANOVA in Section 3, return here and answer based on the Mauchly’s Test of Sphericity table in your SPSS output:

  1. Report Mauchly’s W, the chi-square statistic, degrees of freedom, and p-value.
  2. Based on the p-value, is the sphericity assumption violated (p < .05) or met (p ≥ .05)?
  3. Which row of the Tests of Within-Subjects Effects table should you use to report your F-ratio? Choose from: Sphericity Assumed, Greenhouse-Geisser, or Huynh-Feldt. Justify your choice.
  4. In your own words (2–3 sentences), explain what it means for sphericity to be violated and why it matters for interpreting the F-ratio.

Section 3: Running the Repeated Measures ANOVA (35 points)

Task 3.1: Set Up the ANOVA in SPSS

Using the wide-format dataset (one row per participant with strength_pre, strength_mid, strength_post), follow these steps:

  1. Go to Analyze → General Linear Model → Repeated Measures
  2. In the Repeated Measures Define Factor(s) dialog:
    • Within-Subject Factor Name: type Time
    • Number of Levels: type 3
    • Click Add, then click Define
  3. In the Repeated Measures dialog, assign variables to the factor levels:
    • Move strength_pre to the slot next to Time(1)
    • Move strength_mid to the slot next to Time(2)
    • Move strength_post to the slot next to Time(3)
  4. Click Options:
    • Check Descriptive statistics
    • Check Estimates of effect size
    • Check Homogeneity tests (this produces Mauchly’s test)
    • Under Display Means for, move Time to the right panel
    • Check Compare main effects
    • Under Confidence interval adjustment, select Bonferroni
    • Click Continue
  5. Click Plots:
    • Move Time to the Horizontal Axis box
    • Click Add, then Continue
  6. Click OK to run the analysis
NoteFull SPSS Walkthrough

For a complete step-by-step guide to this procedure — including annotated screenshots of each dialog — see the SPSS Tutorial: Repeated Measures ANOVA in the SMS textbook appendix.

Question 3.1 (5 points): Describe in your own words (3–5 sentences) the general purpose of one-way repeated measures ANOVA. Include: (a) what research question it answers, (b) why using the same participants at each time point increases statistical power compared to a between-subjects design, and (c) what the omnibus F-test tells you (and what it does NOT tell you).

Task 3.2: Descriptive Statistics

SPSS will produce a Descriptive Statistics table showing the mean, standard deviation, and n for each time point.

Question 3.2 (10 points):

  1. Copy the SPSS descriptive statistics table into your report (or recreate it in the following format):
Time Point n M (kg) SD
Pre-training
Mid-training (6 weeks)
Post-training (12 weeks)
  1. Describe the pattern of means across the three time points. Did strength increase progressively, plateau at some point, or show an unexpected pattern?
  2. Which time interval (pre→mid or mid→post) showed the larger absolute increase in mean strength? Calculate the difference between those two means and report it.
  3. Are the standard deviations similar across time points? What might this suggest about consistency of individual responses to training?

Task 3.3: Within-Subjects Effects Table

Locate the Tests of Within-Subjects Effects table in the SPSS output. This table contains four rows for the Time effect: Sphericity Assumed, Greenhouse-Geisser, Huynh-Feldt, and Lower-bound.

WarningSelect the correct row based on Mauchly’s test

You identified the appropriate row in Question 2.2. Use that decision here — report only the row corresponding to your sphericity decision. Do not report all four rows.

Question 3.3 (15 points):

  1. From the correct row of the within-subjects effects table, report:
Source SS df MS F p η²_p
Time
Error (Time)
  1. State your decision about H₀ at α = .05: Do you reject or fail to reject the null hypothesis that strength means are equal across all three time points? Justify using your F-ratio and p-value.
  2. Interpret the partial eta-squared value (η²_p) reported by SPSS. Using Cohen’s (1988) benchmarks (.01 = small, .06 = medium, .14 = large), how would you characterize the size of this effect?
  3. Looking at the Error (Time) row: this is the subjects × time interaction term used in the denominator of the F-ratio. In 2–3 sentences, explain why this error term is smaller than the within-groups error term you would see in a between-subjects ANOVA — and why a smaller denominator is advantageous.

Task 3.4: Means Plot (Profile Plot)

Locate the profile plot (line graph of means across time points) in the SPSS output.

Question 3.4 (5 points):

  1. Include the SPSS profile plot in your report.
  2. Does the line show a consistent upward trend, a leveling off, or any other pattern?
  3. In 2–3 sentences, explain what the profile plot communicates that a table of means alone cannot.

Section 4: Post Hoc Comparisons and Effect Size (22 points)

Task 4.1: Bonferroni-Corrected Pairwise Comparisons

Because the omnibus F-test only tells you that at least one pair of time points differs, you need post hoc comparisons to identify which pairs differ. SPSS produced these automatically via Pairwise Comparisons when you selected Bonferroni correction in the Options dialog.

Locate the Pairwise Comparisons table in the SPSS output.

Question 4.1 (13 points):

  1. Complete the following table using values from the SPSS Pairwise Comparisons output:
Comparison Mean Difference (kg) SE p (adjusted) 95% CI Significant?
Pre → Mid
Pre → Post
Mid → Post
  1. How many of the three pairwise comparisons were statistically significant after Bonferroni correction (p < .05)?
  2. Which time interval showed the largest mean difference in strength? Does this align with what you observed in the descriptive statistics (Task 3.2)?
  3. One of the confidence intervals does not contain zero. What does this indicate about the mean difference for that comparison?
  4. In 2–3 sentences, explain why Bonferroni correction is applied to pairwise comparisons rather than using the unadjusted α = .05 for each test.

Task 4.2: Effect Sizes — η²_p and ω²_p

You already noted η²_p in Question 3.3. Now calculate ω²_p (partial omega-squared), which provides a less biased estimate of effect size, especially in smaller samples.

Calculating ω²_p:

SPSS does not report ω²_p directly but you can obtain it using the Effect Size Calculator in the SMS textbook appendix or by applying the formula using SS values from the within-subjects effects table:

\[ \omega^2_p = \frac{SS_{\text{time}} - (df_{\text{time}} \times MS_{\text{error}})}{SS_{\text{time}} + SS_{\text{error}} + MS_{\text{participants}}} \]

Alternatively, use the Statistical Calculators appendix in the SMS textbook to compute ω²_p by entering your SS values.

TipTip: MS for participants

The MS for participants (between-subjects variability) appears in the Tests of Between-Subjects Effects table in the SPSS output under the “Intercept” or “Error” row. Use the Error mean square from that table for \(MS_{\text{participants}}\).

Question 4.2 (9 points):

  1. Report η²_p (from SPSS output) and ω²_p (calculated or from the SMS calculator). Present them together:
Effect Size Measure Value Interpretation (small/medium/large)
η²_p (partial eta-squared)
ω²_p (partial omega-squared)
  1. Is ω²_p larger or smaller than η²_p? Explain in 1–2 sentences why ω²_p tends to yield a more conservative (smaller) estimate than η²_p.
  2. Regardless of which effect size you use, how would you describe the practical significance of this training program’s effect on muscular strength?

Section 5: Communication of Results (13 points)

Task 5.1: Write an APA Results Paragraph

Question 5.1 (13 points): Write a complete APA-style results paragraph (200–275 words) summarizing your findings. Your paragraph should:

  1. State that a one-way repeated measures ANOVA was conducted and name the dependent variable and within-subject factor
  2. Report Mauchly’s test result and indicate which F-row was used (or that sphericity was assumed)
  3. Report the omnibus F-ratio in APA format: F(df_effect, df_error) = value, p = value, η²_p = value, ω²_p = value
  4. State whether the null hypothesis was rejected and what this means in plain language
  5. Summarize the three Bonferroni-corrected pairwise comparisons, including mean differences, p-values, and 95% CIs
  6. Conclude with a practical statement about what the results mean for the sport scientist and athletes
TipAPA Reporting Format (DO NOT COPY)

Use this template as a structural guide only — replace all bracketed values with your own:

“A one-way repeated measures ANOVA was conducted to examine the effect of training time (pre, mid, post) on muscular strength (kg) in [n] student-athletes. Mauchly’s test indicated that the sphericity assumption [was/was not] violated, W([df]) = [value], p = [value]; therefore, [sphericity-assumed / Greenhouse-Geisser corrected] degrees of freedom are reported. The within-subjects effect of Time was [significant/not significant], F([df_effect], [df_error]) = [value], p [< .001 / = value], η²_p = [value], ω²_p = [value], indicating a [small/medium/large] effect. Post hoc Bonferroni-corrected pairwise comparisons revealed that strength increased significantly from pre to mid (Mdiff = [value] kg, p [< .001 / = value], 95% CI [lower, upper])…”

Evaluation Rubric

Your lab will be graded using the following rubric:

Component Points Criteria
Section 1: Data Preparation 10 Correctly imports data, filters to training group, restructures to wide format, answers conceptual question on format
Section 2: Assumption Checking 20 Accurate normality assessment of difference scores; correct interpretation of Mauchly’s test; justified selection of F-row
Section 3: Running the ANOVA 35 Correct SPSS setup; accurate descriptive statistics; correct F-row selected; accurate interpretation of F, p, η²_p; explanation of error term
Section 4: Post Hoc & Effect Size 22 Accurate pairwise comparisons table; correct identification of significant pairs; ω²_p correctly reported; interpretation of effect size practical significance
Section 5: Communication 13 APA-formatted paragraph with all required elements; accurate statistical reporting; practical interpretation
TOTAL 100

Additional Grading Considerations

  • SPSS Output: All required SPSS output tables must be included (-5 points for each missing table)
  • Formatting: Report should be well-organized with clear section headers (-5 points if poorly formatted)
  • Completeness: All questions must be answered (-5 points per unanswered question)
  • Professional Presentation: Use complete sentences, proper grammar, and appropriate statistical terminology
  • Correct F-Row: Reporting the wrong row from the within-subjects effects table (i.e., ignoring Mauchly’s result) will result in a 10-point deduction

Resources

SPSS Tutorials (from your textbook)

Textbook Chapters

Canvas Resources

  • SPSS via Apporto (Virtual Lab) - link in Canvas
  • Lab submission portal - Canvas Assignments
WarningAcademic Integrity

This lab is an individual assignment. While you may discuss general concepts with classmates, all written work and analysis must be your own. Copying from others or sharing your work constitutes academic dishonesty. Do not use AI tools to generate answers. If you have questions, ask your instructor or attend office hours.

Questions?

If you have questions while completing this lab:

  1. Review the relevant textbook chapters and SPSS tutorials
  2. Attend office hours
  3. Post questions in the Canvas discussion forum (do not share answers)

END OF PART 1: INSTRUCTIONS
(Remember to delete Part 1 before submitting!)

PART 2: YOUR ANSWERS

ImportantSubmission Instructions

Complete all questions below and submit ONLY this Part 2 section (delete Part 1 before submitting).

  • Include your SPSS output (paste as images or tables)
  • Write all interpretations in complete sentences
  • Show your work where calculations are required
  • Name your file: LastName_FirstName_Lab02.pdf

Student Information

Name: __________________________________________________

Course & Section: ____________________________________

Date: ___________________________________________

Section 1: Data Preparation (10 points)

Question 1.1 (2 points)

How many total observations are in the full dataset? How many belong to the training group?

Total observations:

 

Training group observations:

 

Question 1.2 (3 points)

From the SPSS Descriptives output (training group only):

  1. Overall mean strength (kg) across all time points:

Answer:

 

  1. Overall standard deviation:

Answer:

 

  1. Minimum and maximum strength values:

Answer:

 

Paste your SPSS Descriptives output here:

 

 

 

Question 1.3 (5 points)

  1. How many rows does the wide-format dataset have? Does this match the number of training-group participants?

Answer:

 

 

  1. List the three variable names in chronological order:

Answer:

 

  1. Explain why repeated measures ANOVA requires wide-format data:

Answer:

 

 

 

Section 2: Checking Assumptions (20 points)

Question 2.1 (10 points)

  1. Shapiro-Wilk normality results for difference scores:
Difference Variable Shapiro-Wilk W p-value Normal? (Yes/No)
diff_pre_mid
diff_mid_post

Paste SPSS Explore output (Shapiro-Wilk table) here:

 

 

 

  1. Include the Q-Q plot for diff_pre_mid:

 

 

 

 

Describe what the Q-Q plot shows:

Answer:

 

 

  1. Is the normality assumption met? Justify:

Answer:

 

 

 

Question 2.2 (10 points)

(Complete this after running the ANOVA in Section 3)

  1. Mauchly’s test results:
Mauchly’s W χ² df p-value

Paste SPSS Mauchly’s Test table here:

 

 

  1. Is the sphericity assumption violated (p < .05) or met (p ≥ .05)?

Answer:

 

  1. Which row of the within-subjects effects table will you use? Justify:

Answer:

 

 

  1. In your own words, explain what a sphericity violation means and why it matters:

Answer:

 

 

 

Section 3: Running the Repeated Measures ANOVA (35 points)

Question 3.1 (5 points)

In your own words, describe the purpose of one-way repeated measures ANOVA (address parts a, b, and c from the task instructions):

Answer:

 

 

 

 

 

Question 3.2 (10 points)

  1. Descriptive statistics table:
Time Point n M (kg) SD
Pre-training
Mid-training (6 weeks)
Post-training (12 weeks)

Paste SPSS Descriptive Statistics output here:

 

 

 

  1. Describe the pattern of means:

Answer:

 

 

  1. Which time interval showed the larger increase? Calculate the mean difference:

Answer:

 

 

  1. Are SDs similar? What does this suggest?

Answer:

 

 

Question 3.3 (15 points)

  1. Within-subjects effects table (correct row only):
Source SS df MS F p η²_p
Time
Error (Time)

Paste SPSS Tests of Within-Subjects Effects output here:

 

 

 

  1. Decision about H₀ (reject or fail to reject):

Answer:

 

 

  1. Interpret η²_p using Cohen’s benchmarks:

Answer:

 

 

  1. Explain why the Error (Time) term is smaller than a between-subjects error term:

Answer:

 

 

 

Question 3.4 (5 points)

  1. Include SPSS means plot (profile plot) here:

 

 

 

 

 

  1. Describe the pattern shown in the plot:

Answer:

 

 

  1. What does the profile plot communicate beyond a table of means?

Answer:

 

 

 

Section 4: Post Hoc Comparisons and Effect Size (22 points)

Question 4.1 (13 points)

  1. Bonferroni-corrected pairwise comparisons:
Comparison Mean Difference (kg) SE p (adjusted) 95% CI Significant?
Pre → Mid
Pre → Post
Mid → Post

Paste SPSS Pairwise Comparisons output here:

 

 

 

  1. How many comparisons were statistically significant?

Answer:

 

  1. Which interval showed the largest mean difference?

Answer:

 

 

  1. What does a 95% CI that does not contain zero indicate?

Answer:

 

 

  1. Why is Bonferroni correction applied rather than using unadjusted α = .05 for each test?

Answer:

 

 

 

Question 4.2 (9 points)

  1. Effect size summary:
Effect Size Measure Value Interpretation (small/medium/large)
η²_p
ω²_p

Show your ω²_p calculation or note that you used the SMS Statistical Calculator:

 

 

  1. Is ω²_p larger or smaller than η²_p? Why does this occur?

Answer:

 

 

  1. Describe the practical significance of this training program’s effect:

Answer:

 

 

 

Section 5: Communication of Results (13 points)

Question 5.1 (13 points)

Write your APA-style results paragraph (200–275 words) below:

Results:

 

 

 

 

 

 

 

 

 

 

 

 

 

END OF LAB 2