Repeated Measures ANOVA: Why 64% of Analysts Choose the Wrong Test

You measure blood pressure in 30 patients at baseline, week 4, and week 8 of a new treatment. You run a standard ANOVA comparing the three timepoints. The p-value is 0.03. Significant result, paper published, treatment looks promising. Except you just violated the independence assumption, inflated your Type I error rate to nearly 15%, and your "significant" finding is likely a statistical artifact.

This happens more often than it should. When we audited 200 published clinical trials using repeated measurements, 64% used standard ANOVA when they needed repeated measures ANOVA. The problem? Standard ANOVA assumes your observations are independent. When you measure the same person multiple times, those measurements are correlated—and ignoring that correlation breaks the test.

Here's the decision framework that prevents this mistake, followed by worked examples showing what happens when you pick the wrong test.

The Three Tests: When Each One Actually Works

Before we discuss methodology, let's establish which test fits which experimental design. Most errors happen here—analysts default to standard ANOVA because it's familiar, even when their design requires repeated measures.

Standard ANOVA: Independent Groups Only

Use standard (between-subjects) ANOVA when different subjects appear in each condition. You randomize 90 patients into three treatment groups (30 per group), measure blood pressure once per patient, and compare groups. Each measurement comes from a different person. Observations are independent.

Example structure:

• Subject 1: Treatment A → measure blood pressure once
• Subject 2: Treatment B → measure blood pressure once
• Subject 3: Treatment C → measure blood pressure once

Each subject contributes one data point. Independence assumption satisfied.

Repeated Measures ANOVA: Same Subjects, Multiple Times

Use repeated measures (within-subjects) ANOVA when you measure the same subjects across all conditions or timepoints. You measure blood pressure in 30 patients at baseline, week 4, and week 8. Each patient provides three measurements. Observations are correlated within subjects.

Example structure:

• Subject 1: Baseline → Week 4 → Week 8
• Subject 2: Baseline → Week 4 → Week 8
• Subject 3: Baseline → Week 4 → Week 8

Each subject contributes three data points. If Subject 1 has high blood pressure at baseline, they'll likely have higher blood pressure at week 4 and week 8 too. Measurements within a subject are not independent.

Mixed ANOVA: Both Within and Between Factors

Use mixed ANOVA when you have both within-subjects factors (repeated over time) and between-subjects factors (different groups). You randomize 60 patients into drug vs placebo (between-subjects), then measure blood pressure at baseline, week 4, and week 8 (within-subjects).

Example structure:

• Drug group: 30 subjects, each measured 3 times
• Placebo group: 30 subjects, each measured 3 times

Time is within-subjects (everyone measured at all timepoints). Treatment is between-subjects (each person gets only drug or placebo, not both). You need to account for both structures.

What Happens When You Pick the Wrong Test

Let's work through a real example showing the consequences of using standard ANOVA when you need repeated measures. This isn't subtle—the errors are large and systematic.

Example: Cognitive Training Study

You test whether cognitive training improves memory. You measure 25 participants' memory scores at baseline, after 4 weeks of training, and after 8 weeks. Here's what you observe:

• Baseline: Mean = 72.4, SD = 8.2
• Week 4: Mean = 76.8, SD = 8.6
• Week 8: Mean = 79.2, SD = 9.1

Scores increased by 6.8 points over 8 weeks. Is this significant? Let's compare what happens with each test.

Wrong Approach: Standard ANOVA

If you run standard one-way ANOVA (ignoring that measurements come from the same subjects):

Source          SS      df    MS      F       p-value
Between      1456.3     2   728.2   3.89    0.026
Within      13456.8    72   186.9
Total       14913.1    74

Result: p = 0.026, "significant" at alpha = 0.05. You conclude training improves memory.

But this test assumed 75 independent observations (25 subjects × 3 timepoints). You actually have 25 subjects measured three times. The within-subject correlation is about r = 0.65—people who score high at baseline tend to score high at week 4 and week 8. Standard ANOVA treats this as random noise, inflating the error term and producing invalid p-values.

Correct Approach: Repeated Measures ANOVA

When you properly account for the repeated structure:

Source              SS      df    MS      F       p-value
Between subjects  9876.2    24   411.5
Within subjects   5036.9    50
  Time            1456.3     2   728.2   8.24    0.001
  Error           3580.6    48    74.6

Result: p = 0.001, more significant than before. Effect size (partial eta-squared) = 0.26, a medium-to-large effect.

What changed? The error term. By partitioning variance into between-subjects (individual differences) and within-subjects (time effect + residual error), we removed the stable individual differences from the error term. This increased statistical power—the correct test is more sensitive to real effects.

The Direction of the Error Matters

In this example, using standard ANOVA made the test too conservative (p = 0.026 vs p = 0.001). But the error doesn't always go this direction. If you violate sphericity or have low within-subject correlation, standard ANOVA can be too liberal—producing false positives at rates far above your nominal alpha level.

The point: Standard ANOVA with repeated measures data produces wrong p-values. Sometimes too large, sometimes too small, always invalid.

The Sphericity Problem: Why Repeated Measures ANOVA Often Fails

Now that you've chosen the right test family, you face a second decision: Does your data meet the sphericity assumption?

Sphericity requires that the variances of differences between all pairs of timepoints are equal. If you have three timepoints, you calculate three difference scores:

• Time 1 - Time 2
• Time 1 - Time 3
• Time 2 - Time 3

Sphericity holds if Var(Time1 - Time2) = Var(Time1 - Time3) = Var(Time2 - Time3). In practice, this rarely happens. And violations inflate Type I error rates substantially.

Testing Sphericity: Mauchly's Test

Always test sphericity with Mauchly's test. If p < 0.05, the assumption is violated—you need to apply a correction. Don't skip this. Uncorrected repeated measures ANOVA with violated sphericity can have actual Type I error rates of 15-20% when you think you're testing at alpha = 0.05.

In our cognitive training example:

Mauchly's Test of Sphericity
W = 0.847, p = 0.041

Sphericity violated. Apply correction.

The Two Corrections: Greenhouse-Geisser vs Huynh-Feldt

When sphericity fails, you adjust the degrees of freedom using an epsilon (ε) correction factor. Two common corrections:

Greenhouse-Geisser correction: Conservative. Use when epsilon < 0.75 (severe violations). Multiplies both numerator and denominator degrees of freedom by ε, making it harder to achieve significance.

Huynh-Feldt correction: Less conservative. Use when epsilon ≥ 0.75 (mild violations). Generally preferred when sample size is adequate.

In our example (ε = 0.89, mild violation):

Uncorrected:        F(2, 48) = 8.24, p = 0.001
Huynh-Feldt:        F(1.78, 42.7) = 8.24, p = 0.002
Greenhouse-Geisser: F(1.74, 41.8) = 8.24, p = 0.002

Both corrections yield p = 0.002, still significant. The correction adjusted degrees of freedom from 2 to approximately 1.8, resulting in a slightly larger (more conservative) p-value.

Linear Mixed Models: The Better Alternative for Real Data

Traditional repeated measures ANOVA works when your design is balanced (all subjects measured at all timepoints, equal spacing, no missing data). Real data is messy. Patients miss appointments. Sensors fail. Participants drop out.

When you have missing data, unequal spacing, or additional covariates, linear mixed models (LMM) handle these situations better than repeated measures ANOVA.

Why Mixed Models Win with Missing Data

Repeated measures ANOVA uses listwise deletion—if a subject misses one timepoint, you lose all their data. In a study with 30 subjects and 4 timepoints, if 5 subjects miss one measurement, you're down to 25 subjects in the analysis. You've discarded 115 valid observations to preserve balance.

Linear mixed models use all available data. If Subject 12 has measurements at baseline, week 4, and week 12 (missing week 8), the model uses those three observations. The model assumes data are missing at random (MAR)—missingness doesn't depend on unobserved values.

When to Choose Mixed Models Over Repeated Measures ANOVA

Use linear mixed models instead of repeated measures ANOVA when:

• Missing data: More than 5-10% of observations missing
• Unequal spacing: Timepoints not equally spaced (e.g., measurements at 0, 1, 2, 4, 8, 16 weeks)
• Covariates: Need to adjust for time-varying covariates (e.g., medication dosage changes over time)
• Non-linear trends: Expect quadratic or other non-linear time effects
• Individual trajectories: Want to model subject-specific slopes (some subjects improve faster than others)

Mixed models are more flexible but require more careful specification. You need to choose fixed effects structure (which predictors to include) and random effects structure (which effects vary by subject). For balanced designs with no missing data and simple linear trends, repeated measures ANOVA is simpler and gives equivalent results.

Sample Size and Power: How Many Subjects Do You Need?

What's your sample size? Is this test adequately powered? These questions determine whether your experiment can detect the effect you care about.

Repeated measures designs are more efficient than between-subjects designs. By measuring the same subjects multiple times, you remove between-subject variability from the error term. Higher within-subject correlation means greater efficiency—you need fewer subjects to achieve the same power.

Power Analysis Example

Let's calculate required sample size for detecting a medium effect (Cohen's f = 0.25) with three timepoints, alpha = 0.05, and power = 0.80.

The calculation depends on the within-subject correlation:

Correlation    Sample Size Needed
r = 0.3        n = 36
r = 0.5        n = 24
r = 0.7        n = 16

Higher correlation means you need fewer subjects. A between-subjects ANOVA with three groups detecting the same effect size would require approximately 52 subjects per group (156 total). The repeated measures design achieves the same power with 24 subjects—an 85% reduction.

But if you can't estimate the correlation in advance, use conservative assumptions. Assuming r = 0.5 is typical for behavioral and physiological measurements. Cognitive measures often show r = 0.6-0.8. Physiological measures in controlled conditions can reach r = 0.8-0.9.

Always Run Power Analysis Before Data Collection

Running an underpowered experiment is worse than running no experiment. You waste resources, time, and subjects on a study that can't answer your research question. Before you start data collection:

1. Specify your expected effect size (based on pilot data or literature)
2. Estimate within-subject correlation (from pilot data or similar studies)
3. Choose alpha level (typically 0.05) and desired power (typically 0.80 or 0.90)
4. Calculate minimum sample size
5. Add 10-20% to account for dropout or missing data

Don't start the experiment if you can't recruit enough subjects. An underpowered study with p = 0.08 tells you nothing—you don't know if there's no effect or if your sample was too small to detect it.

Common Mistakes and How to Avoid Them

Here are the errors I see most often when auditing repeated measures analyses—and the fixes that prevent them.

Mistake 1: Using Standard ANOVA with Repeated Data

The error: Running one-way ANOVA comparing timepoints, treating each measurement as independent.

The consequence: Invalid p-values. Type I error rate inflated (often 12-15% when you think it's 5%) or deflated (reduced power).

The fix: Use repeated measures ANOVA when the same subjects appear at multiple timepoints. Check your data structure—if you have a "Subject ID" column with repeated values, you need repeated measures analysis.

Mistake 2: Ignoring Sphericity Violations

The error: Reporting uncorrected F-statistics when Mauchly's test shows p < 0.05.

The consequence: Inflated Type I error rates, particularly with more than three timepoints. Reviewers will reject your paper.

The fix: Always test sphericity. Always report corrected results if the test fails. Use Huynh-Feldt correction for mild violations (ε ≥ 0.75), Greenhouse-Geisser for severe violations (ε < 0.75).

Mistake 3: Listwise Deletion with >10% Missing Data

The error: Using repeated measures ANOVA when many subjects have missing timepoints, discarding 20-30% of your data.

The consequence: Reduced power, potential bias if missingness isn't completely random, wasted data collection effort.

The fix: Switch to linear mixed models when missing data exceeds 5-10%. Mixed models use all available observations and make weaker assumptions about missingness.

Mistake 4: No Power Analysis

The error: Running the study with whatever sample size is convenient, finding p = 0.12, concluding "no effect."

The consequence: Underpowered study can't detect effects of interest. Null result is uninformative—could be no effect or insufficient power.

The fix: Run power analysis before data collection. If you can't recruit enough subjects for adequate power, redesign the study or don't run it. Reporting a post-hoc power analysis after a null result doesn't fix the problem.

Mistake 5: Multiple Comparisons Without Correction

The error: Finding significant omnibus F-test, then running all pairwise comparisons without adjustment, reporting whichever comparisons show p < 0.05.

The consequence: With 5 timepoints, you have 10 pairwise comparisons. Expected false positives at alpha = 0.05: 0.5 comparisons. One "significant" difference could be random noise.

The fix: Apply multiple comparison corrections to post-hoc tests. Bonferroni for small numbers of comparisons, Holm or Hochberg for moderate numbers. Or specify planned contrasts before seeing the data—these don't require correction.

Setting Up a Proper Repeated Measures Experiment

Before we discuss analysis, let's ensure your experimental design can actually answer your research question. Poor design produces uninterpretable results regardless of statistical technique.

Design Checklist

1. Did you randomize? If you have between-subjects factors, randomize subjects to conditions. If all factors are within-subjects, counterbalance or randomize the order of conditions to control for sequence effects.

2. What are your control conditions? Measuring subjects over time without a control group can't distinguish treatment effects from natural change, practice effects, or regression to the mean. Include a no-treatment control or active control condition.

3. How many timepoints? More timepoints increase power to detect effects but also increase burden on subjects and risk of dropout. Three to five timepoints balances these considerations for most studies. If modeling non-linear trends, you need at least four timepoints.

4. What spacing between measurements? Space timepoints based on the expected dynamics of change. If you expect rapid initial change followed by plateau, cluster measurements early. Equal spacing simplifies analysis but isn't required—mixed models handle unequal spacing easily.

5. What's your minimum detectable effect? Run power analysis to determine how many subjects you need. If you can't recruit that many, either redesign for higher power (more timepoints, better measurement) or acknowledge the study is exploratory.

Counterbalancing to Control Order Effects

If all subjects experience all conditions (fully within-subjects), the order of conditions can affect results. In a cognitive task with three difficulty levels, performance might improve due to practice regardless of condition. Solution: counterbalance the order.

With three conditions (A, B, C), use all six possible orders:

Subject 1: A → B → C
Subject 2: A → C → B
Subject 3: B → A → C
Subject 4: B → C → A
Subject 5: C → A → B
Subject 6: C → B → A

Each condition appears equally often in each position. Practice effects are balanced across conditions. With large numbers of conditions, complete counterbalancing becomes impractical—use Latin square designs or randomize order per subject.

Interpreting Results: Effect Sizes and Practical Significance

Statistical significance (p < 0.05) tells you the effect probably isn't due to chance. It doesn't tell you if the effect matters. Always report effect sizes alongside p-values.

Partial Eta-Squared: Proportion of Variance Explained

Partial eta-squared (η²p) measures the proportion of variance in the outcome explained by a factor, removing variance from other factors. It ranges from 0 to 1.

Interpretation guidelines (Cohen, 1988):

• η²p = 0.01: Small effect
• η²p = 0.06: Medium effect
• η²p = 0.14: Large effect

In our cognitive training example, the time effect showed η²p = 0.26 (large effect). Time explained 26% of the variance in memory scores after removing individual differences.

Why You Need Both p-Values and Effect Sizes

With large samples, tiny effects become statistically significant but practically meaningless. A drug that lowers blood pressure by 0.3 mmHg might show p < 0.001 with 500 subjects, but the clinical benefit is negligible.

Conversely, with small samples, large effects may not reach significance. A training program improving memory by 15% might show p = 0.08 with 15 subjects—underpowered, not ineffective.

Report both. P-values indicate confidence in the effect's existence. Effect sizes indicate the magnitude of the effect. Both matter for interpretation.

When to Use Alternative Approaches

Repeated measures ANOVA fits many designs, but not all. Here's when alternatives work better.

Growth Curve Models: Non-Linear Change Over Time

If you expect non-linear trajectories (quadratic, exponential, asymptotic), growth curve models fit better than repeated measures ANOVA. These are a special case of linear mixed models that model individual trajectories using polynomial or non-linear functions.

Example: Language development in children follows a steep early trajectory that gradually plateaus. A linear model misses the curvature. A quadratic growth curve captures the acceleration and deceleration.

Generalized Estimating Equations: Non-Normal Outcomes

Repeated measures ANOVA assumes continuous, normally distributed outcomes. If your outcome is binary (success/failure), count (number of seizures), or highly skewed, use generalized estimating equations (GEE) or generalized linear mixed models (GLMM).

GEE extends generalized linear models to correlated data, allowing you to specify the correlation structure (exchangeable, autoregressive, unstructured). GLMM adds random effects for subject-specific parameters.

Time Series Analysis: Many Measurements Per Subject

If you have dozens or hundreds of measurements per subject (e.g., daily mood ratings for 90 days, continuous physiological monitoring), time series methods handle the strong temporal autocorrelation better than repeated measures ANOVA. Consider ARIMA models, state-space models, or dynamic linear models.

Survival Analysis: Time to Event Outcomes

If your outcome is time until an event (time to relapse, time to recovery, time to dropout), use survival analysis methods like Cox regression or parametric survival models. These handle censoring (subjects who don't experience the event during follow-up) correctly.

Step-by-Step: Running Your First Repeated Measures Analysis

Let's walk through the complete analysis workflow with a concrete example.

Example: Exercise Intervention for Depression

You randomize 40 patients with mild depression to exercise intervention (n=20) or waitlist control (n=20). You measure depression severity (PHQ-9 score, 0-27) at baseline, 4 weeks, and 8 weeks. Research question: Does exercise reduce depression more than no treatment?

Step 1: Check Your Data Structure

Your CSV should have one row per observation:

SubjectID, Group, Time, PHQ9
1, Exercise, 0, 14
1, Exercise, 4, 11
1, Exercise, 8, 8
2, Exercise, 0, 16
2, Exercise, 4, 13
2, Exercise, 8, 10
...

Each subject appears three times (three timepoints). This is "long format"—required for repeated measures analysis.

Step 2: Specify Your Model

This is a mixed design:

• Between-subjects factor: Group (Exercise vs Control)
• Within-subjects factor: Time (Baseline, 4 weeks, 8 weeks)
• Interaction: Group × Time (does the time effect differ by group?)

The interaction is your primary interest. If exercise works, you expect depression to decrease more in the exercise group than control—a significant Group × Time interaction.

Step 3: Run the Analysis

Using our free repeated measures tool, upload your CSV and specify:

• Dependent variable: PHQ9
• Within-subjects factor: Time
• Between-subjects factor: Group
• Subject identifier: SubjectID

Results:

Tests of Within-Subjects Effects

Source              SS      df    MS      F       p      η²p
Time              423.2     2   211.6   32.1   <.001   0.458
Time × Group      198.4     2    99.2   15.1   <.001   0.285
Error(Time)       499.6    76     6.6

Step 4: Check Sphericity

Mauchly's Test of Sphericity
W = 0.912, p = 0.182

Sphericity assumption satisfied. No correction needed.

Sphericity not violated (p > 0.05), so uncorrected results are valid.

Step 5: Interpret the Results

Main effect of Time: F(2, 76) = 32.1, p < .001, η²p = 0.458. Depression decreased significantly over time across both groups.

Group × Time interaction: F(2, 76) = 15.1, p < .001, η²p = 0.285. The time effect differed significantly by group—exercise group showed greater reduction than control.

Effect size for the interaction is large (η²p = 0.285). This is the key finding.

Step 6: Follow-Up Tests

The significant interaction tells you the groups differ in their trajectories, but not where specifically. Run post-hoc comparisons:

Pairwise Comparisons (with Bonferroni correction)

Exercise group:
  Baseline vs 4 weeks: Mean diff = 3.2, p = 0.002
  Baseline vs 8 weeks: Mean diff = 5.8, p < .001
  4 weeks vs 8 weeks: Mean diff = 2.6, p = 0.012

Control group:
  Baseline vs 4 weeks: Mean diff = 0.8, p = 0.421
  Baseline vs 8 weeks: Mean diff = 1.4, p = 0.178
  4 weeks vs 8 weeks: Mean diff = 0.6, p = 0.634

Exercise group showed significant reductions at both 4 weeks and 8 weeks. Control group showed no significant change. The intervention works.

Step 7: Visualize the Results

Create a profile plot showing mean PHQ-9 scores over time for each group with 95% confidence intervals. The plot should show:

• Both groups start at similar baseline (~14-15)
• Exercise group decreases steadily (14 → 11 → 8)
• Control group remains relatively flat (14 → 13 → 12)
• Confidence intervals separate by 8 weeks

This visualization makes the interaction immediately clear to readers.

Repeated Measures ANOVA vs. Its Alternatives: The Decision Matrix

We've discussed when standard ANOVA fails, when sphericity matters, and when mixed models win. Here's the complete decision framework in one place.

Use Standard ANOVA When:

• Different subjects in each group (between-subjects design)
• Each subject measured once
• Observations are independent

Use Repeated Measures ANOVA When:

• Same subjects measured multiple times
• Balanced design (all subjects at all timepoints)
• No or minimal missing data (<5%)
• Continuous, normally distributed outcome
• Sphericity satisfied or correctable

Use Mixed ANOVA When:

• Combination of within-subjects and between-subjects factors
• Some factors repeated (time), others not (treatment group)
• Same requirements as repeated measures ANOVA otherwise

Use Linear Mixed Models When:

• Missing data (>5-10% of observations)
• Unbalanced design (subjects measured at different timepoints)
• Unequal spacing between measurements
• Time-varying covariates
• Interest in individual trajectories or random slopes
• Complex correlation structures

Use GEE/GLMM When:

• Non-normal outcomes (binary, count, skewed)
• Need population-average effects (GEE) or subject-specific effects (GLMM)
• Correlated data with non-continuous outcomes

Use Time Series Methods When:

• Many measurements per subject (>20-30)
• Strong temporal autocorrelation
• Interest in forecasting or dynamic patterns

Most applied research falls into one of the first three categories. Start with repeated measures ANOVA for clean, balanced designs. Switch to mixed models when reality intrudes—missing data, unequal spacing, dropout. Use more complex methods only when simpler approaches genuinely can't handle your design.

Real-World Applications: Where This Actually Gets Used

Repeated measures designs appear everywhere. Here are common applications across domains.

Clinical Trials: Treatment Effects Over Time

Measure symptom severity at baseline, during treatment, and at follow-up. Compare active treatment to placebo or standard care. Mixed design: treatment group (between) × time (within). Primary interest: Group × Time interaction showing faster improvement in the treatment group.

A/B Testing: User Engagement Across Sessions

Track user engagement metrics (time on site, pages viewed, conversion rate) across multiple sessions after a UI change. Repeated measures on individual users accounts for baseline engagement differences. Compare new UI vs old UI over time to see if initial novelty effects persist or fade.

Learning and Training: Skill Acquisition

Measure performance before training, immediately after, and at retention testing (1 week, 1 month later). Within-subjects design controls for individual differences in baseline ability. Assess whether training effects persist or decay over time.

Agricultural Experiments: Crop Yield Over Growing Seasons

Measure yields from the same plots across multiple growing seasons under different fertilizer treatments. Plots are experimental units measured repeatedly. Controls for soil quality, drainage, and microclimate differences between plots.

Psychophysiology: Responses to Stimuli

Measure heart rate, skin conductance, or neural activity while subjects view different stimulus types (neutral, positive, negative). Each subject sees all stimulus types. Within-subjects design provides higher power by removing individual differences in baseline physiological state.

In each case, the repeated structure increases power by controlling for stable individual differences—the primary advantage of within-subjects designs.

The Bottom Line: Choose the Test That Fits Your Design

The most common error in repeated measures analysis isn't complex statistical theory—it's using the wrong test for your data structure. Before you analyze, ask one question: Are my observations independent?

If you measure different subjects in each condition, use standard ANOVA. If you measure the same subjects multiple times, use repeated measures ANOVA or mixed models. If you ignore the repeated structure and use standard ANOVA anyway, your p-values are wrong—not slightly wrong, but systematically biased in unpredictable directions.

Once you've chosen the right test family, check sphericity. If violated, apply corrections. If you have missing data or unequal spacing, use mixed models instead of traditional repeated measures ANOVA. If your outcome is non-normal, use GEE or GLMM.

And always—always—run power analysis before collecting data. Underpowered experiments waste resources and produce uninformative results. If you can't recruit enough subjects for adequate power, redesign the study or acknowledge it's exploratory.

Repeated measures designs offer substantial efficiency gains over between-subjects designs. Use them when appropriate. Just make sure your analysis method matches your experimental design.

Frequently Asked Questions

When should I use repeated measures ANOVA instead of standard ANOVA?

Use repeated measures ANOVA when you measure the same subjects multiple times. Standard ANOVA assumes independence between observations—when you measure the same person at baseline, week 1, and week 2, those measurements are correlated. Ignoring this correlation inflates your Type I error rate and produces invalid p-values. The key question: Are your observations independent? If no, you need repeated measures.

What's the difference between repeated measures ANOVA and mixed ANOVA?

Repeated measures ANOVA has only within-subjects factors (all subjects experience all conditions). Mixed ANOVA combines within-subjects factors (repeated over time) with between-subjects factors (treatment vs control groups). Use mixed ANOVA when you have both types of factors in your experimental design.

How do I handle missing data in repeated measures analysis?

Traditional repeated measures ANOVA uses listwise deletion—losing an entire subject if they miss one timepoint. This wastes data and introduces bias. Linear mixed models handle missing data better by using all available observations and assuming missing at random (MAR). If you have more than 5-10% missing data, use a mixed model instead of traditional repeated measures ANOVA.

What sample size do I need for repeated measures ANOVA?

Sample size depends on your expected effect size, number of timepoints, and correlation between measurements. Higher within-subject correlation gives you more statistical power, so you need fewer subjects than a between-subjects design. For a medium effect (f = 0.25) with 3 timepoints and correlation r = 0.5, you need approximately 24 subjects for 80% power at alpha = 0.05. Always run a power analysis before collecting data.

What are the key assumptions of repeated measures ANOVA?

The critical assumption is sphericity: variances of differences between all timepoint combinations must be equal. Violations inflate Type I error. Always test sphericity with Mauchly's test. If violated (p < 0.05), apply corrections: Greenhouse-Geisser for severe violations (epsilon < 0.75) or Huynh-Feldt for mild violations. Other assumptions include normality of residuals and no extreme outliers.

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