Repeated Measures ANOVA Calculator

Advanced Statistical Tests

Enter your data below. Each row should represent a single subject, and each column a different condition or time point. Values can be separated by commas, spaces, or tabs.

Practical Examples

Explore how the Repeated Measures ANOVA Calculator works with these common scenarios.

Drug Efficacy Over Time

Example 1

A study measures a patient's response to a new drug at 1, 2, and 3 months post-treatment.

10, 12, 15
11, 13, 16
9, 11, 14
8, 10, 13

Learning Trials Performance

Example 2

Testing the performance of subjects over four consecutive learning trials.

5, 6, 8, 9
4, 5, 7, 8
6, 7, 9, 10
5, 6, 8, 8
4, 6, 7, 9

Comparing 3 Different Diets

Example 3

Measuring the weight of the same group of individuals after following three different diets for a month each.

85, 82, 80
90, 87, 84
78, 76, 75
92, 90, 88
88, 85, 83
81, 79, 78

Reaction Time Under Different Conditions

Example 4

Measuring reaction time of participants under two conditions: with and without a distraction.

250, 280
265, 290
240, 275
280, 310
255, 285
Other Titles
Understanding Repeated Measures ANOVA: A Comprehensive Guide
Dive deep into the principles, applications, and calculations behind the Repeated Measures ANOVA test.

What is Repeated Measures ANOVA?

  • Core Concept
  • When to Use It
  • Key Assumptions
Repeated Measures ANOVA (Analysis of Variance) is a statistical method used to compare the means of three or more groups in which the same subjects are used in each group. This approach is powerful for analyzing data from longitudinal studies, experiments where participants are exposed to multiple conditions, or any design where measurements are taken from the same entity over time or under different treatments.
Core Concept
The primary advantage of a repeated measures design is its ability to control for individual differences between subjects. Since each participant acts as their own control, the variability in the data that comes from differences between people is removed, leading to a more powerful statistical test. The analysis focuses on the changes in measurements within subjects across the different conditions or time points.
When to Use It
  • Longitudinal Research: Tracking changes in a variable over time (e.g., patient health metrics over several months).
  • Experimental Designs: Exposing participants to multiple experimental conditions (e.g., testing the effect of different types of stimuli on reaction time).
  • Pre-test/Post-test Studies: Comparing scores before and after an intervention, especially with multiple follow-ups.
Key Assumptions
  • Normality: The dependent variable should be approximately normally distributed within each condition.
  • Sphericity: The variances of the differences between all possible pairs of within-subject conditions must be equal. This is a critical assumption. Mauchly's test is used to check for this, and if it's violated, corrections (like Greenhouse-Geisser) are necessary.
  • No Outliers: There should be no significant outliers in the dataset.

Step-by-Step Guide to Using the Calculator

  • Data Entry Format
  • Executing the Calculation
  • Interpreting the Results Table
Our calculator simplifies the process of performing a Repeated Measures ANOVA. Follow these steps to get your analysis.
Data Entry Format
Your data should be organized with one subject per line. On each line, the measurements for the different conditions or time points should be listed, separated by a comma, space, or tab. It's crucial that every subject (row) has the same number of measurements (columns).
Executing the Calculation
Once your data is entered into the text area, simply click the 'Calculate ANOVA' button. The tool will automatically validate the input and perform the necessary calculations.
Interpreting the Results Table
  • ANOVA Summary Table: This is the core output. Look at the 'Within-Subjects' row. The F-value and the associated P-value tell you if there is a statistically significant difference somewhere among your group means.
  • Mauchly's Test for Sphericity: Check the p-value here. If p < .05, the sphericity assumption is violated, and you should refer to the corrected p-values below.
  • Corrections for Sphericity: If sphericity is violated, use the Greenhouse-Geisser or Huynh-Feldt corrected p-values to evaluate the significance of your F-statistic.
  • Partial Eta-Squared (η²p): This is your effect size. It tells you how much of the variance in your outcome is explained by the different conditions or time points.

Mathematical Derivation and Formulas

  • Sum of Squares (SS)
  • Degrees of Freedom (df) and Mean Squares (MS)
  • The F-Statistic
The Repeated Measures ANOVA partitions the total variance in the data into different components to determine the significance of the treatment effect.
Sum of Squares (SS)
  • SS-Total: Total variability in the data.
  • SS-Between-Subjects: Variability due to individual differences between subjects.
  • SS-Within-Subjects: Variability within the subjects themselves, which is further divided into:
    • SS-Treatments (or Conditions): Variability due to the experimental conditions.
    • SS-Error: Unexplained variability or random error.
The key calculation is isolating the SS-Treatments from the SS-Error.
Degrees of Freedom (df) and Mean Squares (MS)
  • df-Treatments = k - 1 (where k is the number of conditions)
  • df-Error = (n - 1) * (k - 1) (where n is the number of subjects)
  • MS (Mean Square) is calculated by dividing the SS by its corresponding df (e.g., MS-Treatments = SS-Treatments / df-Treatments).
The F-Statistic
The F-statistic is the ratio of the variance explained by the treatment to the unexplained variance (error).
F = MS-Treatments / MS-Error
A large F-value suggests that the variation due to the treatment conditions is larger than the random error, indicating a significant effect.