Repeated Measures ANOVA User Guide

1. INTRODUCTION

The Repeated Measures ANOVA module in DATES performs statistical analysis for experiments where identical experimental units (subjects, plots, or samples) are measured repeatedly across multiple consecutive time points or inspection intervals.

In longitudinal studies, observations taken on the same subject over time are correlated, violating standard independent ANOVA assumptions. Repeated Measures ANOVA accounts for within-subject correlation by partitioning variance into Between-Subjects effects and Within-Subjects temporal effects.

Core Features of Repeated Measures ANOVA:

Between-Subjects Factor (Treatment Factor A): Tests overall treatment group differences averaged across time points.
Within-Subjects Factor (Time Factor): Tests changes in response over time points or duration intervals.
Time x Treatment Interaction: Tests whether treatment groups exhibit different temporal response profiles over time.
Sphericity Diagnostics & Corrections: Includes Mauchly's Test of Sphericity, automatically computing Greenhouse-Geisser (GG) and Huynh-Feldt (HF) adjusted p-values.

2. AVAILABLE OPTIONS & SETTINGS

The sidebar control panel and header toolbar provide full control over factor assignments, sphericity correction selection, post-hoc methods, and transformations:

Control / Parameter	Description	Why it is used	When to select / set
Upload Data	Uploads your `.csv`, `.xlsx`, or `.xls` trial dataset into memory.	Loads raw longitudinal trial spreadsheet into memory.	At the start of every Repeated Measures analysis session.
Between-Subjects Factor	Selects categorical column defining treatment groups or conditions.	Partitions overall treatment group variation.	Select primary treatment factor (e.g., Treatment_Group).
Within-Subjects (Time) Factor	Selects the column specifying time points, observation intervals, or durations.	Partitions temporal changes across measurement periods.	Select time factor column (e.g., Week_0, Week_2, Week_4).
Subject / Plot Identifier	Selects column identifying individual subjects or experimental units.	Isolates individual subject baseline variation across time points.	Select unique subject or plot ID column (e.g., Subject_ID).
Target Response Traits	Selects continuous quantitative measurement variables to analyze.	Generates repeated measures ANOVA, time-course profile plots, and sphericity tables.	Select one or multiple quantitative response traits.
Sphericity Correction	Choose between `Auto (Mauchly)`, `Greenhouse-Geisser (GG)`, or `Huynh-Feldt (HF)`.	Adjusts numerator and denominator degrees of freedom when sphericity assumption is violated.	Use Auto to let Mauchly test determine correction; choose GG or HF manually if required.
Alpha Level	Significance threshold (`5%` or `1%`).	Sets critical threshold for F-test significance and confidence intervals.	Set to 5% for standard research or 1% for stringent significance testing.
Mean Separation Test	Selects post-hoc test: `LSD`, `Tukey`, `Duncan`, `Dunnett`, or `None`.	Identifies statistically significant pairwise differences among treatment groups and time points.	Select LSD or Tukey for pairwise checks; use Dunnett to compare treatments against baseline.
Transformations	Applies 15 automated transformations (e.g., Log, Square Root, ArcSine, Box-Cox) to normalize response data.	Stabilizes residual variance when normality or homoscedasticity assumptions are violated.	Toggle on when diagnostic residual plots show non-normality or unequal variance.

3. INPUT DATA FORMAT REQUIREMENT

DATES accepts dataset spreadsheets in standard .xlsx, .xls, or .csv formats. Data can be formatted in tidy long format where each row represents an individual time-point observation for a subject:

Subject_ID	Treatment_Group	Time_Point	Response_Metric	Secondary_Trait
Subject_01	Control_Group	Week_00	42.50	8.20
Subject_01	Control_Group	Week_02	44.10	8.35
Subject_01	Control_Group	Week_04	45.80	8.50
Subject_02	Active_Group	Week_00	42.10	8.15
Subject_02	Active_Group	Week_02	49.60	9.10
Subject_02	Active_Group	Week_04	56.30	9.60

4. MATHEMATICAL FOUNDATIONS & FORMULAS

Repeated Measures ANOVA partitions total variation into Between-Subjects SS (Treatment & Subject Error) and Within-Subjects SS (Time, Time x Treatment, & Time x Subject Error). Below are the plain text formula definitions:

Between-Subjects Partition

Treatment SS (SSA): Variation across between-subject treatment groups.

Subject Error SS (Error_Sub): Variation among subjects within treatment groups.

F-Test Treatment: F_Group = MS_Treatment / MS_ErrorSub

Within-Subjects Partition

Time SS (SSTime): Variation across repeated measurement time points.

Time x Treatment SS (SS_AxTime): Interaction measuring differential treatment trajectories.

Within Error SS (Error_Time): Time x Subject interaction residual error.

Mauchly Test of Sphericity

Mauchly W Statistic: Evaluates equality of variances of differences between time pairs.

Sphericity Violation: If p < 0.05, sphericity is violated; degrees of freedom must be adjusted.

Epsilon DF Adjustments

Greenhouse-Geisser Epsilon: Conservative epsilon multiplier (0 < e < 1) reducing DF for F-test.

Huynh-Feldt Epsilon: Slightly less conservative epsilon correction for moderate sample sizes.

5. STEP-BY-STEP WORKFLOW

Upload Dataset: Click the Upload Spreadsheet area in the sidebar panel to upload your .csv or .xlsx file.
Select Worksheet: If using a multi-tab workbook, pick the active sheet from the dropdown menu.
Map Variables: Map dataset columns to Between-Subjects Factor, Within-Subjects (Time) Factor, and Subject ID.
Select Response Traits: Check one or multiple numeric measurement columns to analyze.
Configure Header Parameters: Set sphericity correction method (Auto/GG/HF), Alpha level (5% or 1%), and post-hoc Mean Separation method (LSD, Tukey, Duncan, Dunnett).
Run Analysis: Click the bold RUN ANALYSIS button in the sidebar panel.
Review Results: Inspect Mauchly's Sphericity Test, Sphericity-Corrected ANOVA Table, Time-Course Trajectory Plots, and Post-Hoc Letter Groupings.
Export Outputs: Download formatted Excel tables (.xlsx), Word summaries (.docx), PowerPoint slide decks (.pptx), or publication-grade PNG images.

6. SAMPLE RESULTS & INTERPRETATION

Below is an example of a Repeated Measures ANOVA Summary Table evaluating 2 Treatment Groups across 4 Time Points:

Source of Variation	Unadjusted df	GG Adjusted df	Sum of Squares (SS)	Mean Square (MS)	F-Statistic	Unadjusted p	GG Adjusted p
Treatment Group (Between)	1	1.000	245.800	245.800	18.908	0.0003	0.0003 (**)
Subject Error (Between)	18	18.000	234.000	13.000	—	—	—
Time Factor (Within)	3	2.226	312.400	140.341	42.528	0.0001	0.0001 (**)
Time x Treatment Interaction	3	2.226	128.600	57.772	17.507	0.0001	0.0001 (**)
Time Error (Within)	54	40.068	178.200	3.300	—	—	—
Total Variation	79	—	1099.000	—	—	—	—

How to Read the Output:

Mauchly Sphericity Test: A significant Mauchly p-value (p = 0.031 < 0.05) indicates sphericity violation. Always read the GG Adjusted p column.
Treatment Group p-Value: Evaluates overall baseline difference between treatment groups averaged across all time points.
Time x Treatment Interaction p-Value: A significant interaction (p < 0.001) confirms that treatment groups showed significantly different change trajectories over time.

7. IMPORTANT NOTES & BEST PRACTICES

Always Check Sphericity Corrections

When sphericity is violated (Mauchly p < 0.05), unadjusted ANOVA p-values produce inflated Type I error rates. Use Greenhouse-Geisser or Huynh-Feldt adjusted p-values for reporting.

Balanced Time Points Across Subjects

Ensure that all subjects are measured at the exact same set of time points. If missing data points occur, DATES automatically handles missing intervals via REML mixed modeling.