Split-Plot Design User Guide

1. INTRODUCTION

The Split-Plot Design module in DATES performs Analysis of Variance (ANOVA) for factorial experiments where experimental factors require different plot sizes or different levels of randomization precision.

In agricultural, industrial, or biological trials, certain factors (such as Irrigation Method, Tillage System, or Temperature) are difficult or costly to change on a small scale and must be applied to large Main Plots. Secondary factors (such as Fertilizer Rate, Chemical Concentration, or Cultivar) can be easily varied on smaller Sub-Plots nested within each Main Plot.

Two-Tier Error Partitioning in Split-Plot ANOVA:

Main-Plot Level (Error A): Used to evaluate Main-Plot Factor effects (e.g., Irrigation). Subject to larger plot size variability and fewer degrees of freedom.
Sub-Plot Level (Error B): Used to evaluate Sub-Plot Factor effects (e.g., Fertilizer) and the Main-Factor x Sub-Factor Interaction. Evaluated with smaller experimental error and higher statistical precision.

Supported Factorial Combinations in DATES:

1x1 Design: Standard Split-Plot with 1 Main-Plot Factor and 1 Sub-Plot Factor.
2x1 Design: Factorial Main-Plot (2 Main Factors) with 1 Sub-Plot Factor.
1x2 Design: 1 Main-Plot Factor with Factorial Sub-Plots (2 Sub Factors).
2x2 Design: Full Factorial Main-Plots (2 Main Factors) with Factorial Sub-Plots (2 Sub Factors).

2. AVAILABLE OPTIONS & SETTINGS

The sidebar control panel and header toolbar provide complete control over factor tier mapping, error structures, mean comparisons, and data 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 trial spreadsheet and populates mapping selectors.	At the start of every Split-Plot analysis session.
Factorial Design Mode	Selects factor structure: `1x1`, `2x1`, `1x2`, or `2x2`.	Determines the number of Main-Plot and Sub-Plot factor slots in the sidebar mapping.	Match to your actual experimental factor arrangement.
Block / Replication Variable	Selects the column representing experimental blocks or replications.	Isolates block variance across main plot units.	Select categorical/numeric column identifying blocks (e.g., Rep_1, Rep_2).
Main-Plot Factor(s)	Selects dataset columns assigned to large Main-Plots (evaluated against Error A).	Partition main plot factor effects and main-plot error.	Select factor(s) applied to large plots (e.g., Irrigation).
Sub-Plot Factor(s)	Selects dataset columns assigned to smaller Sub-Plots (evaluated against Error B).	Partition sub-plot factor effects, interaction, and sub-plot error.	Select factor(s) applied to small sub-plots (e.g., Fertilizer).
Target Response Traits	Selects continuous numeric measurement columns to analyze.	Computes ANOVA tables, trait means, and plots for selected variables.	Select one or multiple quantitative response variables.
ANOVA Type (Sum of Squares)	Selects SS Type: `Type I (Sequential)`, `Type II (Hierarchical)`, or `Type III (Marginal)`.	Determines SS computation order. Automatically selects optimal type if set to Auto.	Use Type I for balanced split-plots; use Type II or Type III for unbalanced layouts.
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 multiple comparison post-hoc test: `LSD`, `Tukey`, `Duncan`, `Dunnett`, or `None`.	Identifies significantly different treatment pairs using Error A for Main Factors and Error B for Sub Factors.	Select LSD or Tukey for pairwise comparisons; use Dunnett to compare treatments against a control.
Lettering Display	Formats mean separation labels: `ABC` (Alphabetical) or `SYM` (Symbolic).	Displays compact letter display groupings for treatment means.	Choose ABC for standard publication tables.
Mean Ordering	Sorts post-hoc mean tables: `High → Low` (Descending) or `Low → High` (Ascending).	Organizes treatment ranking for clarity.	Select High → Low to highlight top-performing treatments.
Transformations	Applies 15 automated transformations (e.g., Log, Square Root, ArcSine, Box-Cox) to normalize response data.	Stabilizes residual variance when ANOVA 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 should be arranged in a tidy relational structure where each row represents an individual sub-plot observation:

Block_Rep	Main_Irrigation	Sub_Fertilizer	Yield_Metric	Protein_Content
Block_1	Drip_Irrigation	Rate_0	42.50	11.20
Block_1	Drip_Irrigation	Rate_50	54.20	12.80
Block_1	Drip_Irrigation	Rate_100	61.80	13.50
Block_1	Flood_Irrigation	Rate_0	38.10	10.80
Block_1	Flood_Irrigation	Rate_50	48.90	11.90
Block_1	Flood_Irrigation	Rate_100	53.40	12.40

4. MATHEMATICAL FOUNDATIONS & FORMULAS

Split-Plot Design partitions total variation into Main-Plot components (Blocks, Main Factor, Error A) and Sub-Plot components (Sub Factor, Interaction, Error B). Below are the plain text formula definitions:

Main-Plot Variance (Error A)

Main Factor Sum of Squares (SSA): SSA = Sum of deviations for Main Factor A across Main Plots.

Error A (Main Plot Error): Error A = Block x Main Factor Interaction SS.

Main Factor F-Test: F_Main = MS_Main / MS_ErrorA

Sub-Plot Variance (Error B)

Sub Factor Sum of Squares (SSB): SSB = Sum of deviations for Sub Factor B across Sub Plots.

Interaction Sum of Squares (SSAB): SSAB = Main Factor x Sub Factor Interaction SS.

Error B (Sub Plot Error): Error B = Residual variation remaining within Main Plots.

Sub Factor F-Test: F_Sub = MS_Sub / MS_ErrorB

Interaction F-Test

Formula Description:

F_Interaction = MS_Interaction / MS_ErrorB

Evaluates whether the sub-factor response varies across main-plot treatment levels.

Standard Errors for Mean Comparison

Main Factor Comparison: SED_Main = Square Root of (2 * MS_ErrorA / (Replications * Sub_Levels))

Sub Factor Comparison: SED_Sub = Square Root of (2 * MS_ErrorB / (Replications * Main_Levels))

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.
Select Design Mode: Choose 1x1, 2x1, 1x2, or 2x2 based on your factor breakdown.
Map Required Factors: Map dataset columns to Block Variable, Main-Plot Factor(s), and Sub-Plot Factor(s).
Select Response Traits: Check one or multiple numeric measurement columns to analyze.
Configure Header Parameters: Set SS Type (Type I/II/III), 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 the two-tier Split-Plot ANOVA Table (Error A and Error B tests), Main & Sub Factor Means, Interaction Means, Post-hoc Letter Groupings, and Diagnostic Plots.
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 Split-Plot ANOVA Summary Table for a 1x1 Irrigation (Main) x Fertilizer (Sub) experiment:

Source of Variation	Degrees of Freedom (df)	Sum of Squares (SS)	Mean Square (MS)	F-Statistic	p-Value	Test Error Term
Replication (Block)	2	18.400	9.200	2.140	0.2340	Error A
Main Factor A (Irrigation)	1	124.500	124.500	28.950	0.0328	Error A (*)
Main Plot Error (Error A)	2	8.600	4.300	—	—	—
Sub Factor B (Fertilizer)	2	210.800	105.400	56.060	0.0001	Error B (**)
Main Factor A x Sub Factor B	2	34.200	17.100	9.095	0.0088	Error B (**)
Sub Plot Error (Error B)	8	15.040	1.880	—	—	—
Total Variation	17	411.540	—	—	—	—

How to Read the Output:

Main Factor p-Value (Error A): Evaluated against Error A MS. Indicates whether large main plot treatments differ significantly.
Sub Factor p-Value (Error B): Evaluated against Error B MS. Usually has higher precision and more error degrees of freedom than Error A.
Interaction p-Value (Main x Sub): Evaluated against Error B MS. A significant interaction indicates that sub-factor treatment response varies significantly depending on main-plot conditions.

7. IMPORTANT NOTES & BEST PRACTICES

Proper Error Term Assignment

Never test Main-Plot Factors against Sub-Plot Error (Error B). DATES automatically uses Error A MS to test Main Factors and Error B MS to test Sub Factors and Interactions.

Precision Hierarchy

Assign your most important factor or the factor expecting smaller differences to the Sub-Plots, as Sub-Plot comparisons benefit from lower experimental error (Error B MS < Error A MS).

Cite DATES in Research Papers

If you use the DATES Split-Plot module for trial analysis in published scientific research, please cite it as follows:

@software{dates_app_2026, author = {DATES Development Team}, title = {DATES: Data Analysis and Trial Evaluation System}, year = {2026}, url = {https://dates-app.org}, note = {Experimental Design — Split-Plot Design Module} }