DATES
USER GUIDES

Pooled Split-Plot Design User Guide

Comprehensive step-by-step guide for performing Pooled Split-Plot Analysis of Variance in DATES across multi-environment trials, featuring two-tier error pooling (Error A and Error B) and multi-way location interactions.

1. INTRODUCTION

The Pooled Split-Plot Design module in DATES performs multi-environment combined Analysis of Variance (ANOVA) for Split-Plot trials repeated across multiple locations, sites, or seasons.

In a standard Split-Plot design, treatments are assigned across two plot tiers: Main-Plots (evaluated against Error A) and Sub-Plots (evaluated against Error B). The Pooled Split-Plot module combines these multi-location trials to evaluate main plot factors, sub-plot factors, and their interactions across testing environments.

Core Features of Pooled Split-Plot ANOVA:

2. AVAILABLE OPTIONS & SETTINGS

The sidebar control panel and header toolbar provide full control over factorial layout selection, column mapping, error models, 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 multi-environment Split-Plot spreadsheet into memory. At the start of every Pooled Split-Plot analysis session.
Factorial Design Type Selects factorial layout: 1x1, 2x1, 1x2, or 2x2. Defines the number of Main-Plot and Sub-Plot factor variables. Select 1x1 for single main & sub factor; select 2x2 for dual main & sub factors.
Environment / Pooling Factor Selects the categorical column specifying trial location, site, or year. Partitions macro-environmental variation across sites. Select environmental column (e.g., Location_A, Location_B).
Block / Replication Variable Selects the column identifying blocks within each location environment. Partitions spatial micro-environmental gradients within trial sites. Select block identifier column (e.g., Rep_1, Rep_2 within Site).
Main-Plot Factor(s) Selects categorical column(s) assigned to Main Plots (evaluated against Error A). Partitions main plot treatment effects and Error A. Select primary factor requiring large plot sizes (e.g., Irrigation_Level).
Sub-Plot Factor(s) Selects categorical column(s) assigned to Sub Plots (evaluated against Error B). Partitions sub-plot treatment effects and Error B. Select secondary factor requiring small plot sizes (e.g., Fertilizer_Rate).
Target Response Traits Selects continuous quantitative measurement variables to analyze. Generates pooled ANOVA tables, interaction means, and diagnostic plots. Select one or multiple quantitative response traits.
ANOVA Type (Sum of Squares) Selects SS Type: Type I (Sequential), Type II (Hierarchical), or Type III (Marginal). Determines SS calculation order. Automatically selects optimal type if set to Auto. Use Type I for balanced layouts; use Type III for unbalanced multi-site data.
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 pooled factor means. Select LSD or Tukey for pairwise checks; use Dunnett to compare treatments against a control.
Transformations Applies 15 automated transformations (e.g., Log, Square Root, ArcSine, Box-Cox) to normalize response data. Stabilizes residual variance when multi-site 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 tidy relational layout where each row represents an individual sub-plot plot observation:

PooledSplitPlot_MultiEnv_Dataset.xlsx — Sheet1 Format: Tidy Multi-Environment Split-Plot Layout
Environment Block_Rep Main_Factor_A Sub_Factor_B Yield_Metric Quality_Score
Site_1Rep_1Main_Factor_Level1Sub_Factor_Level148.208.50
Site_1Rep_1Main_Factor_Level1Sub_Factor_Level254.109.10
Site_1Rep_1Main_Factor_Level2Sub_Factor_Level141.808.20
Site_1Rep_1Main_Factor_Level2Sub_Factor_Level249.608.80
Site_2Rep_1Main_Factor_Level1Sub_Factor_Level152.308.90
Site_2Rep_1Main_Factor_Level1Sub_Factor_Level258.609.35

4. MATHEMATICAL FOUNDATIONS & FORMULAS

Pooled Split-Plot ANOVA partitions total multi-environment variation into Environment SS, Main-Plot SS (Error A), Sub-Plot SS (Error B), and Multi-Way Location Interaction SS. Below are the plain text formula definitions:

Main-Plot Level & Error A

Main Factor A SS (SSA): Variation attributable to Main Factor A.

Error A (Pooled Main-Plot Error): Combined Block x Main Factor interaction across locations.

F-Test Main Factor: F_A = MS_A / MS_ErrorA

Sub-Plot Level & Error B

Sub Factor B SS (SSB): Variation attributable to Sub Factor B.

Error B (Pooled Sub-Plot Error): Residual error within sub-plots across locations.

F-Test Sub Factor: F_B = MS_B / MS_ErrorB

Environmental Interaction SS

Factor A x Env SS: Evaluates main plot stability across locations.

Factor B x Env SS: Evaluates sub-plot factor stability across locations.

Factor A x B x Env SS: Three-way interaction across site environments.

Precision Hierarchy

Error B MS < Error A MS: High precision is maintained for sub-plot factors and interactions across testing sites.

5. STEP-BY-STEP WORKFLOW

  1. Upload Dataset: Click the Upload Spreadsheet area in the sidebar panel to upload your .csv or .xlsx file.
  2. Select Worksheet: If using a multi-tab workbook, pick the active sheet from the dropdown menu.
  3. Select Factorial Layout: Choose 1x1, 2x1, 1x2, or 2x2 design configuration.
  4. Map Variables: Map dataset columns to Environment, Block, Main-Plot Factor(s), and Sub-Plot Factor(s).
  5. Select Response Traits: Check one or multiple numeric measurement columns to analyze.
  6. 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).
  7. Run Analysis: Click the bold RUN ANALYSIS button in the sidebar panel.
  8. Review Results: Inspect the Pooled Split-Plot ANOVA Table (Error A and Error B tests), Multi-Way Location Interactions, and Diagnostic Plots.
  9. 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 Pooled Split-Plot ANOVA Summary Table for a 1x1 factorial trial evaluated across 3 environments:

Pooled Split-Plot ANOVA Summary Table Alpha = 0.05 | Type III SS
Source of Variation Degrees of Freedom (df) Sum of Squares (SS) Mean Square (MS) F-Statistic p-Value Test Error Term
Environment (Location) 2 345.800 172.900 38.422 0.0001 Error A
Block (within Environment) 9 82.400 9.156 2.035 0.0894 Error A
Main Factor A 2 184.200 92.100 20.467 0.0001 Error A (**)
Main Factor A x Environment 4 42.600 10.650 2.367 0.0885 Error A
Pooled Main-Plot Error (Error A) 18 81.000 4.500 — — —
Sub Factor B 2 212.600 106.300 42.520 0.0001 Error B (**)
Sub Factor B x Environment 4 38.400 9.600 3.840 0.0084 Error B (*)
Main Factor A x Sub Factor B 4 96.800 24.200 9.680 0.0001 Error B (**)
Main Factor A x Sub B x Environment 8 44.800 5.600 2.240 0.0385 Error B (*)
Pooled Sub-Plot Error (Error B) 54 135.000 2.500 — — —
Total Variation 107 1263.600 — — — —

How to Read the Output:

7. IMPORTANT NOTES & BEST PRACTICES

Separate Error Terms for Post-Hoc Tests

DATES automatically applies MS Error A for Main Factor post-hoc tests and MS Error B for Sub Factor and Interaction post-hoc comparisons.

Check Homogeneity of Error A and Error B

Verify that both Error A and Error B variances are homogeneous across testing environments before trusting pooled multi-site F-tests.