Partially Replicated Augmented Design (PL-Aug-RBD) User Guide

1. INTRODUCTION

The Partially Replicated Augmented Design (PL-Aug-RBD / PL-Augmented) module in DATES extends single-site augmented designs to multi-environment screening programs (e.g., across multiple trial locations, seasons, or experimental sites).

In a multi-environment screening trial, candidate test entries are evaluated across multiple locations. Some candidate entries may be unreplicated within individual sites, while a subset of test entries and standard control checks are partially replicated across blocks and environments.

Core Advantages of PL-Aug-RBD:

Multi-Location Screening: Evaluates candidate test entries across multiple trial sites simultaneously.
Partially Replicated Entries: Allows candidate entries to be replicated at select key locations while remaining unreplicated at secondary sites.
Pooled Environmental Adjustment: Adjusts test entry performance across locations by pooling control check residuals and site-level block effects.
Entry x Environment Interaction: Evaluates candidate stability across testing locations.

2. AVAILABLE OPTIONS & SETTINGS

The sidebar control panel and header toolbar provide full control over environmental mapping, entry classification, 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 trial spreadsheet and populates variable mapping dropdowns.	At the start of every PL-Aug-RBD analysis session.
Treatment / Entry Variable	Selects the categorical column specifying candidate test entries and control checks.	Identifies unique entries for multi-environment mean adjustment.	Select categorical column containing entry identifiers.
Entry Type Variable	Selects the column designating entry role: `Control / Check` vs `Test / Candidate`.	Distinguishes replicated controls from candidate test entries.	Select column containing entry type classifications.
Environment Variable	Selects the column representing trial location, site, or year.	Partitions macro-environmental variation across sites.	Select environmental column (e.g., Site_A, Site_B, Year_2026).
Block / Replication Variable	Selects the column representing experimental blocks within each environment.	Captures within-site spatial soil or environmental gradients.	Select block identifier column (e.g., Block_1, Block_2 within Site).
Target Response Traits	Selects continuous quantitative measurement variables to analyze.	Generates multi-location ANOVA, pooled adjusted means, and diagnostic plots.	Select one or multiple quantitative response traits.
Estimation Method	Choose between `Normal / OLS` and `REML (Restricted Maximum Likelihood)`.	Determines whether environment and block effects are treated as Fixed or Random.	Use Normal/OLS for balanced layouts; select REML for random environmental effects.
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 multi-site selection.
Mean Separation Test	Selects post-hoc test: `LSD`, `Tukey`, `Duncan`, `Dunnett`, or `None`.	Identifies statistically significant pairwise differences among pooled adjusted entry means.	Select LSD or Tukey for pairwise checks; use Dunnett to compare test entries against control checks.
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 plot observation:

Environment	Block	Entry_Code	Entry_Type	Yield_Metric	Quality_Score
Site_Alpha	Block_1	Control_Std_A	Control	64.50	9.10
Site_Alpha	Block_1	Candidate_101	Test	71.20	9.40
Site_Alpha	Block_2	Control_Std_A	Control	63.80	9.00
Site_Beta	Block_1	Control_Std_A	Control	58.90	8.60
Site_Beta	Block_1	Candidate_101	Test	64.30	8.95
Site_Beta	Block_2	Control_Std_A	Control	57.80	8.50

4. MATHEMATICAL FOUNDATIONS & FORMULAS

PL-Aug-RBD partitions total multi-site variation into Environment SS, Block within Environment SS, Control Treatment SS, Test Entry SS (Adjusted), and Entry x Environment Interaction SS. Below are the plain text formula definitions:

Environment SS (SSEnv)

SSEnv = Sum of squared deviations across testing locations.

Measures macro-environmental variation across sites or seasons.

Block within Environment SS (SSB/E)

SSB/E = Block variation nested inside trial locations.

Isolates spatial micro-environmental gradients specific to each location.

Pooled Adjusted Test Entry Means

Y_pooled_adj = Multi-site adjusted entry means.

Adjusts candidate test entries across location environments using pooled check performance.

Entry x Environment Interaction SS (SSTE)

SSTE = Entry x Environment interaction SS.

Evaluates candidate stability and performance consistency across environments.

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 Treatment / Entry, Entry Type, Environment, and Block.
Select Response Traits: Check one or multiple numeric measurement columns to analyze.
Configure Header Parameters: Set estimation model (Normal/REML), 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 Multi-Environment PL-Augmented ANOVA Table, Pooled Adjusted Entry Means, Entry x Environment Stability, and Residual 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 PL-Augmented Multi-Environment ANOVA Summary Table evaluating 80 candidate entries across 3 locations with 2 control checks:

Source of Variation	Degrees of Freedom (df)	Sum of Squares (SS)	Mean Square (MS)	F-Statistic	p-Value
Environment (Location)	2	412.500	206.250	45.833	0.0001
Blocks within Environment	6	128.400	21.400	4.756	0.0002
Control Checks (Replicated)	1	56.200	56.200	12.489	0.0008
Test Entries (Adjusted)	79	1420.800	17.985	3.997	0.0001
Test Entry x Environment Interaction	158	711.000	4.500	1.850	0.0024
Pooled Residual Error	24	108.000	4.500	—	—
Total Variation	270	2836.900	—	—	—

How to Read the Output:

Environment p-Value: Indicates whether location test sites differ significantly in overall yield/performance levels.
Test Entries (Adjusted) p-Value: Evaluates overall performance differences among candidate test entries across testing sites.
Entry x Environment p-Value: A significant p-value (p < 0.05) reveals that candidate entries perform differently depending on the test location, highlighting environmental adaptation.

7. IMPORTANT NOTES & BEST PRACTICES

Consistent Check Entries Across Sites

Use the same standard control check entries across all testing environments to ensure robust environmental pooling and accurate entry adjustment.

Evaluate Entry Stability

When Entry x Environment interaction is significant, inspect environmental stability plots and site-specific adjusted means before discarding candidate entries.