Augmented Randomized Block Design (Augmented RBD) User Guide

1. INTRODUCTION

The Augmented Randomized Block Design (Augmented RBD / Aug-RBD) module in DATES performs Analysis of Variance (ANOVA) for early-stage screening trials where hundreds of new candidate treatments (or test entries) must be evaluated with limited experimental material.

In an Augmented RBD layout, candidate test entries are included unreplicated (evaluated once across the entire experiment to maximize screening throughput), while a small set of standard control treatments (checks) are replicated across all experimental blocks.

Core Advantages of Augmented RBD:

Replicated Control Checks: Standard control treatments are repeated across every block to measure field spatial variation and estimate residual experimental error.
Unreplicated Test Entries: Candidate entries are assigned to individual plots without replication, saving material and land area.
Block-Adjusted Means: Raw measurements for candidate test entries are adjusted for local block micro-environment effects using control performance in that specific block.
Comprehensive ANOVA Partitioning: Partitions total SS into Blocks, Control Treatments, Test Entries (Eliminating Blocks), and Contrast (Control vs Test).

2. AVAILABLE OPTIONS & SETTINGS

The sidebar control panel and header toolbar provide full control over entry classification, block mapping, error model, 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 trial spreadsheet and populates variable mapping dropdowns.	At the start of every Augmented RBD analysis session.
Treatment / Entry Variable	Selects the categorical column specifying candidate test entries and control checks.	Identifies unique entries for raw and adjusted mean calculations.	Select categorical column containing entry codes or names.
Entry Type Variable	Selects the column designating entry role: `Control / Check` vs `Test / Candidate`.	Distinguishes replicated controls from unreplicated candidate entries.	Select column containing flags (e.g., Control vs Test).
Block Variable	Selects the column identifying experimental blocks.	Captures spatial soil or environmental gradients across blocks.	Select block identifier column (e.g., Block_1, Block_2).
Target Response Traits	Selects continuous quantitative measurement variables to analyze.	Generates ANOVA tables, block adjustments, adjusted means, and plots.	Select one or multiple quantitative response traits.
Estimation Method	Choose between `OLS (Ordinary Least Squares)` and `REML (Restricted Maximum Likelihood)`.	Determines whether block effects are treated as Fixed or Random effects.	Use OLS for classical ANOVA; choose REML for mixed model estimates.
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 sequential block-first adjustment; use Type III for marginal tests.
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 screening thresholds.
Mean Separation Test	Selects post-hoc test: `LSD`, `Tukey`, `Duncan`, `Dunnett`, or `None`.	Identifies statistically significant pairwise differences among 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 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 tidy relational layout where each row represents an individual plot observation:

Block	Entry_Code	Entry_Type	Yield_Metric	Quality_Score
Block_1	Control_Std_A	Control	65.40	9.20
Block_1	Control_Std_B	Control	58.20	8.50
Block_1	Candidate_101	Test	72.10	9.45
Block_1	Candidate_102	Test	61.80	8.10
Block_2	Control_Std_A	Control	64.10	9.05
Block_2	Control_Std_B	Control	56.90	8.35
Block_2	Candidate_103	Test	68.90	9.10

4. MATHEMATICAL FOUNDATIONS & FORMULAS

Augmented RBD partitions total variation into Block SS, Control Treatment SS, Test Entry SS (Adjusted), Contrast SS (Control vs Test), and Residual Error SS. Below are the plain text formula definitions:

Block SS (SSB)

SSB = Computed using replicated control treatments across blocks.

Isolates spatial soil and micro-environment differences across experimental blocks.

Control Treatment SS (SS_Check)

SS_Check = Variation among replicated standard controls.

Measures baseline variability across replicated benchmark controls.

Adjusted Test Entry Means

Y_adj = Y_raw - (Block_Control_Mean - Grand_Control_Mean)

Adjusts unreplicated candidate test entries for block environmental effects.

Residual Error (SSE)

SSE = Residual error derived from control replication across blocks.

Provides error variance for F-tests and standard errors of difference (SED).

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, and Block.
Select Response Traits: Check one or multiple numeric measurement columns to analyze.
Configure Header Parameters: Set estimation model (OLS/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 Augmented RBD ANOVA Table, Adjusted Test Entry Means, Control vs Test Contrasts, and Diagnostic 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 an Augmented RBD ANOVA Summary Table evaluating 50 unreplicated test entries and 2 replicated controls across 4 blocks:

Source of Variation	Degrees of Freedom (df)	Sum of Squares (SS)	Mean Square (MS)	F-Statistic	p-Value
Blocks (Eliminating Checks)	3	85.400	28.467	6.778	0.0003
Control Checks (Replicated)	1	42.600	42.600	10.143	0.0019
Test Entries (Adjusted)	49	892.500	18.214	4.337	0.0001
Control vs Test Contrast	1	68.300	68.300	16.262	0.0001
Residual Error	3	12.600	4.200	—	—
Total Variation	57	1101.400	—	—	—

How to Read the Output:

Control Checks p-Value: Indicates whether baseline benchmark controls differ significantly from each other.
Test Entries (Adjusted) p-Value: Evaluates significant differences among candidate test entries after removing spatial block effects.
Control vs Test Contrast: Evaluates whether the average performance of new candidate entries exceeds standard benchmark controls.

7. IMPORTANT NOTES & BEST PRACTICES

Replicate Controls in Every Block

Ensure that all control check treatments appear in every experimental block. This guarantees accurate block adjustment for unreplicated test entries.

Four Standard Errors of Difference (SED)

Augmented RBD generates four distinct SED values for comparisons: (1) two controls, (2) two test entries in the same block, (3) two test entries in different blocks, and (4) a test entry vs a control. DATES automatically applies the appropriate SED.