Pooled Completely Randomized Design (Pooled CRD) User Guide

1. INTRODUCTION

The Pooled Completely Randomized Design (Pooled CRD / Pool-CRD) module in DATES combines data from homogeneous Completely Randomized Experiments conducted across multiple environments, locations, or time periods into a unified multi-environment Analysis of Variance.

In individual CRD trials, experimental units are assigned to treatments completely at random without blocking. The Pooled CRD module aggregates these multi-location trials to test both overall treatment main effects and the consistency of treatment responses across environments (Treatment x Environment Interaction).

Core Features of Pooled CRD ANOVA:

Multi-Environment Combination: Pools data across trial sites, years, or environmental conditions.
1-Factor & 2-Factor Factorials: Supports 1-Factor treatment pooling as well as 2-Factor factorial cross-classifications.
Treatment x Environment Interaction: Evaluates whether treatment superiority remains stable or shifts across test environments.
Homogeneity of Variance Pre-Test: Assesses residual error variance equality across location trials prior to pooling.

2. AVAILABLE OPTIONS & SETTINGS

The sidebar control panel and header toolbar provide complete control over factor assignments, fixed/random effect models, post-hoc methods, 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 multi-environment trial dataset into memory.	At the start of every Pooled CRD session.
Analysis Type	Choose between `1-Factor Pooled CRD` and `2-Factor Pooled CRD`.	Sets single-factor or two-factor factorial multi-site structure.	Select 1-Factor for single treatment evaluation; choose 2-Factor for dual factorials.
Factor A Variable	Selects the primary treatment factor column.	Computes main treatment effect SS and means.	Select primary treatment factor (e.g., Treatment_Factor).
Factor B Variable	Selects secondary factor column (for 2-Factor designs).	Computes Factor B main effect and Factor A x B interaction.	Select secondary factor column when 2-Factor analysis is active.
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).
Target Response Traits	Selects continuous quantitative measurement variables to analyze.	Generates pooled ANOVA, location-specific means, interaction tables, and plots.	Select one or multiple quantitative response traits.
Estimation Method	Choose between `OLS (Ordinary Least Squares)` and `REML (Restricted Maximum Likelihood)`.	Determines whether environment and factor effects are Fixed or Random.	Use OLS for fixed model designs; select REML for random environmental variance components.
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 treatment 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 plot observation:

Environment	Treatment_Factor	Replicate	Yield_Metric	Quality_Score
Site_Alpha	Treatment_A	1	48.50	8.60
Site_Alpha	Treatment_A	2	50.20	8.80
Site_Alpha	Treatment_B	1	42.10	8.10
Site_Alpha	Treatment_B	2	44.30	8.30
Site_Beta	Treatment_A	1	54.20	9.10
Site_Beta	Treatment_A	2	52.90	8.95

4. MATHEMATICAL FOUNDATIONS & FORMULAS

Pooled CRD partitions total multi-environment variation into Environment SS, Treatment SS, Treatment x Environment Interaction SS, and Pooled Residual Error 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.

Treatment SS (SSTr)

SSTr = Sum of squared deviations for main treatment levels.

Evaluates overall treatment superiority averaged across all environments.

Treatment x Environment Interaction SS (SSTrxE)

SSTrxE = Treatment x Environment interaction SS.

Evaluates whether treatment response patterns change across location environments.

Pooled Residual Error SS (SSE_pooled)

SSE_pooled = Sum of individual location residual errors.

Combines within-site plot error across trials to form denominator MS for F-tests.

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 Factor A, Environment / Pooling Factor, and Replicate (if applicable).
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 Pooled CRD ANOVA Table, Bartlett Homogeneity Test, Treatment x Environment Interaction, 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 Pooled CRD ANOVA Summary Table evaluating 5 treatments across 3 testing locations:

Source of Variation	Degrees of Freedom (df)	Sum of Squares (SS)	Mean Square (MS)	F-Statistic	p-Value
Environment (Location)	2	185.400	92.700	26.486	0.0001
Treatment (Factor A)	4	246.800	61.700	17.629	0.0001
Treatment x Environment Interaction	8	48.200	6.025	1.721	0.1184
Pooled Residual Error	45	157.500	3.500	—	—
Total Variation	59	637.900	—	—	—

How to Read the Output:

Environment p-Value: Indicates whether location test sites differ significantly in overall performance levels.
Treatment p-Value: Evaluates overall treatment superiority averaged across all location environments.
Treatment x Environment p-Value: A non-significant interaction (p > 0.05) indicates consistent treatment ranking across all test environments.

7. IMPORTANT NOTES & BEST PRACTICES

Verify Homogeneity of Variance

Before interpreting pooled ANOVA results, check Bartlett's test for homogeneity of error variances across sites. If error variances differ significantly, apply a data transformation.

Fixed vs Random Environment Models

If environments are chosen at random to represent a broader geographic region, set Environment to Random so that the Treatment MS is tested against the Interaction MS instead of Pooled Error.