Completely Randomized Design (CRD) User Guide

1. INTRODUCTION

The Completely Randomized Design (CRD) module in DATES performs Analysis of Variance (ANOVA) for experiments where treatments are assigned completely at random across homogenous experimental units. In a CRD, there are no environmental blocking restrictions (unlike RCBD or Latin Square designs).

Supported CRD Experimental Variations:

1-Factor CRD (1-F): Evaluates the effect of a single independent factor across multiple treatment levels on numeric response traits.
2-Factor Factorial CRD (2-F): Analyzes main effects of Factor A, Factor B, and their two-way interaction (Factor A x Factor B).
3-Factor Factorial CRD (3-F): Analyzes main effects, three two-way interactions, and the three-way interaction (Factor A x Factor B x Factor C).
Nested CRD (Hierarchical Design): Analyzes designs where levels of a sub-factor are nested uniquely within levels of a major factor (e.g., Sub-treatments within Primary Groups).

Model Estimation Frameworks:

Ordinary Least Squares (OLS): Traditional fixed-effects ANOVA model estimating mean squares and standard F-tests.
Mixed Models (REML / Mixed): Fits models containing combinations of Fixed and Random effects with custom variance component estimations.

2. AVAILABLE OPTIONS & SETTINGS

The sidebar control panel and header toolbar provide comprehensive settings for model structure, mean comparisons, error types, and transformations:

Control / Parameter	Description	Why it is used	When to select / set
Upload Data	Uploads your `.csv`, `.xlsx`, or `.xls` spreadsheet file into memory.	Loads raw experimental trial data and populates factor/trait mapping options.	At the start of every CRD analysis session.
Estimation Method	Toggles model framework: `OLS` (Ordinary Least Squares) or `Mixed` (Mixed Effects).	Determines whether fixed or random effect models and REML variance components are computed.	Select OLS for fixed-effects designs; choose Mixed when assigning random factor components.
Design Structure	Selects design mode: `1-F` (One Factor), `2-F` (Two Factors), `3-F` (Three Factors), or `Nest` (Nested Factor).	Sets the factor breakdown and interaction terms in the ANOVA table.	Match to your actual experimental factor arrangement.
Factor A / B / C Selection	Maps categorical dataset columns to primary, secondary, and tertiary experimental factors.	Identifies experimental treatment conditions for grouping and variance partitioning.	Select all relevant factor columns for your chosen design mode.
Replication Column	Selects the replication/block descriptor column.	Tracks individual experimental unit replicates per treatment.	Map column containing replicate numbers (e.g., Rep 1, Rep 2).
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 for unbalanced data. Automatically selects optimal type if set to Auto.	Use Type I for balanced data; use Type II or Type III for unbalanced designs.
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 when the main ANOVA F-test is significant.	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 experimental unit or plot:

Replicate	Factor_A	Factor_B	Yield_Metric	Quality_Score
Rep_1	Level_1	Variant_A	45.80	8.50
Rep_2	Level_1	Variant_A	48.20	8.75
Rep_3	Level_1	Variant_A	44.10	8.20
Rep_1	Level_2	Variant_A	52.30	9.10
Rep_2	Level_2	Variant_A	54.10	9.30
Rep_3	Level_2	Variant_A	51.90	8.95

4. MATHEMATICAL FOUNDATIONS & FORMULAS

The Completely Randomized Design partitions total variation in response measurements into variation caused by treatment factors and random experimental error. Below are the plain text formula definitions:

Total Sum of Squares (SST)

Formula Description:

SST = Sum of squared deviations of each observation from the grand mean across all units.

Total Degrees of Freedom: df_Total = Total Observations - 1

Treatment Sum of Squares (SSA)

Formula Description:

SSA = Sum of (Replicates per Treatment * (Treatment Mean - Grand Mean)^2) across all levels.

Treatment Degrees of Freedom: df_FactorA = Number of Factor A Levels - 1

Error Sum of Squares (SSE)

Formula Description:

SSE = SST - Sum of all treatment and interaction Sums of Squares.

Error Degrees of Freedom: df_Error = Total Observations - Total Treatment Combinations

F-Statistic & Mean Squares

Mean Square Treatment (MSA): MSA = SSA / df_FactorA

Mean Square Error (MSE): MSE = SSE / df_Error

Calculated F Ratio: F = MSA / MSE

5. STEP-BY-STEP WORKFLOW

Upload Dataset: Click the Upload Spreadsheet panel in the sidebar to upload your .csv or .xlsx file.
Select Worksheet: If using a multi-tab workbook, choose the target worksheet tab.
Select Estimation & Design Mode: Choose OLS or Mixed, then select design mode (1-F, 2-F, 3-F, or Nest).
Map Columns: Map dataset columns to Factor A (and B/C if applicable), Replication Variable, and check desired Numeric Traits.
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 ANOVA Table, Treatment Means, Post-hoc Letter Groupings, and Diagnostic Plots (Residual Plots, Q-Q Plots, Box 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 ANOVA Summary Table generated for a 2-Factor CRD experiment:

Source of Variation	Degrees of Freedom (df)	Sum of Squares (SS)	Mean Square (MS)	F-Statistic	p-Value	Significance
Factor A	2	154.200	77.100	18.450	0.0001	** (Highly Significant)
Factor B	3	88.600	29.533	7.065	0.0024	** (Significant)
Factor A x Factor B	6	42.100	7.017	1.678	0.1780	ns (Not Significant)
Experimental Error	24	100.340	4.181	—	—	—
Total Variation	35	385.240	—	—	—	—

How to Read the Output:

p-Value < Alpha (e.g., p < 0.05): Statistical evidence of significant differences among treatment factor means. Reject the null hypothesis.
p-Value ≥ Alpha (e.g., p ≥ 0.05): No statistically significant difference detected among factor levels.
Interaction Effect (Factor A x Factor B): A significant interaction indicates that the effect of Factor A depends on the level of Factor B, requiring simple main effect post-hoc breakdowns.
Coefficient of Variation (CV %): Reflects experimental precision. Lower CV values (typically < 15%) indicate high trial precision and controlled experimental error.

7. IMPORTANT NOTES & BEST PRACTICES

Homogeneity of Experimental Units

CRD is highly effective when experimental conditions (growth chambers, laboratory environments, homogeneous animal pens) are completely uniform. If environmental gradients exist across your trial area, use Randomized Block Design (RBD) instead.

Handling Unbalanced Replications

If some experimental plots or observations are missing (unbalanced CRD), ensure you select Type II or Type III Sum of Squares in the top toolbar to avoid sequential ordering bias in SS Type I.

Cite DATES in Research Papers

If you use the DATES CRD module for experimental data 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 — Completely Randomized Design (CRD) Module} }