🧪 Experimental Design & Analysis
Comprehensive module for academic researchers — 10 experimental designs with full ANOVA tables, post-hoc tests, effect sizes, APA output, and R verification.
DESIGN SELECTION GUIDE
| Design | When to Use | Controls | Key Output |
|---|---|---|---|
| CRD One-Way ANOVA | Homogeneous units, single factor with k levels | — | F-test, Tukey HSD, η², ω² |
| RCBD Block Design | One nuisance variable (e.g. batch, location, day) | 1 blocking factor | Treatment F, Block F, RE vs CRD |
| Latin Square | Two nuisance variables (e.g. row × column) | 2 blocking factors | Treatment F, row/col F |
| Factorial Two-Way ANOVA | Two (or three) factors; study interactions | — | Main effects, interaction, plots |
| Split-Plot | Hard-to-change factor (whole-plot) + easy factor (subplot) | Blocks | Separate F-tests for WP & SP |
| ANCOVA | Control a continuous covariate (pre-test score, age…) | Covariate | Adjusted means, slopes test |
| Repeated Measures | Same subjects measured at multiple time points | Subjects | Mauchly's W, GG/HF correction |
| Crossover (AB/BA) | Subjects receive all treatments in sequence; clinical trials | Period, carryover | Treatment, period, carryover tests |
| Nested/Hierarchical | Factor B levels differ within each level of factor A | — | Variance components, EMS |
| RSM / CCD | Optimize process; find best factor settings | — | Response surface equation, optimum |
FEATURES
📊 Full ANOVA Tables
All SS, df, MS, F, p-values per source
All SS, df, MS, F, p-values per source
🔬 Post-Hoc Tests
Tukey HSD, Bonferroni, LSD, Scheffé, Duncan
Tukey HSD, Bonferroni, LSD, Scheffé, Duncan
📐 Effect Sizes
η², partial η², ω², Cohen's f
η², partial η², ω², Cohen's f
✅ Assumption Tests
Levene's test, Mauchly's sphericity, normality
Levene's test, Mauchly's sphericity, normality
🤖 AI Interpretation
Plain-language results summary
Plain-language results summary
📝 APA Format
Publication-ready results paragraph
Publication-ready results paragraph
🔁 R Verification
Cross-check via WebR — real R 4.5.1
Cross-check via WebR — real R 4.5.1
📈 Interaction Plots
Visualize factorial interactions & profiles
Visualize factorial interactions & profiles
📁 Demo Data
One-click realistic datasets for each design
One-click realistic datasets for each design
🔵 CRD — Completely Randomized Design
One-Way ANOVA: k treatments, experimental units randomly assigned to treatments. Use when units are homogeneous and no blocking is needed.
DATA & OPTIONS
📋Data format: CSV with one column per treatment group. First row = group names. Each row = one observation per group (unequal sizes: leave blank cells).
Example:
Example:
Control,Drug_A,Drug_B
Editable Data Grid — CRD
💡 Click "Apply to CSV" to transfer grid data to the text area below, then click Run Analysis.
🤖 AI Interpretation
🟦 RCBD — Randomized Complete Block Design
Two-way ANOVA without interaction: partition block variation to increase precision. Each block contains every treatment exactly once.
DATA & OPTIONS
📋Data format: 3 columns —
Treatment, Block, Response. Each treatment must appear exactly once per block.
Editable Data Grid — RCBD
💡 Columns: Treatment, Block, Response. Click "Apply to CSV" when done.
🤖 AI Interpretation
🟧 Latin Square Design
Controls two nuisance factors (rows and columns) simultaneously. Requires n treatments, n rows, and n columns (n×n layout).
DATA & OPTIONS
📋Data format: 4 columns —
Row, Col, Trt, Response. Exactly one observation per (row, col) cell.
Editable Data Grid — Latin Square
💡 Columns: Row, Col, Trt, Response. Click "Apply to CSV" when done.
🤖 AI Interpretation
🟩 Factorial Design (Two-Way ANOVA)
Study main effects and interactions of two (or three) factors simultaneously. Supports balanced and unbalanced designs.
DATA & OPTIONS
📋Data format: CSV columns —
FactorA, FactorB, Response. Each row is one observation. Multiple rows per combination = replicates.
Editable Data Grid — Factorial
💡 Columns: FactorA, FactorB, Response (add FactorC for 3-way). Click "Apply to CSV" when done.
🤖 AI Interpretation
🔷 Split-Plot Design
Factor A applied to whole plots (blocks), Factor B applied to subplots within each whole plot. Uses two separate error terms.
DATA & OPTIONS
📋Data format: 4 columns —
Block, WholePlotA, SubplotB, Response. Each block contains all combinations of A and B.
Editable Data Grid — Split-Plot
💡 Columns: Block, WholePlotA, SubplotB, Response. Click "Apply to CSV" when done.
🤖 AI Interpretation
📊 ANCOVA — Analysis of Covariance
Adjusts group means for a continuous covariate (pre-test score, age, weight…). Increases power and removes covariate bias. Assumes homogeneity of regression slopes.
DATA & OPTIONS
📋Data format: 3 columns —
Group, Covariate, Response. Covariate is measured before treatment (e.g. pre-test score, baseline).
Editable Data Grid — ANCOVA
💡 Columns: Group, Covariate, Response. Click "Apply to CSV" when done.
🤖 AI Interpretation
🔄 Repeated Measures ANOVA
Within-subjects design: same participants measured across time points or conditions. Mauchly's sphericity test with Greenhouse-Geisser and Huynh-Feldt corrections.
DATA & OPTIONS
📋Data format (wide): First column = Subject ID, remaining columns = measurement at each time point. Column names become condition/time labels.
Editable Data Grid — Repeated Measures (wide format)
💡 Row 1 = header (Subject, T1, T2, …). Each subsequent row = one subject. Click "Apply to CSV" when done.
🤖 AI Interpretation
🔀 Crossover Design (AB/BA)
2×2 crossover trial: subjects receive both treatments in different sequences. Tests treatment, period, and carryover effects (Grizzle 1965).
DATA & OPTIONS
📋Data format: 5 columns —
Subject, Sequence, Period, Treatment, Response. Sequence must be AB or BA. Period must be 1 or 2.
Editable Data Grid — Crossover
💡 Columns: Subject, Sequence (AB/BA), Period (1/2), Treatment, Response. Click "Apply to CSV" when done.
🤖 AI Interpretation
🏗️ Nested (Hierarchical) Design
Factor B is nested within Factor A — B levels are not the same across A levels (e.g. technicians within labs, students within classes). Estimates variance components.
DATA & OPTIONS
📋Data format: 3 columns —
FactorA, FactorB, Response. Factor B labels are unique within each level of A (e.g. Lab1-Tech1, Lab1-Tech2, Lab2-Tech1 are different technicians).
Editable Data Grid — Nested Design
💡 Columns: FactorA, FactorB (nested in A), Response. Click "Apply to CSV" when done.
🤖 AI Interpretation
🎯 Response Surface Methodology (CCD)
Fit a second-order polynomial model to find optimal factor settings. Supports 2-factor Central Composite Design. Reports ANOVA for regression, lack-of-fit, and stationary point.
DATA & OPTIONS
📋Data format: 3 columns —
x1, x2, Response. Use coded values (−α, −1, 0, +1, +α) where α = 1.414 for rotatability (2-factor CCD). Include center point replicates.
Editable Data Grid — RSM / CCD
💡 Columns: x1, x2, Response (coded values: −1.414, −1, 0, +1, +1.414). Click "Apply to CSV" when done.
🤖 AI Interpretation