MindStat DOE — Experimental Design & Analysis

🧪 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

🔬 Post-Hoc Tests
Tukey HSD, Bonferroni, LSD, Scheffé, Duncan

📐 Effect Sizes
η², partial η², ω², Cohen's f

✅ Assumption Tests
Levene's test, Mauchly's sphericity, normality

🤖 AI Interpretation
Plain-language results summary

📝 APA Format
Publication-ready results paragraph

🔁 R Verification
Cross-check via WebR — real R 4.5.1

📈 Interaction Plots
Visualize factorial interactions & profiles

📁 Demo Data
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

Significance α

Post-Hoc Method

📋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: Control,Drug_A,Drug_B

📥 Data

Editable Data Grid — CRD

💡 Click "Apply to CSV" to transfer grid data to the text area below, then click Run Analysis.

Data — CSV (paste or import above)

🤖 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

Significance α

Post-Hoc (Treatments)

📋Data format: 3 columns — Treatment, Block, Response. Each treatment must appear exactly once per block.

📥 Data

Editable Data Grid — RCBD

💡 Columns: Treatment, Block, Response. Click "Apply to CSV" when done.

Data — CSV (Treatment, Block, Response)

🤖 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

Significance α

Post-Hoc (Treatments)

📋Data format: 4 columns — Row, Col, Trt, Response. Exactly one observation per (row, col) cell.

📥 Data

Editable Data Grid — Latin Square

💡 Columns: Row, Col, Trt, Response. Click "Apply to CSV" when done.

Data — CSV (Row, Col, Trt, Response)

🤖 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

Significance α

Number of Factors

Post-Hoc (Main Effects)

📋Data format: CSV columns — FactorA, FactorB, Response. Each row is one observation. Multiple rows per combination = replicates.

📥 Data

Editable Data Grid — Factorial

💡 Columns: FactorA, FactorB, Response (add FactorC for 3-way). Click "Apply to CSV" when done.

Data — CSV (FactorA, FactorB, Response)

🤖 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

Significance α

📋Data format: 4 columns — Block, WholePlotA, SubplotB, Response. Each block contains all combinations of A and B.

📥 Data

Editable Data Grid — Split-Plot

💡 Columns: Block, WholePlotA, SubplotB, Response. Click "Apply to CSV" when done.

Data — CSV (Block, WholePlotA, SubplotB, Response)

🤖 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

Significance α

Post-Hoc (Adjusted Means)

📋Data format: 3 columns — Group, Covariate, Response. Covariate is measured before treatment (e.g. pre-test score, baseline).

📥 Data

Editable Data Grid — ANCOVA

💡 Columns: Group, Covariate, Response. Click "Apply to CSV" when done.

Data — CSV (Group, Covariate, Response)

🤖 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

Significance α

Post-Hoc (Bonferroni pairwise)

📋Data format (wide): First column = Subject ID, remaining columns = measurement at each time point. Column names become condition/time labels.

📥 Data

Editable Data Grid — Repeated Measures (wide format)

💡 Row 1 = header (Subject, T1, T2, …). Each subsequent row = one subject. Click "Apply to CSV" when done.

Data — CSV (Subject, Time1, Time2, Time3…)

🤖 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

Significance α

📋Data format: 5 columns — Subject, Sequence, Period, Treatment, Response. Sequence must be AB or BA. Period must be 1 or 2.

📥 Data

Editable Data Grid — Crossover

💡 Columns: Subject, Sequence (AB/BA), Period (1/2), Treatment, Response. Click "Apply to CSV" when done.

Data — CSV (Subject, Sequence, Period, Treatment, Response)

🤖 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

Significance α

Factor A (Fixed or Random)

📋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).

📥 Data

Editable Data Grid — Nested Design

💡 Columns: FactorA, FactorB (nested in A), Response. Click "Apply to CSV" when done.

Data — CSV (FactorA, FactorB, Response)

🤖 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

Significance α

Factor X1 Name

Factor X2 Name

📋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.

📥 Data

Editable Data Grid — RSM / CCD

💡 Columns: x1, x2, Response (coded values: −1.414, −1, 0, +1, +1.414). Click "Apply to CSV" when done.

Data — CSV (x1, x2, Response) — coded values

🤖 AI Interpretation