General Linear Model (GLM)

The General Linear Model tests the relationship between a continuous dependent variable and one or more categorical factors. It handles ANCOVA-style designs, factorial designs, and crossover bioequivalence studies with full regulatory-grade analysis.

"The General Linear Model tests the relationship between a continuous dependent variable and one or more categorical factors. It includes a dedicated 2×2 crossover bioequivalence analysis mode for comparing test vs. reference formulations with 90% confidence intervals and 80-125% acceptance criteria."

Step 1 — Choose the analysis mode

Mode	What it does
General GLM (default)	Standard GLM analysis with continuous outcome and categorical factors
Crossover Bioequivalence	Specialised mode for crossover bioequivalence trials (2×2 and replicate designs)

Step 2 — Provide data (General GLM mode)

Dependent variable values (continuous outcome)
Factor 1 — categorical grouping variable
Factor type — toggle between Fixed and Random
Add Factor / Remove Factor — for multi-factor designs

A ModelInfo panel shows the variation sources, factor types, levels detected, and F-test denominators.

Step 3 — Provide data (Crossover Bioequivalence mode)

Crossover Design — pick from five designs:

Design	Description
2×2 Standard	2 treatments, 2 periods, 2 sequences (RT/TR)
2×2×4 Full Replicate	2 treatments, 4 periods (RTRT/TRTR)
2×3×3 Partial Replicate	2 treatments, 3 periods (TRR/RTR/RRT)
3×3 Latin Square	3 treatments, 3 periods
4×4 Williams	4 treatments, 4 periods

BE Acceptance Criteria:

Criteria Limits

Standard 80% – 125%

Narrow Therapeutic Index 90% – 111.11%

Wide / Reference-Scaled ABE Scaled limits when CVwR > 30%
Built-in sample datasets — seven scenarios available

Criteria	Limits
Standard	80% – 125%
Narrow Therapeutic Index	90% – 111.11%
Wide / Reference-Scaled ABE	Scaled limits when CVwR > 30%

Step 4 — Run the analysis

Click Run GLM Analysis or Run Bioequivalence Analysis.

Step 5 — Results (General GLM)

Grand mean and total N
ANOVA Summary Table — Source / df / SS / MS / F / p / η² for each factor plus Residual and Total
R² and Adjusted R²
Residual Standard Error
Group means per factor level
Interpretation block — identifies significant factors

Step 6 — Results (Crossover Bioequivalence)

Headline cards:

Card	What it shows
Verdict	"BIOEQUIVALENT" or "NOT BIOEQUIVALENT"
T/R Ratio %	Test-to-Reference geometric mean ratio
90% CI	Two-sided 90% confidence interval
Acceptance Window	Effective limits applied

ANOVA Decomposition Table — Sequence, Subject(Sequence), Period, Treatment, Residual

Additional regulatory outputs:

LSMeans for each treatment with standard errors
Difference between Test and Reference LSMeans
Intra-subject CV%
CVwR% (for replicate designs)
Whether reference-scaled ABE was applied

A UniversalChatBot is available after both result types.

Statistical methods used

General GLM

Variance decomposition (Type I sums of squares):

Component	Formula
Factor SS	`Σ_levels nₗ × (ȳₗ − ȳ)²`
Model SS	`Σ Factor SS`
Residual SS	`Total SS − Model SS`
F-value per factor	`MS_factor / MS_residual`
R²	`Model SS / Total SS`
Adjusted R²	`1 − ((1 − R²) × (n − 1) / (n − Model df − 1))`
η² per factor	`Factor SS / Total SS`

Crossover Bioequivalence

T/R ratio with 90% CI (log-scale)

log_diff     = ln(ȳ_T) − ln(ȳ_R)
ratio %      = (ȳ_T / ȳ_R) × 100
90% CI       = exp(log_diff ± t_critical × log_SE) × 100

Decision rule: BIOEQUIVALENT if CI_lower ≥ acceptance_lower AND CI_upper ≤ acceptance_upper

Reference-Scaled ABE (when CVwR > 30%)

σ_WR         = √(ln(1 + (CVwR/100)²))
scaled_limit = exp(0.8930 × σ_WR)

Limits are widened but never tighter than the standard 80%–125%.

Carryover warning: Appended automatically if sequence effect p < 0.05.