biostatistics-workbench

name	biostatistics-workbench
description	Runs frequentist statistical analyses including GLMs, GLMMs, model selection, and assumption diagnostics for ecological data. Use this skill when the user needs statistical tests, linear or mixed models, ANOVA, effect sizes, confidence intervals, AIC-based model selection, residual diagnostics, overdispersion checks, regression analysis, p-value interpretation, normality tests, or hypothesis testing on ecological datasets.
skill_version	1.0.0

Skill: biostatistics-workbench

Domain: Hypothesis testing · GLM/GLMM · Assumptions · Effect sizes · CIs
Phase: 1 — Foundation
Used by: assess-ecological-impact, analyze-community-structure, run-occupancy-analysis, assess-ecosystem-services

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Purpose

Guides the agent through the selection, execution, and interpretation of statistical methods appropriate for ecological data. Covers classical tests, generalised linear models, mixed models, assumption diagnostics, effect size estimation, and model selection.

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When to Invoke

• Choosing a statistical test for a specific research question and data structure
• Fitting GLM or GLMM with ecological response variables
• Checking distributional assumptions (normality, homoscedasticity, independence)
• Reporting effect sizes and confidence intervals
• Performing model selection (AIC, LRT, cross-validation)

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Inputs

Input	Format	Required
Response variable(s)	Numeric or count vector	Yes
Predictor variable(s)	Numeric, categorical, or both	Yes
Random effects structure (if any)	Description or formula	Conditional
Study design description	Text	Recommended

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Outputs

Output	Description
model_summary.txt	Full model output (coefficients, SE, z/t, p)
model_selection_table.csv	AIC/BIC/ΔAIC comparison across candidate models
assumption_diagnostics/	Residual plots, QQ plots, variance inflation factors
effect_sizes.csv	Effect size estimates with 95% CIs
stats_report.md	Plain-language interpretation of results

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Steps

1. Define the Research Question and Data Structure

• Clarify the response variable type: continuous, count, binary, proportion, ordinal
• Clarify the predictor types: fixed categorical, fixed continuous, random grouping
• Identify the sampling design: independent, nested, repeated measures, spatial

2. Select the Appropriate Method

Response	Distribution	Recommended model
Continuous, normal	Gaussian	LM / LMM
Continuous, non-normal	Log-normal, Gamma	GLM Gamma / LM on log
Count, no excess zeros	Poisson	GLM Poisson
Count, overdispersed	Negative binomial	GLM NB
Count, zero-inflated	ZIP / ZINB	Zero-inflated model
Binary (0/1)	Binomial	GLM logistic
Proportion (0–1)	Beta	Beta regression
Ordinal	Ordered	Proportional odds model

3. Check Assumptions Before Fitting

• Collinearity: compute VIF for all predictors (flag VIF > 5; critical > 10)
• Sample size adequacy: events-per-variable rule (EPV ≥ 10 for logistic)
• Independence: confirm no pseudoreplication; identify random effects structure

4. Fit Model(s)

• Fit the global model first
• Fit a set of candidate models based on a priori hypotheses
• Avoid purely data-driven stepwise selection; document candidate model rationale

5. Check Assumptions After Fitting

• Residual plots (Pearson, deviance, randomised quantile residuals for GLMs)
• QQ plot of residuals
• Residuals vs fitted values
• Scale-location plot for heteroscedasticity
• Cook's distance for influential observations

6. Model Selection

• Compute AIC/AICc/BIC for all candidate models
• Report ΔAIC and Akaike weights
• Use LRT for nested model comparison
• Avoid selecting models based on p-value alone

7. Report Effect Sizes and CIs

• Report standardised coefficients (βstd) for comparability
• Report 95% CI for all estimates (profile likelihood preferred over Wald for GLMs)
• Report R²m and R²c for LMMs (marginal and conditional)

8. Generate Outputs

• Write model summary to model_summary.txt
• Write model selection table to model_selection_table.csv
• Save all diagnostic plots to assumption_diagnostics/
• Write stats_report.md with plain-language interpretation

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Decision Points

• Response variable distribution and link function
• Random effects structure and rationale
• Candidate model set and justification
• Model selection criterion used
• Effect size metric chosen

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Tools and Libraries

R: lme4, glmmTMB, MuMIn, DHARMa, emmeans, performance, effectsize
Python: statsmodels, pymer4, pingouin, scipy.stats

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Resources

• resources/test-selection-guide.md — flowchart for test selection
• resources/glm-family-link-reference.md — GLM family and link function guide
• resources/effect-size-reference.md — which effect size to report per test
• examples/ — worked GLM and GLMM examples

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Notes

• Never report p-values without effect sizes
• Multiple comparisons: apply Bonferroni or FDR correction when testing many hypotheses
• Overdispersion in Poisson models must always be checked (dispersion parameter)