what should I use for statistically rigorous experiment analysis

For statistically rigorous experiment analysis, a good default stack depends on your data type and study design, but in general you want tools that give you:

• reproducibility
• good statistical modeling
• clear assumptions and diagnostics
• versioned analysis workflows

Strong default choices

1. R

Best overall choice for classical statistics and experimental analysis.

Use it for:

• t-tests, ANOVA, regression
• mixed-effects models
• survival analysis
• causal inference basics
• power analysis
• Bayesian analysis via packages

Helpful packages:

• tidyverse for data handling
• ggplot2 for visualization
• lme4 or nlme for mixed models
• emmeans for post-hoc comparisons
• car for diagnostics
• broom for tidy outputs
• pwr for power calculations
• brms or rstanarm for Bayesian models

2. Python

Great if your workflow already lives in Python or you need integration with ML / engineering systems.

Use it for:

• regression and hypothesis testing
• simulation and bootstrapping
• experiment pipelines
• causal analysis
• Bayesian modeling

Helpful packages:

• pandas, numpy
• scipy.stats
• statsmodels
• pingouin for easier stats workflows
• matplotlib, seaborn, plotnine
• pymc for Bayesian inference
• scikit-learn for predictive modeling

3. Stan / PyMC / brms

If you need rigorous probabilistic modeling, especially when:

• sample sizes are small
• hierarchical structure matters
• you need partial pooling
• uncertainty quantification is central

These are especially strong for:

• multilevel experiments
• complex random effects
• Bayesian A/B testing
• irregular missingness
• measurement error

4. Jupyter / Quarto / R Markdown

For reproducibility and documentation, use:

• Quarto if you want one system for R, Python, and reports
• R Markdown if mostly in R
• Jupyter notebooks if mainly Python, but be careful about reproducibility

What matters more than the language

A statistically rigorous analysis usually means:

• pre-specifying hypotheses
• defining primary endpoints
• avoiding p-hacking
• correcting for multiple comparisons
• checking assumptions
• reporting effect sizes and confidence intervals
• using power/sample size planning
• validating robustness with sensitivity analyses
• separating exploratory from confirmatory analysis

Practical recommendation

If you want one answer:

• Use R + Quarto for the most statistically rigorous and publication-friendly workflow.
• Use Python + statsmodels/PyMC if you are already in a Python ecosystem.
• Use Bayesian tools like brms or PyMC if your experiment is complex or uncertainty matters a lot.

If you want, I can also recommend the best tools based on your exact experiment type, like:

• A/B testing
• lab experiments
• clinical studies
• manufacturing/quality experiments
• social science experiments