Statistical Inference, Reproducibility, and Open Science
Why Statistics Sits at the Core of Science
Evidence under uncertainty
Scientific data are usually finite, noisy, and incomplete. Statistical inference supplies the rules for updating beliefs or estimates in the presence of sampling error, latent heterogeneity, and measurement noise. At research level, the question is not whether statistics is needed, but which inferential framework is appropriate for the scientific question.
Frequentist and Bayesian inference
Frequentist
- Interprets probability through long-run frequency
- Uses p-values, confidence intervals, and error rates
- Strong in controlled experimental design
Bayesian
- Represents uncertainty through posterior distributions
- Combines prior information with data
- Natural for hierarchical models and decision analysis
Interpretation trap
A p-value is not the probability that the null hypothesis is true.
Which quantity is most directly interpreted as a posterior summary in Bayesian inference?
The posterior distribution is the updated probability distribution over parameters after observing data.
Correct answer: Posterior distribution
Reproducibility and robustness
Reproducibility concerns whether an independent analyst can obtain the same result from the same data and code. Replicability concerns whether the result holds in new data or new experiments. Robust science survives reasonable changes in assumptions, preprocessing, model specification, and measurement noise.
State one reason why a result may fail to replicate even if the original analysis was mathematically correct.
Replicability depends on the stability of the phenomenon and the quality of the design, not only on algebraic correctness.
Correct answer: The original finding may have been a false positive or may depend on a fragile design, hidden confounder, or specific sample.
Open science practices
Frontier topic
Contemporary methodology increasingly uses selective inference, causal discovery, distribution shift analysis, and conformal prediction to provide more honest uncertainty quantification.
A reproducible analysis pipeline
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Step 1: Define the estimand and the target population.
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Step 2: Preprocess data with version-controlled code.
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Step 3: Fit primary and sensitivity models.
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Step 4: Report uncertainty, model checks, and robustness analyses.
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Step 5: Archive code, data provenance, and computational environment.