Advanced Topics, Research Design, and Statistical Practice
From theory to research-grade practice
Model checking and diagnostics
No model is literally true. Advanced practice requires residual analysis, posterior predictive checks, sensitivity analyses, and stress tests against assumption violations.
Why are model diagnostics important?
Diagnostics reveal when the fitted model may be inadequate or misleading.
Correct answer: They help detect assumption violations and poor fit
What is multiple testing and why is it problematic?
If many tests are performed, some appear significant by chance, so procedures like FDR control are needed.
Correct answer: It is the simultaneous testing of many hypotheses, which inflates the chance of false positives unless adjusted.
False discovery rate
The false discovery rate controls the expected proportion of false rejections among all rejected hypotheses. It is especially useful in genomics, imaging, and other large-scale inference problems.
Reproducibility
Reproducible research requires transparent data processing, versioned code, pre-specified analysis plans where possible, and clear reporting of uncertainty and assumptions.
What is the main purpose of FDR control?
FDR methods balance discovery and error control in multiple testing settings.
Correct answer: Control the expected proportion of false discoveries
Name one principle of responsible statistical communication.
Good communication avoids overstating evidence and supports scientific decision-making.
Correct answer: State assumptions, uncertainty, and limitations clearly.
Research-grade statistical workflow
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Step 1: Formulate the scientific question and estimand.
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Step 2: Choose a model or design that matches the data-generating process.
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Step 3: Check identifiability, assumptions, and data quality.
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Step 4: Estimate effects with uncertainty quantification.
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Step 5: Validate with diagnostics, sensitivity checks, or external replication.
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Step 6: Report limitations, assumptions, and reproducible code or analysis details.