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Browse all available quizzes, quizbooks, articles, textbooks, SynLearn templates, and SynPrep practice tracks.

1890 learning items

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Quiz

Principles of Experimental Design & Family-Wise Error

Plan interpretable experiments with randomization, independent replication and local control. Prerequisites: hypothesis testing and basic probability. Identify experimental units, distinguish subsamples from treatment replication, quantify multiple-testing risks, and align planned contrasts with transparent error-control families. Includes single-select and multiselect questions, worked solutions and content-based distractor feedback. References: [NIST: Randomized Blocks](https://www.itl.nist.gov/div898/handbook/pri/section3/pri332.htm), [NIST: Multiple-comparison Control](https://www.itl.nist.gov/div898/handbook/prc/section4/prc473.htm). Cover: Photo by Polina Tankilevitch on Pexels.

statistics

Oct 26, 2026

20 questions

Quiz

Leakage, Nested Validation & Calibration

Build prediction assessments that match deployment information. Prerequisites: cross-validation, regression losses and elementary probability. Audit preprocessing and feature selection, separate nested tuning from testing, choose patient/site/time splits, compare MAE and RMSE, and distinguish probability calibration from ranking. Includes single-select and multiselect questions, worked solutions and content-based distractor feedback. References: [scikit-learn: Leakage](https://scikit-learn.org/stable/common_pitfalls.html), [scikit-learn: Nested Validation](https://scikit-learn.org/stable/auto_examples/model_selection/plot_nested_cross_validation_iris.html), [scikit-learn: Cross-validation](https://scikit-learn.org/stable/modules/cross_validation.html), [scikit-learn: Probability Calibration](https://scikit-learn.org/stable/modules/calibration.html). Cover: Photo by ThisIsEngineering on Pexels.

statistics

Oct 26, 2026

20 questions

Quiz

Cross-Validation & Out-of-Sample Performance

Evaluate predictions beyond the fitting sample with validation splits, K-fold and leave-one-out cross-validation. Prerequisites: regression and squared-error summaries. Calculate observation-weighted CV error, compare paired procedures, assess training-size effects and split uncertainty, and plan a final development-data refit. Includes single-select and multiselect questions, worked solutions and content-based distractor feedback. References: [scikit-learn: Cross-validation](https://scikit-learn.org/stable/modules/cross_validation.html). Cover: Photo by ThisIsEngineering on Pexels.

statistics

Oct 26, 2026

25 questions

Quiz

Transformations & Polynomial Regression

Choose and interpret regression transformations while preserving the scientific target. Prerequisites: regression, logarithms and elementary differentiation. Work with log-linear, linear-log and log-log models, square-root and reciprocal scales, Box-Cox powers and polynomial hierarchy. Analyze exact changes, retransformation and extrapolation. Includes single-select and multiselect questions, worked solutions and content-based distractor feedback. References: [Penn State: Data Transformations](https://online.stat.psu.edu/stat501/Lesson09), [SciPy: Box-Cox](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.boxcox.html). Cover: Photo by ThisIsEngineering on Pexels.

statistics

Oct 26, 2026

25 questions

Quiz

Outliers, Leverage Points & Cook's Distance

Assess influential regression observations in delivery, retail and laboratory settings. Prerequisites: multiple regression, residuals and error variance. Compute leverage screens, deleted residuals, Cook distance, DFFITS and DFBETAS. Investigate masking, rank loss and practical sensitivity without treating diagnostic cutoffs as deletion rules. Includes single-select and multiselect questions, worked solutions and content-based distractor feedback. References: [Penn State: Influential Points](https://online.stat.psu.edu/stat501/Lesson11), [statsmodels: OLS Influence](https://www.statsmodels.org/stable/generated/statsmodels.stats.outliers_influence.OLSInfluence.html). Cover: Photo by ThisIsEngineering on Pexels.

statistics

Oct 26, 2026

30 questions

Quiz

Multicollinearity: Diagnosis & Consequences

Investigate multicollinearity through factory sensors, building costs and correlated scales. Prerequisites: multiple regression, matrix rank and coefficient variance. Calculate VIF, tolerance and condition indices; distinguish separate slopes from identifiable combinations; evaluate data collection, reparameterization, shrinkage and predictive support. Includes single-select and multiselect questions, worked solutions and content-based distractor feedback. References: [Penn State: Multicollinearity](https://online.stat.psu.edu/stat501/Lesson12), [Statistics Canada: Collinearity Diagnostics](https://www150.statcan.gc.ca/n1/pub/12-001-x/2012002/article/11757-eng.pdf). Cover: Photo by ThisIsEngineering on Pexels.

statistics

Oct 26, 2026

25 questions

Quiz

Stratification, Clusters & Design Effects

Design and analyze stratified and clustered samples. Combine stratum estimates, allocate sample sizes, calculate design effects and effective sample sizes, and diagnose why an iid analysis can overstate the information in clustered observations. Practice progresses from concepts through worked applications to assumption checks and synthesis. Prerequisites: probability, sampling distributions and the preceding resampling curriculum. Includes single-select and multiselect practice with worked solutions and distractor analysis.

statistics

Oct 26, 2026

20 questions

Quiz

Sampling Weights & Finite Population Inference

Estimate finite-population totals and means with unequal-probability samples. Interpret inclusion probabilities, Horvitz-Thompson weights, ratio means and finite-population corrections while separating sampling weights from measurement precision. Practice progresses from concepts through worked applications to assumption checks and synthesis. Prerequisites: probability, sampling distributions and the preceding resampling curriculum. Includes single-select and multiselect practice with worked solutions and distractor analysis.

statistics

Oct 26, 2026

20 questions

Quiz

Numerical Optimization, Integration & EM

Practice numerical tools behind statistical fitting: likelihood and log-likelihood, stable log-sum-exp, root finding, quadrature and expectation maximization. Use small calculations to diagnose convergence, local solutions and mixture-model instability. Practice progresses from concepts through worked applications to assumption checks and synthesis. Prerequisites: probability, sampling distributions and the preceding resampling curriculum. Includes single-select and multiselect practice with worked solutions and distractor analysis.

statistics

Oct 26, 2026

20 questions

Quiz

Monte Carlo Error & Variance Reduction

Estimate simulation precision and improve computational efficiency with importance sampling, antithetic pairs and control variates. Distinguish finite simulation noise from uncertainty in the observed study and assess conditions that make variance reduction trustworthy. Practice progresses from concepts through worked applications to assumption checks and synthesis. Prerequisites: probability, sampling distributions and the preceding resampling curriculum. Includes single-select and multiselect practice with worked solutions and distractor analysis.

statistics

Oct 26, 2026

20 questions

Quiz

Two-Sample & Paired Permutation Tests

Apply permutation tests to independent groups, matched pairs and association studies. Choose mean, median or trimmed-mean statistics, calculate small reference distributions and distinguish legitimate rearrangements from invalid iid shuffles. Practice progresses from concepts through worked applications to assumption checks and synthesis. Prerequisites: probability, sampling distributions and the preceding resampling curriculum. Includes single-select and multiselect practice with worked solutions and distractor analysis.

statistics

Oct 26, 2026

25 questions

Quiz

Permutation Test Theory & Exact Null Distributions

Build exact and Monte Carlo permutation reference distributions. Work with exchangeability, attainable significance levels, tied statistics, tail conventions and finite-simulation uncertainty before using permutation tests in applications. Practice progresses from concepts through worked applications to assumption checks and synthesis. Prerequisites: probability, sampling distributions and the preceding resampling curriculum. Includes single-select and multiselect practice with worked solutions and distractor analysis.

statistics

Oct 26, 2026

20 questions