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1890 learning items

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Showing 601–612 of 1890 items

Quiz

Parametric vs. Non-parametric Bootstrap

Choose a bootstrap data-generating mechanism that matches the study. Contrast parametric simulation with empirical, residual, pairs and block resampling, including model misspecification, dependent observations and nonregular targets. 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

Bootstrap Confidence Intervals

Compare bootstrap confidence intervals for uncertain estimates in reliability, service operations and environmental monitoring. Calculate endpoints, examine transformations and studentization, and diagnose when nominal coverage is not credible. 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

30 questions

Quiz

Bootstrap Standard Errors & Bias Estimation

Estimate uncertainty and bias through bootstrap replications. Prerequisites: the empirical bootstrap, variance, standard errors and Monte Carlo averaging. Calculate replicate spread and bias corrections, derive simple exact conditional examples and distinguish finite-data limitations from simulation noise. Analytical challenges examine units, shifts, degenerate samples, mean-squared error, reproducibility and the uncertainty of a small estimated bias. Cover: Photo by ClickerHappy on Pexels.

statistics

Oct 26, 2026

25 questions

Quiz

The Bootstrap Principle & Empirical CDF

Build the empirical-distribution foundation for the ordinary nonparametric bootstrap. Prerequisites: sampling distributions, probability and basic descriptive statistics. Calculate empirical probabilities and CDFs, enumerate replacement samples, analyze record inclusion and apply the plug-in analogy. Worked examples distinguish the original data, empirical bootstrap world and actual population while preserving paired measurements. Cover: Photo by ClickerHappy on Pexels.

statistics

Oct 26, 2026

20 questions

Quiz

Non-parametric Rank Correlation Tests

Test ordinal association with Spearman and Kendall procedures. Prerequisites: descriptive rank correlation, concordance, standard errors and hypothesis tests. Apply approximate standardization, calculate null-tail probabilities and build exact independence references while preserving ties. Original scenarios distinguish effect magnitude from evidence, directional alternatives from two-sided tests, zero correlation from independence and iid assumptions from clustered designs. Detailed worked explanations address every alternative. Cover: Photo by ThisIsEngineering on Pexels.

statistics

Oct 26, 2026

20 questions

Quiz

Friedman Test for Randomized Complete Blocks

Compare repeated treatment measurements in complete blocks with the Friedman test. Prerequisites: independent-group rank methods and the logic of matched designs. Rank within blocks, aggregate treatment ranks, calculate Q and tie adjustments, and interpret Nemenyi comparisons using average-rank distances. Applications address missing conditions, nuisance block offsets, approximation limits and what the omnibus result establishes. Cover: Photo by cottonbro studio on Pexels.

statistics

Oct 26, 2026

20 questions

Quiz

Kruskal-Wallis One-Way Non-parametric ANOVA

Develop Kruskal-Wallis inference for several independent groups. Prerequisites: rank-sum methods, chi-square testing and multiplicity. Practice pooled ranks, the H statistic, tie correction and reference calibration, then compute and interpret Dunn follow-ups. Original examples emphasize design suitability, rank normalization, small samples, shape assumptions and clear reporting of omnibus versus pairwise evidence. Cover: Photo by ThisIsEngineering on Pexels.

statistics

Oct 26, 2026

25 questions

Quiz

Mann-Whitney U Test (Wilcoxon Rank-Sum Test)

Compare two independent samples using Mann-Whitney U and the Wilcoxon rank-sum statistic. Prerequisites: pooled ranks, exchangeability and hypothesis testing. Compute rank sums, pairwise ordering effects, complementary U values and null approximations; examine ties, directional claims, sample imbalance and exact label allocations. Analytical questions separate distributional evidence from median-shift and causal interpretations. Cover: Photo by ThisIsEngineering on Pexels.

statistics

Oct 26, 2026

30 questions

Quiz

Runs Test for Sequence Randomness

Investigate randomness in ordered binary sequences with the Wald-Wolfowitz runs test. Prerequisites: elementary probability, standardized statistics and hypothesis testing. Count runs, compute conditional null moments, distinguish clustering from alternation, and evaluate exact versus approximate inference when outcome counts are uneven. Original sequence problems also explore coding choices and the limits of non-rejection. Cover: Photo by ClickerHappy on Pexels.

statistics

Oct 26, 2026

15 questions

Quiz

Wilcoxon Signed-Rank Test

Practice the Wilcoxon signed-rank test for one-sample deviations and paired changes. Prerequisites: the sign test, ranking and elementary null distributions. Build absolute ranks, handle zeros and ties, calculate signed sums and normal approximations, and investigate exact sign references, symmetry, resolution and transformation effects. Original scenarios progress from method recognition to diagnostic interpretation, with worked answers and content-based distractor rationales. Cover: Photo by cottonbro studio on Pexels.

statistics

Oct 26, 2026

25 questions

Quiz

Maximum Likelihood Estimation (MLE) Derivations

Build a rigorous understanding of maximum likelihood estimation (mle) derivations through 35 original single-select and multiselect questions. Begin with core definitions, then work through calculations, assumptions, counterexamples and advanced diagnostic challenges. Prerequisites: the earlier core Statistics curriculum, including probability distributions, expectation, calculus and the preceding mathematical-statistics sets. Competencies: Define likelihood, log-likelihood and score; Derive Bernoulli likelihood maximizers including endpoints; Derive Poisson score and curvature with zero-count cases; Derive exponential rate and scale estimators; Derive normal location and variance likelihood estimators; Retain uniform parameter-dependent support; Check constrained optimization and attainment; Distinguish invariance, local maxima and global MLE claims. Every item includes a worked explanation and reasons for rejecting distractors. Further reading: [Likelihood, score and regularity conditions](https://www.statlect.com/fundamentals-of-statistics/maximum-likelihood), [Maximum likelihood examples and boundary support](https://hanbaeklyu.com/wp-content/uploads/2020/10/lecturenote_170s.pdf).

statistics

Oct 26, 2026

35 questions

Quiz

Method of Moments (MOM)

Build a rigorous understanding of method of moments (mom) through 25 original single-select and multiselect questions. Begin with core definitions, then work through calculations, assumptions, counterexamples and advanced diagnostic challenges. Prerequisites: the earlier core Statistics curriculum, including probability distributions, expectation, calculus and the preceding mathematical-statistics sets. Competencies: Construct empirical raw moment equations; Solve single-parameter moment estimators; Solve normal and gamma two-moment systems; State gamma rate and scale conventions; Derive general uniform moment endpoints; Check existence, feasibility and identification; Explain nonlinear bias and consistency; Diagnose overidentification and numerical sensitivity. Every item includes a worked explanation and reasons for rejecting distractors. Further reading: [Point estimation: method of moments, exponential, normal, uniform and gamma examples](https://hanbaeklyu.com/wp-content/uploads/2020/10/lecturenote_170s.pdf).

statistics

Oct 26, 2026

25 questions