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1890 learning items

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Quiz

Survival Analysis & Time-to-Event Data

Study time-to-event data through censoring examples, survival and hazard interpretation, Kaplan–Meier calculations and log-rank comparisons. Practice interpreting incomplete follow-up without treating censored observations as failures. Prerequisites: probability, statistical inference and the preceding core curriculum. Original single-select and multiselect scenarios progress from interpretation to worked applications and assumption-sensitive challenges. Detailed solutions explain the alternatives; this is educational statistical practice.

statistics

Oct 26, 2026

25 questions

Quiz

Rolling-Origin Evaluation & Forecast Uncertainty

Evaluate operational forecasts with rolling origins, horizon-specific errors, scaled losses and interval calibration. Diagnose temporal leakage, residual structure and changes in demand; assess coherent forecasts across aggregation levels. Prerequisites: time-series models and predictive validation. Original single-select and multiselect scenarios progress from interpretation to worked applications and assumption-sensitive challenges. Detailed solutions explain the alternatives; this is educational statistical practice.

statistics

Oct 26, 2026

20 questions

Quiz

Sign Test for Median (Single-Sample & Paired)

Use one-sample and paired sign tests for continuous medians and directional changes. Prerequisites: binomial probabilities, medians and paired differences. Encode signs, state tie conventions, calculate exact one-sided and two-sided tails, and use continuity-corrected normal approximations when appropriate. Original service and training scenarios examine discreteness, dependence, magnitude information and the distinction between a median of differences and a difference of medians. Cover: Photo by Artem Podrez on Pexels. Further reading: [Source 1](https://online.stat.psu.edu/stat415/book/export/html/836); [Source 2](https://www.stat.ethz.ch/R-manual/R-devel/library/stats/html/binom.test.html).

statistics

Oct 26, 2026

20 questions

Quiz

Foundations of Non-parametric Methods & Efficiency

Compare nonparametric and robust approaches according to their assumptions and scientific targets. Prerequisites: medians, sampling distributions, location tests and basic regression. Calculate MAD, trimmed means and Huber loss; interpret asymptotic relative efficiency under a specified location model. Cases distinguish distribution-free testing from resistance to contamination and examine leverage, ties and robust uncertainty. Cover: Photo by Lukas Blazek on Pexels. Further reading: [Source 1](https://online.stat.psu.edu/stat415/book/export/html/836); [Source 2](https://www.stat.ethz.ch/CRAN/web/packages/robsurvey/vignettes/basic.html); [Source 3](https://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/mad.htm).

statistics

Oct 26, 2026

15 questions

Quiz

Factorial Design, Aliasing & Response Surfaces

Choose efficient factorial screening and response-surface designs. Prerequisites: factorial effects, contrasts and basic derivatives. Derive defining relations and aliases, interpret resolution III–V, and distinguish center-point curvature checks from identification of separate quadratic terms. Explore central composite augmentation, local optimization and the whole-plot versus subplot uncertainty created by restricted randomization. Cover: Photo by Mikhail Nilov on Pexels. Further reading: [Source 1](https://www.itl.nist.gov/div898/handbook/pri/section3/pri334.htm); [Source 2](https://www.itl.nist.gov/div898/handbook/pri/section3/pri3343.htm); [Source 3](https://www.itl.nist.gov/div898/handbook/pri/section3/pri3344.htm).

statistics

Oct 26, 2026

20 questions

Quiz

Analysis of Covariance (ANCOVA)

Combine categorical treatments and continuous baseline predictors through ANCOVA. Prerequisites: linear regression, interaction and ANOVA. Calculate adjusted means and contrasts, assess common regression slopes and interpret treatment effects at meaningful covariate values. Examine precision, support, noisy baseline measurements, post-treatment adjustment and the difference between a fitted comparison and a causal claim. Cover: Photo by Kampus Production on Pexels. Further reading: [Source 1](https://online.stat.psu.edu/stat502/Lesson09); [Source 2](https://pmc.ncbi.nlm.nih.gov/articles/PMC2562926/); [Source 3](https://pmc.ncbi.nlm.nih.gov/articles/PMC10699339/).

statistics

Oct 26, 2026

20 questions

Quiz

Repeated Measures ANOVA & Sphericity

Understand the covariance reasoning behind repeated-measures ANOVA. Prerequisites: paired contrasts, variance-covariance calculations and factorial ANOVA. Distinguish compound symmetry from sphericity, interpret Mauchly diagnostics and apply Greenhouse-Geisser or Huynh-Feldt reference corrections. Worked examples and counterexamples address difference variances, epsilon, order effects, missing visits and covariance-aware alternatives. Cover: Photo by ThisIsEngineering on Pexels. Further reading: [Source 1](https://online.stat.psu.edu/stat502/Lesson11); [Source 2](https://www.stat.ethz.ch/R-manual/R-devel/library/stats/html/mauchly.test.html); [Source 3](https://support.sas.com/documentation/onlinedoc/stat/121/glm.pdf).

statistics

Oct 26, 2026

25 questions

Quiz

Randomized Complete Block Design (RCBD)

Plan and analyze randomized complete block experiments in agriculture, production and paired studies. Prerequisites: factorial means, ANOVA and treatment contrasts. Practice within-block randomization, additive partitions, treatment uncertainty and the paired t connection. Evaluate the efficiency gain from removing nuisance variation alongside degrees-of-freedom costs, missing cells, subsampling and treatment-by-block variation. Cover: Photo by Maria Firman on Pexels. Further reading: [Source 1](https://www.itl.nist.gov/div898/handbook/pri/section3/pri332.htm); [Source 2](https://online.stat.psu.edu/stat503/Lesson04).

statistics

Oct 26, 2026

25 questions

Quiz

Two-Way Factorial ANOVA & Interaction Effects

Analyze experiments crossing two factors, from treatment cells and main effects to conditional contrasts and interaction. Prerequisites: ANOVA, contrasts and variance of independent means. Calculate balanced sums of squares, degrees of freedom and F tests; interpret textual interaction plots, marginal versus simple effects, imbalance and missing combinations. Advanced cases examine scale dependence, estimability and model hierarchy. Cover: Photo by Mikhail Nilov on Pexels. Further reading: [Source 1](https://www.itl.nist.gov/div898/handbook/prc/section4/prc437.htm).

statistics

Oct 26, 2026

35 questions

Quiz

Post-Hoc Multiple Comparisons & Contrasts

Learn to compare treatment means while matching multiplicity protection to the scientific question. Prerequisites: one-way ANOVA, pooled error variance, t and F inference. Work with planned orthogonal contrasts, Tukey HSD and Tukey-Kramer, Bonferroni, Scheffé and Dunnett. Original laboratory and process scenarios develop contrast estimates, precision, simultaneous intervals and selection-aware interpretation, with worked solutions and distractor rationales. Cover: Photo by Lukas Blazek on Pexels. Further reading: [Source 1](https://www.itl.nist.gov/div898/handbook/prc/section4/prc472.htm); [Source 2](https://www.itl.nist.gov/div898/handbook/prc/section4/prc471.htm); [Source 3](https://www.stat.uchicago.edu/~yibi/teaching/stat222/2019/C05_2019.pdf).

statistics

Oct 26, 2026

30 questions

Quiz

ANOVA Assumptions & Diagnostic Tests

Assess the assumptions behind one-way mean comparisons. Prerequisites: one-way ANOVA and residual diagnostics. Distinguish within-group normality, independence and equal variance; compare Bartlett, Levene and median-centered Brown-Forsythe variance tests; use Welch appropriately and evaluate pretest, clustering and robustness limitations. Includes single-select and multiselect questions, worked solutions and content-based distractor feedback. References: [NIST: Levene Variance Test](https://www.itl.nist.gov/div898/handbook/eda/section3/eda35a.htm), [SciPy: Classical and Welch ANOVA](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.f_oneway.html), [NIST: One-way ANOVA](https://www.itl.nist.gov/div898/handbook/ppc/section2/ppc231.htm). Cover: Photo by Polina Tankilevitch on Pexels.

statistics

Oct 26, 2026

20 questions

Quiz

One-Way ANOVA: Partitioning Sum of Squares

Build the one-way ANOVA table from group means and within-group deviations. Prerequisites: regression, variance and F inference. Calculate weighted grand means, treatment and error sums of squares, degrees of freedom, mean squares and global tests. Explore merging, rescaling, replication and degenerate designs. Includes single-select and multiselect questions, worked solutions and content-based distractor feedback. References: [NIST: One-way ANOVA](https://www.itl.nist.gov/div898/handbook/ppc/section2/ppc231.htm). Cover: Photo by Polina Tankilevitch on Pexels.

statistics

Oct 26, 2026

35 questions