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1890 learning items

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Quiz

Scatter Plots, Covariance & Linear Association

Describe paired numerical data using scatter-plot structure and covariance. Calculate sample and population forms, track product units, and analyze shifts, rescaling, pairing integrity, curved relationships and clustered data. Prerequisites: means, centered deviations and variance. Examples build from direct calculations to diagnostic interpretation of numerical and visual summaries. Includes single-select and multiselect practice with worked explanations and misconception-specific feedback. Further reading and method references: NIST: scatter plots NumPy: covariance definitions

statistics

Oct 23, 2026

20 questions

Quiz

Simpson's Paradox & Confounding in Categorical Data

Investigate how case mix can reverse aggregate comparisons even when subgroup results agree. Compute pooled and standardized rates, analyze changing weights and distinguish common causes, mediators and selection effects. Original service and admissions scenarios introduce Simpson reversals and Berkson selection with explicit assumptions. Prerequisites: conditional proportions and weighted averages; causal claims remain carefully qualified. Includes single-select and multiselect practice with worked explanations and misconception-specific feedback. Further reading and method references: Stanford Encyclopedia: Simpson’s paradox

statistics

Oct 23, 2026

15 questions

Quiz

Metrics of Association for Categorical Variables

Compare categorical associations using risk differences, risk ratios, odds ratios, signed phi, Cramér V and directional Goodman–Kruskal lambda. Work through transparent numerical examples and diagnose reference coding, zero cells, case-control sampling and prediction-error limitations. Prerequisites: two-way frequencies, proportions and square roots. Formulas are supplied for less familiar measures; significance testing is deferred. Includes single-select and multiselect practice with worked explanations and misconception-specific feedback. Further reading and method references: SciPy: relative risk SciPy: odds ratios SciPy: categorical association Minitab: Goodman–Kruskal measures

statistics

Oct 23, 2026

20 questions

Quiz

Joint, Marginal & Conditional Relative Frequencies

Learn to choose the correct denominator in two-way tables. Original survey, workplace and service scenarios develop joint, marginal and conditional relative frequencies, weighted summaries, 100% stacked bars and mosaic areas. Diagnose reversed conditioning, overlapping categories, empty groups and rounding. Prerequisites: fractions, percentages and basic categorical data. Includes single-select and multiselect practice with worked explanations and misconception-specific feedback. Further reading and method references: OpenStax: contingency tables

statistics

Oct 23, 2026

20 questions

Quiz

Descriptive Skewness & Tail Weight

Explore empirical skewness and tail weight using explicitly stated moment conventions. Calculate standardized third and fourth moments, compare raw and excess kurtosis, and reason about outliers, affine transformations, constant data and estimator differences. Prerequisites: centered deviations, variance, powers and square roots. Population-moment existence is discussed conceptually without integration. Includes single-select and multiselect practice with worked explanations and misconception-specific feedback. Further reading and method references: NIST: skewness and kurtosis

statistics

Oct 23, 2026

20 questions

Quiz

Standard-Deviation Bands & Normal-Shape Intuition

Build intuition for standard-deviation bands and the empirical rule through measurement, delivery and process-quality scenarios. Practice interval endpoints, tail estimates, expected counts and practical tolerance bands while examining distribution shape and the limits of descriptive coverage. Prerequisites: mean, standard deviation and z-scores; no calculus or inferential tests required. Includes single-select and multiselect practice with worked explanations and misconception-specific feedback. Further reading and method references: OpenStax: normal distribution

statistics

Oct 23, 2026

20 questions

Quiz

Frequency Distributions, Binning & Contingency Tables

Build practical confidence in frequency distributions, binning & contingency tables through 20 original single-select and multiselect questions. Prerequisites: Data types, sampling and study-design basics. Interpret raw and relative frequencies with explicit denominators. Construct and invert cumulative frequencies. Check bin endpoints, widths and coverage. Read joint counts and marginal totals. Explain information loss and binning sensitivity. Audit rounding, missing responses and table consistency. Questions progress from basic recognition to application, interpretation and diagnostic challenges. Worked feedback explains the reasoning and the alternatives; no programming or calculus is needed. Further reading: [Reference 1](https://openstax.org/books/introductory-statistics-2e/pages/1-3-frequency-frequency-tables-and-levels-of-measurement); [Reference 2](https://openstax.org/books/introductory-statistics-2e/pages/2-2-histograms-frequency-polygons-and-time-series-graphs); [Reference 3](https://openintro-ims.netlify.app/explore-categorical). Photo by Artem Podrez on Pexels.

statistics

Oct 23, 2026

20 questions

Quiz

Sampling Biases, Observational Studies & Controlled Experiments

Build practical confidence in sampling biases, observational studies & controlled experiments through 20 original single-select and multiselect questions. Prerequisites: Population, sample and sampling-design vocabulary. Diagnose selection, voluntary response and nonresponse bias. Identify response and social desirability effects. Separate observation from randomized intervention. Recognize confounding and alternative explanations. Evaluate masking and placebo comparisons. Assess survivorship, attrition and limits of causal generalization. Questions progress from basic recognition to application, interpretation and diagnostic challenges. Worked feedback explains the reasoning and the alternatives; no programming or calculus is needed. Further reading: [Reference 1](https://openintro-ims.netlify.app/data-design); [Reference 2](https://openstax.org/books/introductory-statistics-2e/pages/1-4-experimental-design-and-ethics). Photo by Polina Tankilevitch on Pexels.

statistics

Oct 23, 2026

20 questions

Quiz

Populations, Samples & Sampling Methodologies

Build practical confidence in populations, samples & sampling methodologies through 20 original single-select and multiselect questions. Prerequisites: Data types and measurement scales. Distinguish target population, sampling frame and realized sample. Distinguish population parameters from sample statistics. Recognize simple random sampling and its limitations. Compare stratified, cluster and multistage designs. Diagnose systematic sampling periodicity. Identify mismatches between sampling and target units. Questions progress from basic recognition to application, interpretation and diagnostic challenges. Worked feedback explains the reasoning and the alternatives; no programming or calculus is needed. Further reading: [Reference 1](https://openintro-ims.netlify.app/data-design); [Reference 2](https://openstax.org/books/introductory-statistics-2e/pages/1-2-data-sampling-and-variation-in-data-and-sampling). Photo by Tima Miroshnichenko on Pexels.

statistics

Oct 23, 2026

20 questions

Quiz

Data Types & Stevens' Scales of Measurement

Build practical confidence in data types & stevens' scales of measurement through 15 original single-select and multiselect questions. Prerequisites: The arithmetic and mathematical-language bridge. Distinguish categorical variables from counts and measurements. Recognize nominal and ordinal scales. Interpret equal intervals and meaningful zero points. Separate numerical labels from quantitative values. Analyze recording resolution and coarsening. Evaluate permissible comparisons and construct interpretations. Questions progress from basic recognition to application, interpretation and diagnostic challenges. Worked feedback explains the reasoning and the alternatives; no programming or calculus is needed. Further reading: [Reference 1](https://openstax.org/books/introductory-statistics-2e/pages/1-3-frequency-frequency-tables-and-levels-of-measurement); [Reference 2](https://openintro-ims.netlify.app/data-hello). Photo by Ron Lach on Pexels.

statistics

Oct 23, 2026

15 questions

Quiz

Sets, Logic & Reading Mathematical Claims

Build practical confidence in sets, logic & reading mathematical claims through 20 original single-select and multiselect questions. Prerequisites: Basic functions and mathematical notation. Distinguish membership, subset and set equality. Compute unions, intersections and complements. Translate quantifiers and their negations. Distinguish necessary, sufficient and equivalent conditions. Construct counterexamples and respect assumptions. Evaluate quantified claims including empty collections. Questions progress from basic recognition to application, interpretation and diagnostic challenges. Worked feedback explains the reasoning and the alternatives; no programming or calculus is needed. Further reading: [Reference 1](https://discrete.openmathbooks.org/dmoi2/sec_intro-sets.html); [Reference 2](https://discrete.openmathbooks.org/dmoi2/sec_intro-statements.html); [Reference 3](https://discrete.openmathbooks.org/dmoi2/sec_quantifiers.html). Photo by DS stories on Pexels.

statistics

Oct 23, 2026

20 questions

Quiz

Functions, Graphs & Summation Notation

Build practical confidence in functions, graphs & summation notation through 20 original single-select and multiselect questions. Prerequisites: Elementary algebra, powers and logarithms. Read coordinates and interpret slopes with units. Evaluate functions and identify valid domains. Invert or compose functions with appropriate restrictions. Expand and transform finite indexed sums. Evaluate finite products and factorials. Reason about piecewise boundaries and limits of tabular inference. Questions progress from basic recognition to application, interpretation and diagnostic challenges. Worked feedback explains the reasoning and the alternatives; no programming or calculus is needed. Further reading: [Reference 1](https://openstax.org/books/college-algebra-2e/pages/3-1-functions-and-function-notation); [Reference 2](https://openstax.org/books/college-algebra-2e/pages/9-4-series-and-their-notations). Photo by Sergey Meshkov on Pexels.

statistics

Oct 23, 2026

20 questions