Statistics Learning Hub
Explore our library of free resources, cheat sheets, and statistical guides.
Understanding statistics at a conceptual level is the first step toward performing well on your coursework. Our editorial team — made up of university professors, doctoral statisticians, and quantitative research consultants — writes every guide in this library to address the specific concepts that cause students to lose marks on university assignments and exams. Each article in this hub connects directly to a real assignment type or course topic, giving you both the conceptual foundation and the practical exam strategy you need to succeed.
Confidence Interval
The confidence interval guide is one of the most important resources in this library because confidence intervals appear on virtually every university statistics exam from STAT 101 through graduate biostatistics. The guide explains the correct interpretation of a 95% confidence interval — a concept that research consistently shows is misunderstood by the majority of students and, in published studies, by many practicing researchers. It walks through the complete calculation process using both the z-distribution and t-distribution, explains when each formula applies, and provides an exam-ready interpretation template that earns full marks on written analysis questions. Students who read this guide before their confidence interval homework assignment consistently avoid the most common interpretation error that professors specifically test for.
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The mean, median, and mode guide addresses the most foundational decision in descriptive statistics: choosing the right measure of central tendency for your specific dataset and research context. Most students can calculate all three measures from memory, but far fewer can correctly identify which measure is appropriate when the data is skewed, contains outliers, or is measured on an ordinal or nominal scale. This guide provides a decision framework you can apply directly on exams, along with real-world examples using income data, clinical trial results, and consumer survey responses that parallel the scenarios professors use in assignment questions. It also covers the relationship between distribution shape and the relative positions of mean, median, and mode — a topic that appears on virtually every statistics midterm.
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The normal distribution guide covers the bell curve from first principles through practical application, including the mathematical properties of symmetry and the mean-equals-median-equals-mode relationship, the Empirical Rule (68-95-99.7%), the standard normal distribution, Z-score calculation, and the use of standard normal tables to find probabilities. The guide is structured specifically around the types of normal distribution problems that appear on university exams, including left-tail, right-tail, and between-values probability calculations. It also addresses the single most common student error: forgetting to standardize the variable before looking up a probability, which results in entirely incorrect answers even when all other steps are correct.
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The statistics cheat sheet guide teaches students how to build an effective reference document for open-note exams rather than simply providing a formula list to memorize. Research in cognitive science demonstrates that the act of constructing a cheat sheet — deciding which formulas to include, organizing them logically, and writing them in your own notation — produces significantly better exam performance than studying a pre-made sheet. This guide walks through the key formula families every cheat sheet should contain: descriptive statistics, probability rules, the Empirical Rule, hypothesis testing decision rules, confidence interval formulas, and regression equations. It also includes a hypothesis testing decision tree that helps students select the correct test based on data type and research question during an exam.
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The p-value guide provides a comprehensive, jargon-free explanation of one of the most misunderstood concepts in all of statistics. A 2016 paper in the European Journal of Epidemiology found that the majority of psychology researchers, biology faculty, and even statistics professors hold at least one incorrect belief about p-value interpretation. This guide corrects all of the major misconceptions — including the common belief that p equals 0.04 means there is a 96% probability that the research hypothesis is true — and explains the correct frequentist interpretation in plain English. It also covers the relationship between p-values and the alpha threshold, one-tailed versus two-tailed tests, and the ongoing scientific debate about statistical significance that is increasingly relevant in graduate-level methodology courses.
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Learn how statistics can be manipulated with our expert guide. Discover real examples of p-hacking, misleading graphs, and how to spot bad data.
