Free statistics guides
Statistics guides
Plain-English, no-paywall guides on the concepts students get stuck on - hypothesis testing, p-values, choosing a test, and confidence intervals - with the same reasoning behind StatRise's 39 calculators, 54 lessons, and 660 practice questions.
Hypothesis Testing Explained: The Five Steps, Worked Through
A step-by-step walkthrough of hypothesis testing: null and alternative hypotheses, significance level, test statistic, p-value, and conclusion.
8 min read
What Is a P-Value? A Plain-English Explanation
What a p-value really means, what it does not, how it relates to the significance level, and the misinterpretations to avoid.
7 min read
How to Choose the Right Statistical Test
A framework for choosing the right statistical test: identify variable types, group count, and goal, then pick t-test, chi-square, ANOVA, or regression.
8 min read
Confidence Intervals Explained (Without the Jargon)
What a confidence interval really means: the confidence level, margin of error, its link to hypothesis tests, and the mistakes to avoid.
7 min read
Understanding Standard Deviation: What It Measures and Why It Matters
What standard deviation measures, how it relates to variance, why we square deviations, the empirical rule, and sample vs population formulas.
7 min read
T-Test vs Z-Test: Which One Should You Use?
T-test vs z-test: when to use each, why the t-distribution has heavier tails, and how sample size and the standard deviation decide it.
7 min read
Common Statistics Mistakes and How to Avoid Them
Common statistics errors to avoid: correlation vs causation, p-value misreadings, ignoring assumptions, and confusing significance with importance.
8 min read
AP Statistics Exam Guide: What to Study and How to Answer
How to prepare for the AP Statistics exam: the four big themes, writing free-response answers in context, and the reasoning that scores.
8 min read
Normal Distribution Explained: The Bell Curve, Z-Scores, and the Empirical Rule
What makes a distribution normal, how mean and standard deviation define the bell curve, how z-scores standardize values, and what the empirical rule says.
8 min read
Mean vs Median vs Mode: Choosing the Right Measure of Center
What the mean, median, and mode each measure, how outliers and skew pull them apart, and how to choose the right measure of center for your data.
8 min read
Type I vs Type II Error: False Positives, False Negatives, and Power
What Type I and Type II errors are, how alpha and beta control them, why power equals 1 − beta, and how sample size and effect size shift the trade-off.
8 min read
Correlation vs Causation: What a Correlation Can and Cannot Prove
What the correlation coefficient r actually measures, why it never establishes cause, and how confounders, reverse causation and Simpson's paradox mislead.
8 min read
How to Read a Box Plot: Quartiles, IQR, Whiskers, and Outliers
How to read a box plot: the five-number summary, quartiles and the IQR, where the whiskers really stop, and the 1.5 × IQR rule for flagging outliers.
8 min read
Chi-Square Test Explained: Goodness-of-Fit vs Test of Independence
How the chi-square test works: expected counts, degrees of freedom, and when to use goodness-of-fit versus a test of independence, with worked examples.
9 min read