Statistics glossary — 36 terms in plain English

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Alpha (α): The false-positive rate you are willing to accept, fixed before the test. α = 0.05 means that if the null hypothesis is true you will wrongly reject it 5% of the time. See statistical significance.
Alternative hypothesis: The claim that there is an effect — a difference, an association, a non-zero slope. A test never proves it; it can only find the null implausible.
ANOVA: Analysis of variance: a test of whether three or more group means differ, by comparing variation between groups with variation within them. See ANOVA.
Bayes' theorem: The rule for updating a probability when evidence arrives. It is why a 99%-accurate test for a rare condition still produces mostly false positives. See Bayes' theorem.
Beta (β): The false-negative rate: the chance of missing a real effect. Power is 1 − β. See statistical power.
Bonferroni correction: Divide α by the number of comparisons. Crude, conservative, and always defensible when you have run several tests.
Central limit theorem: The result that sample means are approximately normal whatever the population's shape, provided the sample is not tiny. Most tests on this site depend on it.
Chi-square test: A test of counts in categories, asking whether the observed table differs from what independence predicts. See chi-square.
Cohen's d: An effect size: the difference between two means measured in pooled standard deviations. 0.2 small, 0.5 medium, 0.8 large — conventions, not laws. See effect size.
Confidence interval: A range of values consistent with the data at a stated confidence level. 95% of intervals built this way contain the true value; this one either does or does not. See confidence interval.
Correlation: How tightly two variables move together, from −1 to 1. Measures linear association only, and never implies causation. See correlation.
Degrees of freedom: The number of values free to vary once the estimates are fixed. Usually n − 1 for one sample; it sets which t or chi-square curve applies.
Effect size: How big the difference is, on a scale that does not depend on sample size. The number a p-value cannot give you. See effect size.
Interquartile range: The distance from Q1 to Q3 — the middle half of the data. Robust to outliers, unlike the range or the standard deviation. See quartiles.
Kurtosis: How heavy a distribution's tails are relative to a normal. Excess kurtosis of 0 means normal-like tails; positive means more extreme values than normal.
Mann-Whitney U: The rank-based alternative to a two-sample t-test; assumes no normality. See Mann-Whitney.
Mean: The arithmetic average. Sensitive to every value, including the wrong ones. See mean, median and mode.
Median: The middle value once sorted. Unmoved by outliers, which is why incomes are quoted as medians.
Null hypothesis: The assumption that nothing is going on — no difference, no association. Tests measure how surprising the data would be if it were true.
Odds ratio: The ratio of the odds of an outcome in two groups. Not the same as relative risk, and further from 1 whenever the outcome is common. See odds ratio.
Outlier: A value far from the rest. Flagged by a rule, explained by context, and deleted only with a reason from outside the data. See outlier detection.
p-value: The probability of data at least this extreme if the null hypothesis were true. Not the probability that the null is true. See p-value.
Percentile: The value below which a given share of the data falls. The 90th percentile is the value 90% of observations sit below. See percentiles.
Power: The probability of detecting a real effect of a given size. 80% is the usual minimum. See statistical power.
R-squared: The share of the variance in y that the model explains. Never falls when you add a predictor, which is why adjusted R² exists. See R².
Regression: Fitting an equation that predicts one variable from others. See linear regression.
Sample size: How many observations you need — decided before the study, from the effect you want to detect and the power you want. See sample size.
Skewness: The asymmetry of a distribution. Positive means a long right tail, which drags the mean above the median.
Standard deviation: The typical distance from the mean, in the data's own units. See standard deviation.
Standard error: How much a statistic — usually the mean — would vary between samples. Falls as 1/√n. See standard error.
Statistical significance: A result unlikely under the null hypothesis at the chosen α. Says nothing about importance. See statistical significance.
t-test: A test comparing means, using the t distribution because σ is estimated from the data. See t-test.
Type I error: Rejecting a true null hypothesis — a false positive. Its rate is α.
Type II error: Failing to reject a false null hypothesis — a miss. Its rate is β.
Variance: The average squared deviation from the mean; the square of the standard deviation. See variance.
z-score: How many standard deviations a value sits from the mean. Puts any value on any scale onto one comparable ruler. See z-score.