Statistics Glossary
Plain-English definitions of the statistics terms you’ll meet in research and reporting — no jargon for its own sake. Many link to a free calculator or a worked R example.
A
Alpha (α) — the significance level: the false-positive rate you’re willing to accept, conventionally 0.05. If the p-value is below α, the result is called “statistically significant.”
ANOVA (analysis of variance) — a test comparing the means of three or more groups at once, avoiding the inflated error rate of many t-tests. See the ANOVA calculator.
B
Binomial distribution — the distribution of the number of successes in a fixed number of independent yes/no trials with constant probability. See the binomial calculator.
Bonferroni correction — a simple way to control false positives when running many tests: divide α by the number of comparisons.
Boxplot — a compact picture of a distribution showing the median, quartiles and outliers. See how to read a boxplot.
C
Chi-square test — a test of association between two categorical variables (test of independence) or of fit to expected proportions (goodness of fit). See the chi-square calculator.
Cohen’s d — a standardized effect size for the difference between two means, in standard-deviation units (≈0.2 small, 0.5 medium, 0.8 large). See the Cohen’s d calculator.
Confidence interval (CI) — a range of plausible values for a parameter; a 95% CI is built by a procedure that captures the true value 95% of the time. See the CI calculator.
Correlation — the strength and direction of association between two variables, from −1 to +1. See the correlation calculator and Pearson vs Spearman.
Cronbach’s alpha — a measure of internal-consistency reliability for a multi-item scale. See Cronbach’s alpha in R.
D
Degrees of freedom (df) — the number of values free to vary when estimating a statistic; it sets the exact shape of the t, chi-square and F distributions.
E
Effect size — how big a difference or relationship is, independent of sample size — the essential companion to a p-value. Examples: Cohen’s d, r², odds ratio.
F
F-test — the test behind ANOVA and regression, comparing explained to unexplained variance via the F distribution.
Fisher’s exact test — an exact test of association in a 2×2 table, valid for small samples where chi-square isn’t. See the Fisher’s exact calculator.
H
Hazard ratio — the relative instantaneous risk of an event between groups, from a Cox survival model. See Cox proportional hazards in R.
I
Interquartile range (IQR) — the spread of the middle 50% of the data (Q3 − Q1); a measure of spread that resists outliers.
K
Kruskal–Wallis test — the non-parametric alternative to one-way ANOVA, comparing three or more groups by ranks.
L
Linear regression — fitting a straight line to predict an outcome from a predictor; gives a slope, intercept and R². See the regression calculator.
M
Mann–Whitney U test — the non-parametric alternative to the two-sample t-test, comparing two groups by ranks.
Mean — the arithmetic average; sensitive to outliers.
Median — the middle value; robust to outliers and the better centre for skewed data.
N
Normal distribution — the symmetric bell curve underlying many tests; summarised by its mean and standard deviation. See the z-score calculator.
Null hypothesis (H₀) — the “no effect / no difference” default that a test tries to disprove.
Non-parametric test — a test that doesn’t assume a specific distribution, using ranks instead. See parametric vs non-parametric.
O
Odds ratio (OR) — the ratio of the odds of an outcome between two groups; 1 means no association. See logistic regression in R.
One-tailed vs two-tailed — whether a test looks for an effect in one pre-specified direction or either direction. See one-tailed vs two-tailed.
Outlier — a data point far from the rest; can distort means, correlations and regressions.
P
p-value — the probability of data at least as extreme as yours if the null hypothesis were true; small values are evidence against the null. It is not the probability the null is true. See the p-value calculator and how to interpret p-values.
p-hacking — trying many analyses and reporting only the significant ones, which inflates false positives. The cure is pre-registration.
Power — the probability of detecting a real effect (1 − β); 0.80 is a common minimum, driven mostly by sample size. See the power calculator.
Q
Quartile — the values splitting ordered data into quarters (Q1, Q2 = median, Q3).
R
R-squared (R²) — the proportion of variation in the outcome explained by a model; equals the correlation squared in simple regression.
S
Sample size — the number of observations; the main lever for power and precision. Plan it with the sample size calculator.
Sensitivity & specificity — a diagnostic test’s true-positive and true-negative rates. See the diagnostic test calculator.
Skewness — asymmetry in a distribution; a long right tail pulls the mean above the median.
Standard deviation (SD) — the typical distance of values from the mean; describes the spread of the data.
Standard error (SE) — the precision of an estimate (e.g., the mean); SE = SD/√n, so it shrinks as the sample grows. See SD vs SE.
Survival analysis — methods for time-to-event data, including Kaplan–Meier curves and Cox regression. See Kaplan–Meier in R.
T
t-test — a test comparing one or two means using the t distribution. See the t-test calculator and Welch vs Student.
Type I & Type II error — a false positive (rejecting a true null, rate α) and a false negative (missing a real effect, rate β). See Type I vs Type II error.
W
Wilcoxon signed-rank test — the non-parametric alternative to the paired t-test, comparing paired measurements by ranks.
Z
Z-score — how many standard deviations a value is from the mean; maps directly to a percentile. See the z-score calculator and z-scores explained.
Know the term but need the analysis done? That’s what we do — or start with the free calculators.