Mathematical reference
An introductory glossary for the published statistics lessons.
Use these definitions alongside the lessons and browse research citations with one-click BibTeX copying.
Base rate
The prevalence or prior probability of an event before additional evidence is considered.
Bootstrap
A resampling procedure that estimates a statistic’s sampling behavior by sampling with replacement from an empirical dataset.
Central limit theorem
A family of results giving asymptotic normality for suitably standardized sums or means.
Conditional probability
Probability of one event given that another event is known to occur.
Confidence interval
An interval produced by a procedure calibrated to include a fixed parameter at a specified long-run frequency under its assumptions.
Confounding
Distortion or ambiguity in a causal association due to differences in variables linked to exposure and outcome.
Data provenance
The documented origin, collection, transformations, limitations, and permissions associated with a dataset.
Mean
The sum of observed values divided by their number.
Median
The middle of the ordered values; for even sample sizes, the mean of the two central values.
Normal distribution
A symmetric continuous probability distribution determined by its mean and variance.
Ordinary least squares
A regression fitting method minimizing the sum of squared residuals.
P-value
Under a specified null model, the probability of a test statistic at least as extreme as the observation by the pre-specified criterion.
Parameter
A numerical characteristic of a population.
Percentile bootstrap interval
An interval using the corresponding lower and upper empirical quantiles of a bootstrap distribution; its nominal coverage can be unreliable in some settings.
Population
The complete set of units about which an investigation seeks to draw conclusions.
Positive predictive value
Probability of the condition conditional on a positive screening result.
R-squared
For a least-squares fit with intercept and nonzero total sum of squares, one minus residual sum of squares divided by total sum of squares.
Randomization test
A procedure comparing an observed statistic to its distribution under treatment allocations allowed by the actual assignment design.
Regression residual
An observed response minus its model-predicted response.
Sample
A subset of units actually observed.
Sample standard deviation
The square root of the sum of squared deviations from the sample mean divided by n−1.
Sampling distribution
The probability distribution of a statistic across repeated samples under a specified design.
Selection bias
A systematic distortion introduced by how observations enter the dataset.
Sensitivity
Probability of a positive screening result conditional on having the condition.
Simpson’s paradox
A reversal of a descriptive association when data are aggregated across groups with different weights.
Specificity
Probability of a negative screening result conditional on not having the condition.
Standard error
The standard deviation of a statistic’s sampling distribution.
Statistic
A numerical characteristic computed from a sample.