Bar 05 · Reference
Glossary of statistical terms
A short reading of the vocabulary used across this reference, gathered in one place for quick consultation. Each entry gives the term and the sense in which it is used here.
- Random variable
- A measurable map from a sample space to the real line. It assigns a number to each outcome.
- Probability measure
- A map from events to the real line that is non-negative, equals one for the whole space, and adds across disjoint parts.
- Mass function
- The function giving the probability of each single value of a discrete random variable.
- Density
- A non-negative function whose integral over an interval gives the probability that a continuous random variable lies in that interval.
- Cumulative distribution function
- The probability that a random variable does not exceed a given level; non-decreasing, right-continuous, and running from zero to one.
- Expectation
- The integral of a random variable against the probability measure; a measure of central position.
- Variance
- The expectation of the squared deviation from the mean; a measure of spread.
- Standard deviation
- The square root of the variance, written σ, in the units of the variable itself.
- Covariance
- The expectation of the product of the deviations of two variables from their means; a measure of linear association.
- Correlation
- The covariance divided by the two standard deviations; a number without units between minus one and one.
- Covariance matrix
- The square, symmetric arrangement of the covariances of several variables, with variances on the diagonal.
- Positive semi-definite
- A property of a symmetric matrix stating that every quadratic form built from it is non-negative.
- Independence
- The condition that the joint probability of any pair of events factorises into the product of their separate probabilities.
- Stationarity
- The property that the probabilistic character of a series does not move as the clock advances.
- Autocovariance
- The covariance between the values of a series at two times; a function of the lag between them.
- Autocorrelation
- The autocovariance divided by the variance, so that the curve begins at one.
- Spectral density
- A non-negative function that spreads the variance of a stationary series across frequencies.
- White noise
- A sequence of uncorrelated variables of constant mean and constant variance.
- Estimator
- A rule mapping an observed record to an approximation of an unknown feature of the law.
- Bias
- The difference between the expectation of an estimator and the feature it estimates.
- Consistency
- The property that an estimator converges in probability to the feature it estimates as the record grows.
- Maximum likelihood
- The method that chooses the value of an unknown feature making the observed record most probable.
- Confidence interval
- A random range whose covering rule attains a stated long-run frequency.
- Null hypothesis
- The claim held until the record speaks strongly against it, stating a precise restriction on the law.
- p-value
- The probability, under the null, of a result at least as extreme as the one observed.
- Power
- The probability of rejecting a false null, taken against a stated alternative.
Where a term has several senses in the wider literature, the reading given here is the one used on the pages of this reference. Readers who want the fuller treatment of any entry will find it on the page devoted to that topic, linked from the bar rail above and the index at the foot of every page.