Where does variance collide?

The expected squared deviation of a random variable from its mean, the basic measure of how spread out a distribution is. R. A. Fisher named it in his 1918 paper The Correlation between Relatives on the Supposition of Mendelian Inheritance, where the total variance of a trait could be split among its causes. The referent is a distribution or a sample, the unit is the square of whatever the variable is measured in, and the quantity is computed, never granted or negotiated. In machine learning the same quantity appears in the bias, variance decomposition of Geman, Bienenstock, and Doursat (1992): a model's expected error splits into a bias term and a variance term, and cutting one tends to raise the other. Here variance is a property of an estimator across hypothetical resamplings, still a squared spread, still a number.[1][2]

Unit

The square of the variable's units (a mathematical quantity)

Recovery means

Not applicable

Measured by

Computed as the mean squared deviation from the mean, on a sample or a distribution

In management accounting a variance is the difference between a standard or budgeted figure and the actual figure realised, the object of variance analysis. Horngren, Datar, and Rajan define it as the budgeted amount less the actual amount, split into price and quantity components and labelled favorable when it raises operating income and unfavorable when it lowers it. The referent is a pair of monetary or quantity figures for one period, the unit is currency or physical units, and the number is a signed gap, not a squared spread. It shares the word with the statistical meaning and little else: no expectation, no squaring, no distribution, just planned minus actual for a cost, a revenue, or a usage.[3]

Unit

Currency or physical units (a signed budget-to-actual gap)

Recovery means

Not applicable

Measured by

Standard or budgeted amount minus the actual amount, reported by line item

In land-use law a variance is an administrative permission to use land in a way a zoning ordinance forbids, granted by a board of adjustment when strict application would impose an unnecessary hardship on the owner. Juergensmeyer and Roberts, in Land Use Planning and Development Regulation Law, separate an area variance, which relaxes a dimensional rule such as a setback or height limit, from a use variance, which permits an otherwise prohibited use, each conditioned on statutory findings. The referent is a specific parcel and its owner, the unit is a granted or denied application, and the thing is a decision, not a quantity. Unlike every other meaning, this variance is not measured or computed; it is applied for, argued, and either granted or refused.[4]

Unit

A granted or denied application (an administrative act)

Recovery means

Not applicable

Measured by

Not measured; decided by a zoning board on statutory hardship findings

In quantitative genetics the genetic variance is the part of a trait's total (phenotypic) variance attributable to differences in genotype, and it partitions further into additive, dominance, and interaction components. Falconer and Mackay's Introduction to Quantitative Genetics defines narrow-sense heritability as the additive genetic variance divided by the phenotypic variance, the ratio that predicts a population's response to selection. Visscher, Hill, and Wray (2008) restate the same partition for the genomics era and caution against reading heritability as a fixed or causal property. The referent is a population and a trait, the unit is the square of the trait's units, and although this is a variance in the strict statistical meaning, it names a specific decomposition, additive against dominance, that the other three meanings have no counterpart for.[5][6]

Unit

The square of the trait's units (a partitioned population variance)

Recovery means

Not applicable

Measured by

Estimated from resemblance among relatives, as additive and dominance components of phenotypic variance