Normal Distribution
nothing is called 95% until it has been counted
Concept

Eigenvector — where it appears

A direction a matrix only stretches, never turns: multiplying by the matrix returns the same vector scaled by its eigenvalue. The eigenvector with the largest eigenvalue is the matrix's dominant direction, and reading it is how a pairwise matrix becomes a single column.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Also named here as exchange graph — the same set of essays touches all of them, so they are one junction rather than several.

The pairing recovers most of it and passes nothing. How much of the separating direction each probe carries, over 100 designs of 14 units whose admissible set is enumerated and split in two. The four rows the pairing adds are the dominant direction of what each blocking matrix keeps past its degrees, and the cut that direction's signs induce. Counted, they read 0.5266 and 0.5258 against the counted per-unit share's 0.3854 — most of the gap between that share and the design's own leverage at 0.5395, closed. Modelled, they read 0.4274 and 0.4954 against 0.4272. Nothing built from the active set passes leverage, and the projected fourth power is still ahead of all of them at 0.6583.

A set of pairs, not a vector

The active set is a graph on the units, and every probe built from it so far has been its degree. Read as a graph it recovers 0.1326 of the alignment the summary lost — and draws level with leverage rather than passing it.

blocked · Randomisation Separation, how far against whether. The median separation each probe carries between the pieces of a split admissible set, over the 100 designs whose set is split. The share refused per unit carries 1.953; the refusal pairing's direction 3.103, and with the saturated pairs dropped 2.917. The depth pairing's direction carries 2.345, and each unit's mean depth 3.836 — exactly the leverage's. A random direction carries 0.942 and the projected fourth power 5.080.

How far, not whether

The blocking matrix records whether a tolerance box refuses an exchange. Dropping the pairs it refuses for certain changes nothing. Recording instead how far each exchange moves the balance vector turns the pairing into its degree plus a part that lies inside the rule's own span — and the degree is the design's leverage, exactly. The heuristic that beat every reading of what the rule blocks was the unclamped pairing's degree all along.

blocked · Randomisation

Named alongside it

The objects these essays reach for when they reach for this one.

Assignment mechanismCovariate balanceExact enumerationExchange graphExperimental designImbalanceLeverageProjectionRandomisation testRerandomisationAssortativityClosed form

All concepts