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

Randomised block design — where it appears

An arrangement that groups units expected to be alike and randomises within each group, so the variation between groups leaves the comparison. It removes the between-group variation from the comparison exactly, which is why a block's sum and its difference carry quite different information.

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

What each rule leaves behind, at 120 patients. Four allocation rules over the same cohorts and the same seeds, each scored on three imbalances: the number of patients in each arm, the worst of the nine factor levels, and the worst of the 24 cells of the cross-classification. No rule holds all three. Permuted blocks hold the totals exactly and leave the margins near a coin's. Blocks inside every cell hold the cells and let the totals drift, because 24 part-filled blocks do not have to end level. Minimisation holds the margins and the totals and is at 83% of a coin's cell imbalance. Each of the three columns is somebody's definition of a balanced trial.

Balancing what is known in advance

Four allocation rules, three definitions of balance, and no rule that holds more than one of them. Minimisation keeps the worst factor margin near three patients whether the trial has forty or six hundred and forty — and lets the imbalance in the cross-classified cells climb to 86% of a coin's, because the cells are not what it is watching.

covadapt · Assignment The same 40 units, arranged two ways. Both designs estimate the same effect of 0.5 and both are unbiased — 0.488 and 0.497. The blocked design's estimate has standard deviation 0.318 against 0.692, a variance ratio of 0.21 where the model predicts 0.20.

The variance removed before the data

Arranging forty units in pairs rather than assigning them at random cuts the variance of the estimated effect to a fifth — and the fifth is knowable in advance, because it is exactly the share of the variance the pairs do not carry.

design · Blocking

Named alongside it

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

RandomisationAllocationBlockingConfoundingCovariate-adaptive randomisationCovariate balanceExperimental designInteractionMinimisationPermuted blocksPredictabilityStratified randomisation

All concepts