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

Dunnett — where it appears

The multiple-comparison procedure for several treatments against one shared control, which accounts for the correlation those comparisons have through the control. It is the case where the dependence between comparisons is known rather than estimated, so the correction can be exact rather than a bound.

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

A trial designed 2:1:1, and what two scores deliver. 500 trials of 180 patients, three arms, a target of 2:1:1. The shaded bars are a minimisation score that divides each arm's count by the share that arm is supposed to receive before measuring the spread; it delivers 49.9% : 25.1% : 25.1%. The others are the same rule with the counts left raw, which delivers 33.4% : 33.3% : 33.3% — the balance it enforces inside every factor level is equality, and equality is what it gets. The marks are the shares that were asked for.

Balancing towards unequal targets

A three-arm trial allocating two to one to one is the ordinary case, and a balancing rule built from raw counts does not know it. It balances the arms towards equality inside every factor level, delivers a third to each arm, and reports that it minimised imbalance.

multiarm · Allocation 3 arms against one control, 360 units in all. Every control size, enumerated. The best is 132 on the control and 76 on each arm — a ratio of 1.74, against √3 = 1.73. Splitting the units evenly over all 4 groups costs 7.2%, which is small; what the larger control also does is lower the correlation between the comparisons, from 0.50 to 0.37, and that changes which multiplicity correction is right.

One control, many arms

The control appears in every comparison, so it is worth √k treatment arms — and the same sharing makes the k tests correlated at n/(n+n₀), which is the quantity Bonferroni ignores. Both facts come out of one design decision, and it is the size of the control.

allocation · Multiplicity

Named alongside it

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

AllocationAllocation ratioExperimental designBonferroniCorrelationCovariate-adaptive randomisationCovariate balanceFamilywise error rateImbalance scoreMinimisationMonte CarloMultiple comparisons

All concepts