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

Main effect — where it appears

The average change in the response when one factor moves from its low setting to its high one, taken across every combination of the others. In a factorial it is estimated from every run rather than from the two that changed that factor, which is the efficiency a factorial exists for.

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

Two factors that interact — where each design looks. The true response at the four corners is -10, 6, 4, 0. One factor at a time visits three of them, sees that raising either factor alone helps, and recommends raising both — a corner it never ran, and one that is worse than either single change. It picks the best corner 0.0% of the time against the factorial design's 99.4%, on the same number of runs.

One factor at a time

Changing one thing per experiment estimates each effect from two conditions; changing everything at once estimates each from every run. The ratio is (k+1)/2 and it is exact — and when two factors interact, the one-at-a-time design recommends a setting it never tried.

design · Factorial What a 8-run fraction of 4 factors confounds. The defining relation is I = ABCD, so the resolution is 4. A is estimated as A + BCD; B is estimated as B + ACD; C is estimated as C + ABD; D is estimated as D + ABC. Each of those is an identity about the design rather than an approximation about the data.

The word a fraction costs

A half fraction estimates each main effect as an exact sum of that effect and everything it is confounded with — no error term, no sample-size argument. With every interaction at 0.8 the design reports a true effect of −1 as −0.20, and the design cannot test the assumption that makes the number mean anything.

design · Factorial

Named alongside it

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

Factorial designInteractionAlias structureConfoundingDesign resolutionExperimental designFractional factorialHidden replicationLeast squaresReplicationStudy design

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