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

Fractional factorial — where it appears

A factorial design in which only a stated fraction of the combinations is run, built by setting each extra factor equal to a product of the others. Its columns are still orthogonal, so its coefficients have the standard errors of any design its size; what it gives up is which effect each coefficient belongs to.

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

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 What one lost run costs a 16-run factorial fitting 11 coefficients. Every run is worth the same: dropping any one multiplies every coefficient's variance by 1.2000, which is 1 + 1/(N − p) with N = 16 and p = 11, and gives every pair of coefficients a correlation of 0.1667 where the complete design had exactly zero.

The run that did not happen

Lose one run from any orthogonal design and every coefficient's variance is multiplied by exactly 1 + 1/(N − p), and every pair of coefficients acquires a correlation of exactly 1/(N − p + 1) where there was none. The price is set by the design's spare capacity and by nothing else, and a saturated design cannot survive it at all.

design · Factorial

Named alongside it

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

Experimental designFactorial designLeast squaresStudy designAlias structureBox behnken designCentral composite designConfoundingCorrelationDegrees of freedomDesign resolutionInteraction

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