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Equation 15 · Part 1 · A Showdown Ladder Rating Measures the Ladder, Not the Player

Symbol X

SEM=SDX1−reliability\mathrm{SEM} = \mathrm{SD}_X\sqrt{1 - \text{reliability}}
XX

What this part means

X is one of the signed contributions combined to compute the quantity on the left.

Its job in the formula

X is one of the signed contributions combined to compute the quantity on the left.

The passage around this formula

Classical Test Theory gives psychometrics its founding decomposition: an observed score X on any single administration of a test equals a true score T — the score a person would get on average across infinitely many parallel administrations — plus measurement error E , so X = T + E , with E assumed to average to zero and to be uncorrelated with T across a population of test-takers [ 4…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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