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Equation 15 · Part 4 · A Showdown Ladder Rating Measures the Ladder, Not the Player

subtraction

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

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Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

Its job in the formula

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

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 ] . From that single axiom the whole apparatus of reliability follows: reliability is the proportion of observed-score variance attributable to true-score variance, and the standard error of measurement, SEM\mathrm{SEM} = SDX\mathrm{SD}_X1−reliability\sqrt{1 - \text{reliability}} , is the quantity that turns a single observed…

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Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

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