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Equation 12 · Part 5 · A Showdown Ladder Rating Measures the Ladder, Not the Player

addition

X=T+EX = T + E
addition

What this part means

Add the term after the plus sign to the term or group before it.

Its job in the formula

Add the term after the plus sign to the term or group before it.

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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Learn the underlying idea

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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Sources cited in the surrounding passage

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