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Equation 15 · Part 5 · A Showdown Ladder Rating Measures the Ladder, Not the Player

subscript

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

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

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

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

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