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Scales of Measurement

Scales of Measurement. Notation. m( O i ) = our measurement of the amount of some attribute that object i has t( O i ) = the true amount of that attribute that object i has. Ordinal Data. m(O 1 )  m(O 2 ) only if t(O 1 )  t(O 2 )

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Scales of Measurement

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  1. Scales of Measurement

  2. Notation • m(Oi) = our measurement of the amount of some attribute that object ihas • t(Oi) = the true amount of that attribute that object i has

  3. Ordinal Data • m(O1 )m(O2 ) only if t(O1 )t(O2 ) • m(O1 ) > m(O2 ) only if t(O1 ) > t(O2) • That is, there is a positive monotonic relationship between m and t

  4. Interval Data • m(Oi) = a + bXi • b> 0 • That is, the measurements are a positive liner function of the true values. • t(O1 ) ‑ t(O2 ) = t(O3 ) ‑ t(O4 ) if m(O1 ) ‑ m(O2 ) = m(O3 ) ‑ m(O4 )

  5. Ratio Data • a = 0, that ism(Oi) = bXi • that is, there is a “true zero point.” • m(O1 )m(O2 ) = bX1bX2 = X1X2 • we can interpret the ratios of ratio measurements as the ratio of the true magnitudes

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