Chapter7.7 lecture notes - SECTION 7.7 The Operating...

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SECTION 7.7. The Operating Characteristic Curves Bring Table 8 (P.585 and p.586) and Table 3(P574-575). 1. OC CURVE : Graph of L( μ )= P(Accept Ho for mean = μ | sample size=n and α ). . L( μ ) = β ( μ ) if μ is a value for which H 1 is true. = 1- α if μ = μ 0 > 1- α if μ is a value for which H 0 is true. Example: Compute the value of the OC curve for n=4 α =0.05 two sided for μ 0 =6 for the case where μ =12, 6, 0 and σ =4. Using the result P(Z> c) = P(Z< -c) = 1- Φ (c) = Φ (-c) . (1) For μ 1 < μ 0 β = P(Z> [ n( μ 0 - μ 1 )/ σ ] -z α }=P(Z<[ n( μ 1 - μ 0 )/ σ ] +z α })= Φ [Z α -( n|( μ 1 - μ 0 )|/ σ )]}. (2)For μ 1 > μ 0 β = P[ Z < Z α + ( n( μ 0 - μ 1 )/ σ ) ] = Φ [ Z α - n|( μ 1 - μ 0 )|/ σ ] L( μ ) is a function of d= | μ 1 - μ 0 |/ σ = standardized departure from Ho or “effect size ”, n and α wherever μ is a value in H 1 . Note that as d increases L( μ ) decreases for a given n and α . Also note that as n increases L( μ ) decreases for a given d and α and that as α increases L( μ ) decreases for a given n and d Power = P( Reject Ho for mean= μ ) = 1- L( μ ) if μ is a value under which H 1 is true.
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  • Fall '03
  • Mendell
  • Power, Statistical significance, OC, Effect size, OC Curve

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