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Statistics and Data Analysis

Statistics and Data Analysis. Professor William Greene Stern School of Business IOMS Department Department of Economics. Statistics and Data Analysis. Part 22 – Statistical Tests: 1. 35/42. The Power of a Test Procedure.

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Statistics and Data Analysis

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  1. Statistics and Data Analysis Professor William Greene Stern School of Business IOMS Department Department of Economics

  2. Statistics and Data Analysis Part 22 – Statistical Tests: 1

  3. 35/42 The Power of a Test Procedure • Power = The probability it will correctly reject a false hypothesis. • A type II error occurs when you fail to reject a false hypothesis. • β = probability of a type II error. (Standard notation in statistics – yes, it does conflict with the standard notation for regression coefficients.) • Power = 1 – β • Power depends on what the true value is (remember, the null is false, so something else is true).

  4. 36/42 Power of the Test of a Mean Rejection region. Probability= 0.025 Rejection region. Probability= 0.025 29745.2 30,000 30254.2

  5. 37/42 Power Against a Specific Alternative

  6. 38/42 Power Function for the test of μ = $30,000 Alternative Power of Test $29,600 .87 $29,650 .77 $29,700 .64 $29,750 .49 $29,800 .34 $29,850 .21 $29,900 .12 $29,950 .07 $30,000 .05 $30,050 .07 $30,100 .12 $30,150 .21 $30,200 .34 $30,250 .49 $30,300 .64 $30,350 .77 $30,400 .87

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