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

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Statistics and Data Analysis Part 22 – Statistical Tests: 1

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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). 35/42

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

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Power Against a Specific Alternative 37/42

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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 38/42

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Power of a test. power The power of a test (against a specific alternative value) Is a tests ability to detect a false hypothesis Is the probability that.

Power of a test. power The power of a test (against a specific alternative value) Is a tests ability to detect a false hypothesis Is the probability that.

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