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Unformatted text preview: 1 Properties of hypothesis tests Type I error  size Construct the test statistic t = coefficient/standard deviation for each experiment, and look at frequency with which null is rejected when it is true (by design) This is an empirical measure of the probability of Type I error  the size of the test For male wage premium we reject 4.56% of the time (theoretical value is 5%) Sampling distribution of tstatistic for male wage premium = population value4.303.542.792.031.270.52 0.24 0.99 1.75 2.51 Type II error power Type II error occurs when null is accepted, but alternative is true Probability of Type II error depends on the alternative considered Tests have less power against alternatives which are close to the null Minimising probability of Type II error equivalent to maximising power defined by Power = 1 Prob(Type II error ) Both size and power are related to the probability that H is rejected  leads to idea of power function 2 Hypothesis tests: size and power Accept H Reject H H is true Correct decision Type I error Prob = size H is false Type II error Correct decision Prob = power Graph of power function for ttest on male premium: 132 observations 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.3 0.0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 Rejection probability Power (1%) Power (5%) Power (10%) Power (ideal) Graph of power function for ttest on male premium: 330 observations 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.3 0.0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 Rejection probability Power (1%) Power (5%) Power (10%) 3 Size, power and sample size Finite sample tradeoff between size and power:...
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This note was uploaded on 03/07/2012 for the course ECON 201 taught by Professor Cowell during the Spring '10 term at LSE.
 Spring '10
 Cowell
 Economics

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