Lecture 3

Lecture 3 - 1 Properties of hypothesis tests Type I error -...

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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 t-statistic for male wage premium = population value-4.30-3.54-2.79-2.03-1.27-0.52 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 t-test on male premium: 132 observations 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.3 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 t-test on male premium: 330 observations 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.3 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 trade-off 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.

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Lecture 3 - 1 Properties of hypothesis tests Type I error -...

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