stat104_lecture24v1_1up

stat104_lecture24v1_1up - Stat 104: Quantitative Methods...

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Unformatted text preview: Stat 104: Quantitative Methods for Economists Class 24: Hypothesis Testing- Part III 1 Introduction to P-values If P is low, H o must go P-value mantra Other mantras 2 Some people don’t like the rigidness of hypothesis testing- either we accept or reject the null. The P-value is a numerical measure of how much statistical evidence exists. From the P-value, we can make an informed decision about the hypothesis. Hypothesis testing can be difficult since you need to look up cut-off values. The cut-off values depend on if you have lots of data, or just a little, and if the test is two-sided or ne ided. 3 one-sided. P-values (which stand for probability values) are a way to make interpretation of hypothesis tests easier The basic idea is that the farther out in the tails of the distribution the t (test statistic) value is, the more we want to reject . The p-value is just a way of telling people how far out in the tail the t value is. 4 The p-value is the prob of getting something as far or farther out in the tails than the observed t value. Example H H o a o : : μ μ μ μ = ≠ Suppose you were testing Test statistic Reject or Fail to reject How do you feel ? Confident, unsure, just ok 1.05 5 1.94 2.05 10.34 A small p-value indicates that there is ample evidence to support the alternative hypothesis A large p-value indicates that there is little evidence to support the alternative hypothesis P-value Interpretation 6 Less than 0.01 Highly statistical significant Very strong evidence against H o 0.01 to 0.05 Statistically significant Adequate evidence against H o Greater than 0.05 Insufficient evidence against H o Reject Ho small pval reject null P-values and testing: 7 big pval fail to reject the null If P is low, H o must go Example : A random sample of 18 young men (20-30 years old) were asked how many minutes of sports on tv they watched daily. Test to see if the amount watched (on average) is greater than 50 minutes. 8 : o H : a H 9 Hypothesis test results: μ : mean of Variable H : μ = 50 H A : μ > 50 Conclusion ? Example: A low-handicap golfer who uses Titleist brand golf balls observed that his drive on average is 230 yards. Nike has a new golf ball endorsed by Tiger Woods. Nike claims their ball will travel farther than Titleist. To test the claim the golfer hits 100 drives with a Nike ball and measures the distance....
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This note was uploaded on 03/27/2012 for the course STATS 104 taught by Professor Michaelparzen during the Fall '11 term at Harvard.

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stat104_lecture24v1_1up - Stat 104: Quantitative Methods...

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