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Unformatted text preview: Stat 104: Quantitative Methods for Economists Class 24: Hypothesis Testing Part III 1 Introduction to Pvalues If P is low, H o must go Pvalue mantra Other mantras 2 Some people don’t like the rigidness of hypothesis testing either we accept or reject the null. The Pvalue is a numerical measure of how much statistical evidence exists. From the Pvalue, we can make an informed decision about the hypothesis. Hypothesis testing can be difficult since you need to look up cutoff values. The cutoff values depend on if you have lots of data, or just a little, and if the test is twosided or ne ided. 3 onesided. Pvalues (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 pvalue is just a way of telling people how far out in the tail the t value is. 4 The pvalue 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 pvalue indicates that there is ample evidence to support the alternative hypothesis A large pvalue indicates that there is little evidence to support the alternative hypothesis Pvalue 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 Pvalues 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 (2030 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 lowhandicap 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.
 Fall '11
 MichaelParzen
 PValues

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