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Unformatted text preview: Introduction to Hypothesis Testing 9 of 14 Tells us the likelihood of supporting a true alternative hypothesis (making the correct decision). Good tests have powers of at least 0.8-0.9. Generally not simple to calculate, depends on (1) level, (2) sample size, (3) effect size, (4) specific test being used, (5) variance in population, ... Before doing a study to support a hypothesis: you should determine the minimum effect size you wish to detect and the desired power, then calculate the required n . If we fail to reject the null hypothesis there are 3 possibilities: 1. The null hypothesis is true, there is no true effect. (Must calculate to support this conclusion.) 2. The study design is too weak to detect a true alternative hypothesis (true effect). 3. The study had a good power, but random chance (sampling error) pre- vented us from rejecting a true alternative hypothesis. Importance of Power Analysis: Before conducting a study, we need to ensure that the sample size is large enough so it will be likely that we can actually detect a true alternative hy- pothesis. If the study design is too weak, the alternative hypothesis may be true but it is unlikely that we would be able to detect this. To determine the sample size n we must decide what is the minimum effect size difference from the null hypothesis that we are interested in detecting. 1.3 Single sample proportion test USE Often used to help answer: 1. Is the proportion of a population equal to p ? Is the proportion of people who smoke 20%? 2. Is the proportion of a population different than p ? Is the proportion of people who smoke more than 20%? Is the proportion of contaminants in the water below the EPA standard? COMPUTATION Single sample proportion test. Definition 1.8 To support an alternative hypothesis concerning a population propor- tion: requirements (1) simple random sample, (2) binomial distribution, (3) normal approximation of binomial np, nq 5....
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This note was uploaded on 02/10/2012 for the course MAT 1670 taught by Professor Tanbakuchi during the Spring '11 term at University of Florida.
- Spring '11