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Univariate Inferences about a Mean. Shyh-Kang Jeng Department of Electrical Engineering/ Graduate Institute of Communication/ Graduate Institute of Networking and Multimedia. Scenarios. To test if the following statements are plausible
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Univariate Inferences about a Mean Shyh-Kang Jeng Department of Electrical Engineering/ Graduate Institute of Communication/ Graduate Institute of Networking and Multimedia
Scenarios To test if the following statements are plausible A clam by a cram school that their course can increase the IQ of your children A diuretic is effective An MP3 compressor is with higher quality A claim by a lady that she can distinguish whether the milk is added before making milk tea
Tests of Hypotheses Developed by Fisher, Pearson, Neyman, etc. Two-sided One-sided
Origin of the Name “Student” • Pseudonym of William Gossett at Guinness Brewery in Dublin around the turn of the 20th Century • Gossett use pseudonym because all Guinness Brewery employees were forbidden to publish • Too bad Guinness doesn’t run universities
Selection of a • Often chosen as 0.05, 0.01, or 0.1 • Actually, Fisher said in 1956: • No scientific worker has a fixed level of significance at which year to year, and in all circumstances, he rejects hypotheses; he rather gives his mind to each particular case in the light of his evidence and hid ideas
Evaluating Normality of Univariate Marginal Distributions 14
Statistical Significance vs. Practical Significance • The cram school claims that its course will increase the IQ of your child statistically significant at the 0.05 level • Assume that 100 students took the courses were tested, and the population standard deviation is 15 • The actual IQ improvement to be statistically significant at 0.05 level is simply
More Specific Hypotheses • Null hypothesis • Alternative hypothesis
Power • The probability of concluding that the sample came from the H1distribution (i.e., concluding there is a significant difference), when it really did from the H1distribution (there is a difference)
Power vs. Difference of Means power 1 0
Effective Sizes • How many samples are required to validate the following claim of the cram school: • Our course will raise IQ levels of your child by 5 points • statistically significant at 0.05 level, and the type II error is 0.1 • Normal IQ mean is 100, with standard deviation 15 • Sample standard deviation is assumed to be 15, too