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Hypothesis testing is one of the mainstays of medical research literature. You would be hard-pressed to find a research article in a clinical journal that doesn't contain the results of at least one hypothesis test. So it's important to think critically about hypothesis tests and what they mean--what they can and can't tell us about our data. I've presented three situations below. Write up a brief description of the problem with the conclusion drawn from the hypothesis test. Note that the problem is not in the calculations--assume the calculations are correct--but in the interpretation of the test.
1. In an observational study of the effect of a physician quality reporting system, the mean age of the patients of physicians participating in the program is 72.675 years, while the mean age of the patients of physicians not participating in the program is 72.950 years. The total sample size is nearly 11,000 patients. The p-value for the hypothesis test that the mean ages are different is 0.001 (Null hypothesis: the difference in mean ages of the two groups is zero; alternative hypothesis: the difference in means is greater than or less than zero). The analyst concludes that the patients of physicians not participating in the program are older than the patients of participating physicians and therefore not a good comparison group for an observational study.
2. A 1999 study looked at the effect of exposure to perchlorate on rats' thyroids. 30 rats were exposed to perchlorate and their thyroids were compared to 30 rats not exposed to perchlorates. Two of the rats exposed to perchlorate were found to have a rare type of thyroid tumor. Zero of the rats not exposed to perchlorate had tumors. The experimenters performed a hypothesis test for the difference in number of tumors and got a p-value of 0.48. They concluded that perchlorate exposure does not cause thyroid tumors in rats.
3. Three psychiatrists studied a sample of schizophrenic and non-schizophrenic people. They measured 77 variables for each subject - religion, family background, childhood experiences etc. They wanted to determine what factors cause people to later become schizophrenic. Using their data they ran 77 hypothesis tests of the significance of the differences between the two groups of subjects, and found 2 significant at the 2% level. They immediately published their findings.
We suspect that automobile insurance premiums (in dollars) may be steadily decreasing with the driver's driving experience (in years), so we choose a random sample of drivers who have similar automobile insurance coverage and collect data about th..
Use the Internet to find a website that shows an example or application correlation or regression in the area of your interest or in your profession. Discuss how correlation or regression was used and summarize your finding.
A medical researcher is interested in whether patient's left arms or right arms are longer. if 14 patients participate in this study (so that n left arms and n right arms are measured), how many degrees of freedom should the researcher use in her ..
Why might supposition of normal population be doubtful? Problem arises when?
Predict the final average of a student who made an 83 on the first test. Give the value of r and r squared for this model. Interpret the value of r squared in the context of this problem.
For a normal population with u. = 80 and a = 20 which of the following samples is least likely to be obtained?
Suppose B^0 and B^1(beta hut 0 and beta hut 1) are the least squares estimates of B0 and B1 of the first model. Find the estimates of B0* and B1* in terms of B^0 and B^1.
The next 20% a B, the next 42% a C, the next 18% a D and the bottom 12% an F. What average must you exceed to obtain an A?
Frequently, tests that yield abnormal results are repeated for confirmation. What is the probability that for a normal person a test will be at least 1.5 times as high as the upper limit of normal on two separate occasions?
A drawer contains 11 identical red socks, and 8 identical black socks. Suppose that you choose 2 socks at random in the dark
What is the probability that a randomly selected bag has between 1000 and 1200 chips? What is the probability that a randomly selected bag has fewer than 1000 chips?
Let μ be the hourly wage (excluding tips) for workers who provide hotel room service in a large city. A random sample of a number (more than 30) of such workers yielded a 95% confidence interval for μ of $8.46 to $9.86 using the normal distributio..
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