Download Confidence Intervals and Hypothesis Tests - Discussion 7 | STAT 371 and more Exams Statistics in PDF only on Docsity! STAT 371 DISCUSSION 7 TA: Lane Burgette Office: 1245F MSC, 1300 University Avenue E-mail: burgette@stat.wisc.edu URL: www.stat.wisc.edu/˜burgette/371.html or naviagate from stat.wisc.edu Office Hours: M 1:15-2:15; T 9:25-10:25 1 Confidence Intervals and Hypothesis Tests Hypothesis tests and confidence intervals are equivalent. If we wish to test the hypothesis that µ1−µ2 = c, where c is some constant (usually zero), and we have a CI of the right size, all we need to do is see if the CI covers c. If it does, then we cannot reject. If it does not cover c, we can reject the null hypothesis. 2 Wilcoxon-Mann-Whitney Test The Wilcoxon-Mann-Whitney test is an alternative to the t-test when the normality assumption is violated. Steps: (1) For each data point in the first group, look at how many data points are less than that point in the second group. Ties count as .5. The sum is K1. (2) Repeat for the second group. This is K2. (3) The observered value of your test statistic Us is the larger of K1 and K2. (4) Use the Table 6 in the text to see if we can reject or not. n is the larger of the sample sizes, and n′ is the smaller. Note that we are given critical values in the table, so if your Us appears in the .05 column, you can still reject. (5) You can check your work, because K1 + K2 = n1n2. If this test has fewer assumptions, why don’t we always use it? 3 Experimental Design An experimental study is one where you can assign the treatments. You don’t have that option with an observational one. It can be impossible to separate out confounded effects with an observational study. Always remember that association does not imply causation. Randomization is necessary for many reasons, but essentially it is a way to smooth over con- founding effects. Consider the following. You are a doctor treating a terminal disease, and you are testing a new procedure, which you think is quite effective. Two patents enter the trial. One looks like a lost cause. The other is in dire need of help, but not quite so bad off. How would you assign treatments you had the choice (ie, you are not randomizing)? How would this affect the outcome of the trial? We use blocking to eliminate some explainable variability. As a researcher, you almost always want to reject the null hypothesis, and the test statistic to do that will look similar to a t-statistic. In particular, you divide by a variance component, so if you can reduce the variability, you will have a better chance of rejecting. 1
