Nhớ lại rằng nếu X và Y là độc lập, E (XY) = (EX) (EY), giá trị kỳ vọng của các hiệp phương sai và do đó mối tương quan của X và Y là số không. Nếu X và Y tăng nhiều hơn hoặc ít hơn với nhau như làm, ví dụ, chiều cao và trọng lượng của cá nhân, hiệp phương sai của mình và sự tương quan của họ sẽ được tích cực để chúng ta nói | CHAPTER 5 DESIGNING AN EXPERIMENT OR SURVEY 131 FIGURE Group-sequential design menu in S SeqTrial. clinical trial. The design and analysis of such experiments is best done with specialized software such as S SeqTrial from http . For example Fig. is the main menu for designing a trial to compare binomial proportions in a treatment and control group with the null hypothesis being p in both groups and the alternative hypothesis that p in the treatment group using an O Brien-Fleming design with a total of four analyses three interim analyses and a final analysis . The resultant output see sidebar begins with the call to the seqDe-sign function that you would use if working from the command line rather than using the menu interface. The null hypothesis is that Theta the difference in proportions . survival probability between the two groups is and the alternative hypothesis is that Theta is at least . The last section indicates the stopping rule which is also shown in the next plot. After 1565 observations split roughly equally between the two groups we should analyze the interim results. At the first analysis if the treatment group has a survival probability that is 10 greater than the control group we stop early and reject the null hypothesis if the treat- 132 STATISTICS THROUGH RESAMPLING METHODS AND MICROSOFT OFFICE EXCEL ment group is doing 5 worse we also stop early and accept the null hypothesis at this point it appears that our treatment is actually killing people there is little point in continuing the trial . Any ambiguous result in the middle causes us to collect more data. At the second analysis time the decision boundaries are narrower with lower and upper boundaries 0 and 5 stop and declare success if the treatment group is doing 5 better stop and give up if the treatment group is doing at all worse. The decision boundaries at the third analysis time are even narrower and at the final time 6260 total .
