tailieunhanh - INTRODUCTION TO STATISTICS THROUGH RESAMPLING METHODS AND MICROSOFT OFFICE EXCEL phần 5

sau đó chúng ta biết rằng xác suất là 68% một quan sát thực hiện từ một dân số nằm trong độ lệch tiêu chuẩn cộng hoặc trừ một trong những dân số có nghĩa là. Nếu chúng ta có hai mẫu và không chắc chắn cho dù họ đến từ cùng một dân số, một trong những cách để kiểm tra là để thể hiện sự khác biệt trong mẫu có nghĩa là, | CHAPTER 3 DISTRIBUTIONS 83 FIGURE Preparing to estimate difference in population means. 2 3 4 5 6 7 8 9 18 11 12 13 14 15 16 V 18 19 28 2Ĩ Entering data and sample sizes in the BoxSampler worksheet. FIGURE 84 STATISTICS THROUGH RESAMPLING METHODS AND MICROSOFT OFFICE EXCEL . Are Two Variables Correlated Yet another example of the bootstrap s application lies in the measurement of the correlation or degree of agreement between two variables. The Pearson correlation of two variables X and Y is defined as the ratio of the covariance between X and Y and the product of the standard deviations of X and Y. The covariance of X and Y is given by the formula Ân 1 X - X Yk - Ỹ n -1 . Recall that if X and Y are independent the E XY EX EY so that the expected value of the covariance and hence the correlation of X and Y is zero. If X and Y increase more or less together as do for example the height and weight of individuals their covariance and their correlation will be positive so that we say that height and weight are positively correlated. I had a boss more than once who believed that the more abuse and criticism he heaped on an individual the more work he could get out of them. Not. Abuse and productivity are negatively correlated heap on the abuse and work output declines. The reason we divide by the product of the standard deviations in assessing the degree of agreement between two variables is that it renders the correlation coefficient free of the units of measurement. If X -Y so that the two variables are totally dependent the correlation coefficient usually represented in symbols by the Greek letter p rho will be -1. In all cases -1 p 1. Is systolic blood pressure an increasing function of age To find out I entered the data from 15 subjects in an Excel worksheet as shown in Fig. . Each row of the worksheet corresponds to a single subject. As described in Section Resampling Stats was used to select a single bootstrap sample of subjects. That is .