tailieunhanh - Statistical Methods in Medical Research - part 3

So sánh hai tội Giả sử x1 là một số có thể được giả định theo phân phối Poisson với m1 có nghĩa là. Tương tự như vậy cho x2 là một tính độc lập sau khi phân phối Poisson có nghĩa là m2. Làm thế nào chúng ta có thể kiểm tra giả thuyết rằng m1 Â m2? | 156 Analysing variances Comparison of two counts Suppose that Xi is a count which can be assumed to follow a Poisson distribution with mean Pq. Similarly let x2 be a count independently following a Poisson distribution with mean p2- How might we test the null hypothesis that Pq p2 One approach would be to use the fact that the variance of Xi x2 is Pl p2 by virtue of and . The best estimate of Pl p2 on the basis of the available information is X x2. On the null hypothesis E xi x2 Pj p2 0 and X x2 can be taken to be approximately normally distributed unless Pl and p2 are very small. Hence X1 - x2 z r ự xi x2 can be taken as approximately a standardized normal deviate. A approach has already been indicated in the test for the comparison of proportions in paired samples . Of the total frequency Xi x2 a portion X1 is observed in the first sample. Writing r Xi and n Xi x2 in we have xĩ 4 xi x2 _ Xi - x2 z 5 ự xi -V ự xi x2 as in . The two approaches thus lead to exactly the same test procedure. A third approach uses a rather different application of the X2 test from that described for the 2 X 2 table in the total frequency of Xi x2 now being divided into two components rather than four. Corresponding to each observed frequency we can consider the expected frequency on the null hypothesis to be 4 xi x2 Observed X x2 Expected 4 xj x2 4 X1 2 Applying the usual formula for a X2 statistic we have V1 _ 1 - 2 1 x2 x2 - I Xl x2 2 2 xi x2 I Xl x2 xi - x2 2 ------ X1 x2 As for A2 follows the X 1 distribution which we already know to be the distribution of the square of a standardized normal deviate. It is therefore not surprising that A2 given by is precisely the square of z given by . The third approach is thus equivalent to the other two and forms a particularly useful method of computation since no square root is involved in . Inferences from counts 157 Consider now an estimation problem. What can be said about the ratio .

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