Supplementary Exercise 9.40 of IPS7e ------------------------------------ Many solutions are possible, and they are all valid (provided the table indeed shows no association). The simplest, but not too interesting examples are when all counts of the table are identical. Only slightly more interesting are situations where the three rows (or columns) are identical. In such cases, it is obvious that the marginal and conditional distributions are the same. Further complicated again are tables where the numbers of the second row are twice those of the first row, and the third row twice those of the second row. For example, 5 10 25 10 20 50 20 40 100 Also here it is intuitively obvious that the marginal and conditional distributions are the same. One could also compute the expected values for each cell and check that they are equal to the observed values. For example for cell (1,1): e11 = 40*35/280 = 5, where - the sum of the first row = 40 - the sum of the first column = 35 - the total sum = 280. Any table where all the rows are multiples of the first row (say), has no association between row and column variables.