In Section 13.7 we pointed out that in the chi-square analysis of an r × c table we do not take into account a possible ordering of the rows and/or columns. When the rows and the columns are both ordered, we indicated an alternative to the chi-square analysis in Exercises 14.73 and 14.74 on page 419. When only the rows or only the columns are ordered, we look upon the categories that are not ordered as treatments, and we replace the ones that are ordered by consecutive integers. For instance, in the 3 × 3 table on page 370 we look upon the three cities as three different treatments, and we replace the column headings by 1, –1, and 0, reflecting an ordering from favoring B ( not favoring A) to being indifferent to favoring A. Thus, the sample of size n1 = 400 from Los Angeles consists of 174 ones, 93 minus ones, and 133 zeros; the sample of size n2 = 500 from San Diego consists of 196 ones, 124 minus ones, and 180 zeros; and so on. Looking at the r × c table in this way, we then perform a one- way analysis of variance. Use this method to analyze the 3 × 3 table on page 370, testing the null hypothesis that the treatment effects are all equal to zero at the 0.05 level of significance, and compare the result with that obtained in Exercise 13.79 on page 380.
Answer to relevant QuestionsUse the method of Exercise 15.21 to analyze the 3 × 3 table of Exercise 13.78 on page 380, and compare the result with the result obtained in that exercise. The experiment described in Exercise 15.23 was repeated, with the following results. Combining these data with those of Exercise 15.23, perform an appropriate analysis of variance to test the null hypotheses involving fuels, ...Perform multiple-range tests to characterize the differences among compressor designs and among regions in Example 15.3. Use the 0.05 level of significance. A Latin-square experiment was performed to compare the solder-bond strength of a tin-can body (in pounds force required to break the bond). Five different methods of soldering, involving different fluxes, solders, and solder ...For the two-way analysis of variance with a treatments and b blocks, show that
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