# hw1a - Solutions to Assignment 1 Stat 512 Spring 2010...

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Solutions to Assignment 1 Stat 512, Spring 2010 Grading policy: In general, each homework problem in Stat 512 is worth 5 points. 1. (a) This is an experimental study, because the treatment factor (curriculum) was ran- domly assigned to classrooms. (b) A nice way to envision this design is by the following table. Computer Standard School 1 Sec 1, Sec 2 Sec 1, Sec 2 School 2 Sec 1, Sec 2 Sec 1, Sec 2 School 3 Sec 1, Sec 2 Sec 1, Sec 2 The factors are school (3 levels) curriculum (2 levels, crossed with school) section (2 levels, nested within cells of high school × curriculum) One could also call student a factor with 24 levels, nested within section. Some might say that Section has four levels, because there are four sections per school. But it is more correct to say that Section has two levels, because there are two sections per school-curriculum combination. (c) This is a randomized complete block design, with schools as blocking factor. (d) Unit of randomization is section; unit of observation is student. 2. In a CR design, units are assigned to treatments completely at random. In an RCB design, units are grouped into homogeneous blocks, and within each block they are assigned to treatments at random. In this example, a balanced CR design would assign half of the subjects to Compound X and half to Lipitor without regard for the sites. On average, we would expect to get 10 subjects receiving Compound X and 10 subjects receiving Lipitor in each site. However, because we have left it up to chance, the probability of obtaining a perfectly balanced outcome would be slim. An RCB design would randomly assign 10 subjects to Compound X and 10 subjects to

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hw1a - Solutions to Assignment 1 Stat 512 Spring 2010...

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