Chapter 4.2, Problem 80E

(a)

To determine

To explain why a randomized block design would be better than a completely randomized design in this setting.

Explanation of Solution

In this question, the researchers are comparing the weight loss treatments on the subjects. A randomized block design can group the subjects into blocks which have a common characteristics and thus a randomized block design allows us to take into account the change of one or more extra variables. A completely randomized design is only able to take into account the changes of the predictor variables. Thus, a random block design will allow us to take into account the excess weights. That is why a randomized block design would be better than a completely randomized design in this setting.

(b)

To determine

To explain should researchers form blocks of size $\text{4}$ based on the subjects’ last names in alphabetical order or by how overweight the subjects are.

Answer to Problem 80E

The researchers form blocks of size $\text{4}$ based on by how overweight the subjects are.

Explanation of Solution

In this question, the researchers are comparing the weight loss treatments on the subjects. And a randomized block design would be better than a completely randomized design in this setting. A randomized block design can group the subjects into blocks which have a common characteristic and thus a randomized block design allows us to take into account the change of one or more extra variables. Thus we can then best use blocks based on how overweight the subjects are, because the alphabetical order has no interesting characteristics that we want to investigate.

(c)

To determine

To use a technology or Table D to carry out the random assignment required by your design.

Explanation of Solution

In this question, the researchers are comparing the weight loss treatments on the subjects. And a randomized block design would be better than a completely randomized design in this setting. So, we will do the random assignment as:

Firstly, we will form blocks of size 4 based on how overweight the subjects are:

  $\begin{array}{l}\text{BLOCK 1 = Birnbaum, Nevesky, Tran, Wilansky}\\ \text{BLOCK 2 = Brown, Cruz, Jackson, Stall}\\ \text{BLOCK 3 = Loren, Obrach, Rodrigues, Brunk}\\ \text{BLOCK 4 = Kendall, Marm, Santiago, Smith}\\ \text{BLOCK 5 = Deng, Moses, Williams, Hernandez}\end{array}$

Then, every individual in each block should receive a different treatment.

  $\begin{array}{l}\text{A=0,1}\\ \text{B=2,3}\\ \text{C=4,5}\\ \text{D=6,7}\\ \text{Ignore=8,9}\end{array}$

Line $120$ from table D:

  $35476,55972,39421,65850,04266,35436,43742,11937$

Then we obtain (the letter indicates the treatment) as:

  $\begin{array}{l}\text{BLOCK 1 = Birnbaum B, Nevesky C, Tran D, Wilansky A}\\ \text{BLOCK 2 = Brown D, Cruz C, Jackson B, Stall A}\\ \text{BLOCK 3 = Loren B, Obrach C, Rodrigues B, Brunk A}\\ \text{BLOCK 4 = Kendall A, Marm D, Santiago C, Smith B}\\ \text{BLOCK 5 = Deng C, Moses A, Williams B, Hernandez D}\end{array}$