Question

Carbon dioxide and tree growth The concentration of carbon dioxide (CO2) in the atmosphere is increasing rapidly due to our use of fossil fuels. Because plants use CO2 to fuel photosynthesis, more CO2 may cause trees and other plants to grow faster. An elaborate apparatus allows researchers to pipe extra CO2 into a 30-meter circle of the forest. We want to compare the growth in the base area of trees in treated and untreated areas to see if extra CO2 does in fact increase growth. We can afford to treat three circular areas.46

(a) Describe the design of a completely randomized experiment using 6 well-separated 30-meter circular areas in a pine forest. Sketch the circles and carry out the randomization your design calls for.

(b) Areas within the forest may differ in soil fertility. Describe a matched pairs design using three pairs of circles that will reduce the extra variation due to

different fertility. Sketch the circles and carry out the randomization your design calls for.

Short answer

Part(a)

Part (b)

Step-by-step solution

Part (a) Step 1. Outline completely randomized design

The treatments are assigned to all the experimental units completely by chance.

The outline of the completely randomized design is shown as follows:

Here the probability of getting the group 1 (or group 2) is given as follows:

$\begin{array}{c}p=\frac{3}{6}\\ =\frac{1}{2}\end{array}$

Part (a) Step 2. Perform Completely Randomized Design

To carry out the completely randomized design, the below-mentioned steps can be followed:

1. Create 6 identical paper slips and mark them with 6 numbers representing the number of circles and place them in a hat.
2. Shuffle the 6 identical paper slips so that the outcome of getting any paper slip is equally likely and unbiased.
3. Draw out 3 paper slips from the hat.
4. Assign the chosen paper slip with the treated one and the remaining 3 in the hat with the untreated one.

Part (b) Step 1. Outline the matched pair design

Matched Pair Design:

Random assignment of treatment to the pair of circles.

The outline of the matched pair design is shown as follows:

Part (b) Step 2. Perform matched pair design

To carry out the matched pair design, the below-mentioned steps can be followed:

1. Create 6 identical paper slips and mark them with 6 numbers representing the number of circles and place them in a hat.
2. Select two paper slips at a time and consider it as a pair and repeat twice.
3. Randomly assign treatment to anyone circle in each pair.