Question

Arsenic is a naturally occurring chemical that can enter groundwater through eroding granite or from a burned forest. A health organization recommends drinking water should contain no more than 10 parts per billion ( ppb ) of arsenic. A company produces filters to clean arsenic from private wells that could be affected by the groundwater.
The company wants to investigate the effectiveness of a new filter compared to that of an older filter. They will test the filters on a field that is bordered on one side by a granite ledge and on the other side by a burned forest. The field is divided into 8 square plots of equal size, and a well to collect groundwater is drilled in the center of each plot. One filter will be used in each well. The following diagram shows the placement of the wells in the field.
The company will use four of each type of filter to conduct the investigation. A randomized block design will be used.

(a) Assuming there is a difference in the effectiveness of the two filters, under what conditions will a randomized block design be better for detecting the difference than a completely randomized design?

(b) Identify the wells, by number, that will be included in each block.

(c) Describe how to assign filters to wells to create a randomized block design.

Answer 1

Answer:

a. Treating side bordered by a granite ledge and side bordered by a burned forest’

As two blocks would bring out the effect of these two factors as also the interaction effect between filter and these two factors, if any.

b. The identification of the wells, by number, that will be included in each block, would be the following:

Adjoining side                       Filter 1                     Filter 2

granite hedge                   Plots 1 and 4          Plots 6 and 8

burned forest                  Plots 2 and 3           Plots 5 and 7

c. The Method to assign filters to wells to create a randomized block design is the follwong:

Take Plot 1, toss a coin and if it turns H, assign the plot to Filter 1, if T to Filter 2

Take Plot 2, toss a coin and if it turns H, assign the plot to Filter 1, if T to Filter 2

Use complimentary assignments for the plots 3 and 4.

Follow the same procedure for plots 4 to 5

Step-by-step explanation:

a. The conditions that a randomized block design be better for detecting the difference than a completely randomized design are the following:

First, if eroding granite and burned forest are likely to have an impact on the arsenic content in the ground water.

In that case, treating side bordered by a granite ledge and side bordered by a burned forest

As two blocks would bring out the effect of these two factors as also the interaction effect between filter and these two factors, if any.

b. The identification of the wells, by number, that will be included in each block, would be the following:

Let the 4 plots adjoining granite hedge be numbered 1 to 4 and the other 4 plots adjoining burned forest be numbered 5 to 8.

Then one of the assignments would be:

Adjoining side                       Filter 1                     Filter 2

granite hedge                   Plots 1 and 4          Plots 6 and 8

burned forest                  Plots 2 and 3           Plots 5 and 7

c. The Method to assign filters to wells to create a randomized block design is the follwong:

Take Plot 1, toss a coin and if it turns H, assign the plot to Filter 1, if T to Filter 2

Take Plot 2, toss a coin and if it turns H, assign the plot to Filter 1, if T to Filter 2

Use complimentary assignments for the plots 3 and 4.

Follow the same procedure for plots 4 to 5