Name: Experimental Design

Transcription

1 Name: Experimental Design Period: 2001 Number 4 1. Students are designing an experiment to compare the productivity of two varieties of dwarf fruit trees. The site for the experiment is a field that is bordered by a densely forested area on the west (left) side. The field has been divided into eight plots of approximately the same area. The students have decided that the test plots should be blocked. Four trees, two of each of the two varieties, will be assigned at random to the four plots within each block, with one tree planted in each plot. The two blocking schemes shown below are under consideration. For each scheme, one block is indicated by the white region and the other block is indicated by the gray region in the figures. (a) Which of the blocking schemes, A or B, is better for this experiment? Explain your answer. (b) Even though the students have decided to block, they must randomly assign the varieties of the trees to the plots with each block. What is the purpose of this randomization in the context of this experiment? (a) Blocking scheme A is better because it creates homogenous blocks with respects to exposure/proximity to forest. By choosing Blocking Scheme A I am assured that I will have 2 of each type of tree adjacent to the forest. With Blocking Scheme B it is possible that I could have only 1 type of tree adjacent to the forest. Name some reasons why for this experiment I would want to block. The forest could block light; the soil next to the forest could be more fertile; the forest animals are more likely to eat the trees adjacent to the forest. (b) Due to uncontrolled variations in the site, some plots might be better for tree growth. Thus, the purpose for the random assignment is to help equalize the effects of any unknown variables in hopes that they will not confound the results. The site is blocked in acknowledgment of the differences that are the result of proximity to the forest, there is likely to be uncontrolled for differences in moisture content and soil hardness. Hopefully randomization will evenly distribute these differences.

2 2006 B Number 5 2. When a tractor pulls a plow through an agricultural field, the energy needed to pull that plow is called the draft. The draft is affected by environmental conditions such as soil type, terrain, and moisture. A study was conducted to determine whether a newly developed hitch would be able to reduce draft compared to the standard hitch. (A hitch is used to connect the plow to the tractor.) Two large plots of land were used in this study. It was randomly determined which plot was to be plowed using the standard hitch. As the tractor plowed that plot, a measurement device on the tractor automatically recorded the draft at 25 randomly selected points in the plot. After the plot was plowed, the hitch was changed from the standard one to the new one, a process that takes a substantial amount of time. Then the second plot was plowed using the new hitch. Twenty-five measurements of draft were also recorded at randomly selected points in this plot. (a) What was the response variable in this study? Identify the treatments. What were the experimental units? (b) Given that the goal of the study is to determine whether a newly developed hitch reduces draft compare to the standard hitch, was randomization used properly in this study? Justify your answer. (c) Given that the goal of the study is to determine whether a newly developed hitch reduces draft compare to the standard hitch, was replication used properly in this study? Justify your answer. (d) Plot of land is a confounding variable in this experiment. Explain why. (a) The response variable is the draft/energy needed to pull the plow. The treatments are the type of hitch that was used-the standard hitch and the new hitch. The experimental units are the 2 different fields. (b) ization was properly applied because the two hitches, the treatments, were randomly assigned to the fields, the experimental units, which were plowed. (c) Replication was not properly employed. Each treatment was applied to only one experimental unit. For replication to have occurred, the treatments/hitches would need to be used on multiple experimental units/plots of land. (d) The plot of land is a confounding variable in this experiment because differing soil conditions between plots such as rockiness, soil compaction, root growth, and wetness will impact the draft. Thus, we are not able to determine whether the hitch or the plot is creating the differences in the draft. The plot is confounded with the hitch.

3 Test 2009 Form B Question 6 3. Two treatments, A and B, showed promise for treating a potentially fatal disease. A randomized experiment was conducted to determine whether there is a significant difference in the survival rate between patients who receive treatment A and those who receive treatment B. Of 154 patients who received treatment A, 38 survived for at least 15 years, whereas 16 of the 164 patients who received treatment B survived at least 15 years. (a) Treatment A can be administered only as a pill, and treatment B can be administered only as an injection. Is it possible for this randomized experiment to be performed as a double-blind experiment? Give an explanation and the methodology that prevents or permits this experiment to be performed as a double blind experiment. (a) It is possible for the experiment to be performed in a double-blind manner. To be double blind, neither the experimenter nor the subject can know which subjects are receiving which treatment. Both Treatment Groups must be administered both a pill and a shot. Treatment group A will receive a pill marked A that is actual medication and will receive a shot marked A that is a placebo/saline Solution. Treatment group B will receive a pill marked B that is a placebo and a shot marked B that is actual medication. The administrators/ data collectors will only know that a subject is assigned to treatment group A and Treatment group B but will not know who is getting the real medication by shot and who is getting it by pill.

4 Test 2002 Question 2 4. A manufacturer of boots plans to conduct an experiment to compare a new method of waterproofing to the current method. The appearance of the boots is not changed by either method. The company recruits 100 volunteers in Seattle, where it rains frequently, to wear the boots as they normally would for 6 months. At the end of the 6 months, the boots will be returned to the company to be evaluated for water damage. a. Describe a design for this experiment that uses the 100 volunteers. Include a few sentences on how it would be implemented. b. Could your design be double blind? Explain. (a) I would use a matched pairs design such that each participant would be wearing a current method boot and a new method boot. Treatment A: Waterproofing Method on Left boot and new method on Right Boot. Treatment B: Waterproofing Method on Right boot and new method on Left Boot. I would place the 100 names in a hat and mix. The first 50 names would be assigned to treatment group A and the remaining 50 would be assigned to treatment group B. At the end of 6 months I would compare water damage to the boots. What variable did I control for by blocking? I blocked by individual so that each type of boot would be exposed to the same number of rain hours and the same work conditions: person with an indoor job, a person with an outdoor job, a person with a long walk, persons in low lying areas, etc. Why did I randomize? I randomized to help spread out the effects of uncontrolled variables. (b) This could be performed as a double blind experiment such that neither the subject nor the data collector is aware of the treatments imposed. Subjects are assigned to the treatment groups above. Because the appearance of the boots is not affected by the waterproofing methods, neither the subjects nor the boot evaluators would not know which foot had the current method boot and which foot had the new method boot.

5 Besides gender, what would be an additional obvious block that could be used to improve this experimental design and how would I diagram it? Block by Job Type Indoors vs. Outdoor Outdoor Indoor Group B Group A Group B Group A Compare Results Treatment A: Waterproofing Method on Left boot and new method on Right Boot. Treatment B: Waterproofing Method on Right boot and new method on Left Boot. Block by Gender ized Block Design Group 1 Male Group 2 Male Group 3 Female Group 4 Female Treatment 1 Medication Treatment 2 Medication Treatment 1 Medication Treatment 2 Medication Compare Results