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A biologist would like to determine which of two brands of weed killer, X or \(Y\), is less likely to harm the plants in a garden at the university. Before spraying near the plants, the biologist decides to conduct an experiment using 24 individual plants. Which of the following two plans for randomly assigning the treatments should the biologist use? Why? Plan A: Choose the 12 healthiest-looking plants. Then flip a coin. If it lands heads, apply Brand X weed killer to these plants and Brand Y weed killer to the remaining 12 plants. If it lands tails, do the opposite. Plan B: Choose 12 of the 24 plants at random. Apply Brand X weed killer to those 12 plants and Brand \(Y\) weed killer to the remaining 12 plants.

Short Answer

Expert verified
Plan B is better due to unbiased randomization, ensuring balanced treatment groups.

Step by step solution

01

Identify Criteria for a Good Experimental Design

In order to decide the better plan for assigning treatments, we need to consider the criteria for a good experimental design: randomization and control. Randomization helps to eliminate bias by ensuring each plant has an equal chance of receiving any treatment. Control ensures that any differences in effects can be attributed to the treatments themselves rather than other variables.
02

Analyze Plan A

In Plan A, 12 healthiest plants are selected first and then a coin flip assigns the weed killers. This could introduce selection bias; the initial choice relies on plant health which is a strong variable that could confound results if either group ends up healthier by chance.
03

Analyze Plan B

In Plan B, 12 plants are selected at random for each treatment. This ensures that the selection process is unbiased and that all plants have an equal opportunity to receive either treatment. Randomly dividing the sample minimizes the influence of any pre-existing differences among the plants.
04

Determine the Better Plan

Plan B is preferred because its random assignment of treatments to plants ensures that each treatment group is likely balanced in terms of plant health, reducing bias and allowing for a clearer attribution of differences in outcomes to the treatments themselves rather than initial differences in plant conditions.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Randomization
Randomization is a crucial element in any experimental design, especially in scientific studies like the one involving weed killers. It involves randomly assigning subjects to different treatment groups to ensure that each subject has an equal chance of receiving any treatment. This process helps to eliminate selection bias, making sure that each group is comparable, and thus, any differences in the outcomes can be attributed to the treatments rather than pre-existing differences among the subjects.
In the biologist's experiment, Plan B exemplifies randomization effectively by choosing 12 plants at random for each treatment group. By doing so, it ensures that the assignment process is unbiased, and every plant, irrespective of its initial health status, could receive either Brand X or Brand Y weed killer.
  • Randomization balances both known and unknown factors across groups.
  • It provides a strong foundation to draw valid conclusions from the experiment.
Considering these advantages, randomization is a powerful tool to enhance the credibility and reliability of experimental findings.
Control in Experiments
Control in experiments refers to the practice of managing all other variables to ensure that the only factor affecting the outcome is the treatment itself. This concept is fundamental to experimental design as it helps establish a clear relationship between the treatment and the observed effects.
In the weed killer experiment, control can be seen as ensuring that both groups of plants experience the same environmental conditions such as sunlight, water, and soil type. This way, any observed differences in plant health can be confidently linked to the effect of the weed killers rather than external factors.
When an experiment has strong control, it becomes easier to assert that the results are due to the treatment. This clarity is pivotal for scientific inquiry.
  • Control helps to isolate the impact of the treatment.
  • It increases the confidence in attributing outcomes to the experimental intervention.
Implementing good control is crucial for producing valid and reliable results.
Bias Reduction in Experiments
Bias reduction is a key objective in experimental designs because bias can skew results, leading to misleading conclusions. There are various forms of bias, such as selection bias and measurement bias, that can affect the results of an experiment.
Plan A in the biologist's study introduces selection bias by picking the 12 healthiest plants, potentially confounding the results since these plants might inherently be more resilient. In contrast, Plan B reduces this bias by randomly selecting plants. This method helps ensure that each treatment group's baseline characteristics are similar, minimizing difference-related biases.
Bias reduction is essential for:
  • Enhancing the reliability of the study results.
  • Ensuring the findings are accurate and applicable to broader contexts.
By proactively designing experiments that account for and minimize bias, researchers can improve the trustworthiness of their conclusions. Focusing on eliminating as many sources of bias as possible is key to any robust experimental setup.

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Most popular questions from this chapter

Identify the experimental units, the explanatory and response variables, and the treatments. A maker of fabric for clothing is setting up a new line to "finish" the raw fabric. The line will use either metal rollers or natural-bristle rollers to raise the surface of the fabric; a dyeing-cycle time of either 30 or 40 minutes; and a temperature of cither \(150^{\circ}\) or \(175^{\circ} \mathrm{C}\). An experiment will compare all combinations of these choices. Three specimens of fabric will be subjected to each treatment and scored for quality.

Identify the experimental units, the explanatory and response variables, and the treatments. Ability to grow in shade may help pines found in the dry forests of Arizona to resist drought. How well do these pines grow in shade? Investigators planted pine seedlings in a greenhouse in either full light, light reduced to \(25 \%\) of normal by shade cloth, or light reduced to \(5 \%\) of normal. At the end of the study, they dried the young trees and weighed them.

Workers who survive a layoff of other employees at their location may suffer from "survivor guilt." A study of survivor guilt and its effects used as subjects 120 students who were offered an opportunity to earn extra course credit by doing proofreading. Each subject worked in the same cubicle as another student, who was an accomplice of the experimenters. At a break midway through the work, one of three things happened: Treatment 1 : The accomplice was told to leave; it was explained that this was because she performed poorly. Treatment 2 : It was explained that unforeseen circumstances meant there was only enough work for one person. By "chance," the accomplice was chosen to be laid off. Treatment 3: Both students continued to work after the break. The subjects' work performance after the break was compared with performance before the break. \({ }^{35}\) Describe how you would randomly assign the subjects to the treatments (a) using slips of paper. (b) using technology. (c) using Table D.

Which of two brands (X or Y) of electric razor shaves closer? Researchers want to design and carry out an experiment to answer this question using 50 adult male volunteers. Here's one idea: Have all 50 subjects shave the left sides of their faces with the Brand X razor and shave the right sides of their faces with the Brand Y razor. Then have each man decide which razor gave the closer shave and compile the results. (a) Identify any flaws you see in the proposed design for this experiment. (b) Describe how you would design the experiment. Explain how your design addresses each of the problems you identified in part (a).

A high school's student newspaper plans to survey local businesses about the importance of students as customers. From an alphabetical list of all local businesses, the newspaper staff chooses 150 businesses at random. Of these, 73 return the questionnaire mailed by the staff. Identify the population and the sample.

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