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Chapter 12: Problem 28

Tomatoes II The chapter also described a completely randomized two-factor experiment testing OptiGro fertilizer in conjunction with two different routines for watering the plants. Describe a strategy to randomly assign the 24 tomato plants to the six treatments.

Short Answer

Expert verified
Randomly shuffle 24 labeled plants and assign them to 6 treatments equally, 4 plants per treatment.

Step by step solution

01

Understand the Factors and Levels

We have two factors: fertilizer type and watering routine. Let's assume OptiGro has two levels (use and no use), and the watering routine has three levels (routine A, B, and C). This results in a combination of six possible treatments (2 levels for fertilizer \( \times \) 3 levels for watering routine).
02

Identify the Number of Replicates

Given that there are 24 tomato plants and 6 treatments, we need to assign each treatment to the plants equally. Calculate the number of replicas per treatment by dividing the total number of plants by the number of treatments: \( \frac{24}{6} = 4 \). Thus, each treatment will have 4 plants.
03

Label Each Plant

Label each of the 24 tomato plants with a unique identifier, ranging from 1 to 24. This will make it easier to assign treatments randomly.
04

Generate Random Assignment

Use a random number generator or a software tool like Excel to shuffle numbers 1 through 24. Assign the first 4 shuffled numbers to the first treatment, the next 4 to the second treatment, and continue this process until all treatments have been assigned.
05

Assign Treatments to the Plants

Based on the shuffled order, assign each set of 4 plants to one of the six different treatment combinations. For example, if numbers 5, 7, 14, and 20 were first, they receive treatment 1; assign the next group of four numbers to treatment 2, and so forth.

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Key Concepts

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

Random Assignment
Random assignment is a foundational concept in experimental design. It involves allocating subjects or experimental units, like the 24 tomato plants in this exercise, to different groups purely by chance. This process is important because it minimizes bias and ensures that each plant has an equal opportunity to be assigned to any treatment.

The goal of random assignment is to create comparable groups. In our example, once you have labeled the plants from 1 to 24, these numbers are randomly shuffled. You can use tools like a random number generator or software such as Excel. By doing so, each plant's number is randomly assigned to one of the six treatment combinations, ensuring that each treatment is represented equally and fairly.
  • Random assignment helps achieve fairness and balance.
  • It reduces the impact of confounding variables.
  • It's critical for the validity of the experiment's results.
Two-Factor Experiment
A two-factor experiment is an experiment that includes two different independent variables (factors) that can influence the outcome. In this exercise, the two factors are the fertilizer type (OptiGro usage) and watering routine.

Each factor can have different levels. For instance, the OptiGro fertilizer has two levels: use and no use. The watering routine has three levels: routine A, B, and C. The combination of these factors and their respective levels results in the different treatment combinations applied to the tomato plants.
  • Two factors allow you to study the interaction between variables.
  • It helps in understanding if the combination of factors has a different effect than individual factors alone.
  • This setup is more realistic and can offer insights into practical applications.
Replication
Replication in an experiment is the practice of assigning multiple experimental units to each treatment. This ensures that the results are not due to random chance. In the tomato plant experiment, with 24 plants divided into 6 treatments, each treatment is replicated 4 times (four plants each).

Replication increases the reliability of the results as any variations can be observed over multiple trials. It also provides a better estimate of the treatment effect, helping researchers to identify whether a treatment truly influences the outcome or not.
  • Increases reliability and validity.
  • Helps estimate variance and treatment effects accurately.
  • Essential for making statistically sound conclusions.
Treatment Combinations
Treatment combinations in an experimental context refer to the unique configurations of levels within factors that subjects or units receive. In our two-factor experiment, we have 2 levels of fertilizer and 3 levels of watering routines. These combine to form 6 different treatment combinations.

Understanding treatment combinations is critical because it explains how various factors come together to potentially influence the results. For example, one combination might be using OptiGro with watering routine A, while another might be no OptiGro with watering routine C.
  • Each combination provides a unique perspective on factor interactions.
  • Helps in understanding complex interactions between multiple factors.
  • Critical for broad and detailed analysis within experiments.

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Most popular questions from this chapter

Insomnia again Exercises 10 and 22 describe an experiment investigating the effectiveness of exercise in combating insomnia. Researchers randomly assigned half of the 40 volunteers to an exercise program. a) Why was it important to randomize in deciding who would exercise? b) What would be the advantages and disadvantages of using 100 subjects instead of \(40 ?\)

Low-cal dog food A dog food company wants to compare a new lower calorie food with their standard dog food to see if it's effective in helping inactive dogs maintain a healthy weight. They have found several dog owners willing to participate in the trial. The dogs have been classified as small, medium, or large breeds, and the company will supply some owners of each size of dog with one of the two foods. The owners have agreed not to feed their dogs anything else for a period of 6 months, after which the dogs' weights will be checked. a) Identify the treatments, the experimental units, and the response variable. b) Describe a method of assigning treatments if this is to be a randomized block design with size of the breed as the blocking variable. c) Is blinding important in this experiment? Doubleblinding? How could blinding be conducted?

Tomatoes Describe a strategy to randomly split the 24 tomato plants into the three groups for the chapter's completely randomized single factor test of OptiGro fertilizer.

Multiple sclerosis (MS) is an autoimmune disease that strikes more often the farther people live from the equator. Could vitamin D - which most people get from the sun's ultraviolet rays - be a factor? Researchers compared vitamin D levels in blood samples from 150 U.S. military personnel who have developed MS with blood samples of nearly 300 who have not. The samples were taken, on average, five years before the disease was diagnosed. Those with the highest blood vitamin D levels had a \(62 \%\) lower risk of MS than those with the lowest levels. (The link was only in whites, not in blacks or Hispanics.) a) What kind of study was this? b) Is that an appropriate choice for investigating this problem? Explain. c) Who were the subjects? d) What were the variables?

Read each brief report of statistical research, and identify a) whether it was an observational study or an experiment. If it was an observational study, identify (if possible) b) whether it was retrospective or prospective. c) the subjects studied and how they were selected. d) the parameter of interest. e) the nature and scope of the conclusion the study can reach. If it was an experiment, identify (if possible) b) the subjects studied. c) the factor(s) in the experiment and the number of levels for each. d) the number of treatments. e) the response variable measured. f) the design (completely randomized, blocked, or matched). g) whether it was blind (or double-blind). h) the nature and scope of the conclusion the experiment can reach. Depression The May \(4,2000,\) issue of Science News reported that, contrary to popular belief, depressed individuals cry no more often in response to sad situations than non depressed people. Researchers studied 23 men and 48 women with major depression and 9 men and 24 women with no depression. They showed the subjects a sad film about a boy whose father has died, noting whether or not the subjects cried. Women cried more often than men, but there were no significant differences between the depressed and non depressed groups.
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