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Suppose you grow tomato plants in a greenhouse and sell the tomatoes by weight, so the amount of money you make depends on plants producing a large total weight of tomatoes. You want to determine which of two fertilizers will produce a heavier harvest of tomatoes, fertilizer A or fertilizer \(\mathrm{B}\). There are two distinct regions in the greenhouse: one on the southern side that gets more light and one on the northern side that gets less light. There is room for 20 tomato plants on the southern side and 20 on the northern side. Assume that all the plants are beefsteak tomato plants. a. Identify the treatment and response variables. b. Describe a simple randomized design to test whether fertilizer A is better than fertilizer \(\mathrm{B}\). c. Describe a blocked design to test which fertilizer produces a greater weight of tomatoes, blocking by southern side and northern side of the greenhouse. Explain why creating blocks based on whether plants are on the southern or northern side makes sense. d. Explain why researchers might prefer a blocked design.

Step by step solution

01

Identify Variables

The treatment variables are the fertilizers, A and B. The response variable is the total weight of tomatoes produced.

02

Simple Randomized Design

A simple randomized design can be achieved by randomly selecting half the plants (20 out of 40) to get fertilizer A, and giving fertilizer B to the other half. Relevant steps include: \n1. Number the plants from 1 to 40. \n2. Use a random number generator to select 20 different numbers, corresponding to the plants for fertilizer A. \n3. The remaining plants get fertilizer B. \n4. Compare the total weight of tomatoes produced by the plants using each fertilizer.

03

Blocked Design

For a blocked design, differentiate between the two locations: northern and southern. \n1. Among the 20 plants in the southern side, randomly select 10 to receive fertilizer A and the other 10 to get fertilizer B. \n2. Do the same on the northern side. \n3. Compare the total weight of tomatoes within each side for fertilizers A and B.

04

Justification for Blocked Design

A blocked design is advantageous over a random design in this situation because it considers the locations' differences. The different amounts of light the plants receive on the southern and northern sides of the greenhouse might affect their growth. By controlling this extraneous variable, the researchers can isolate the effects of the fertilizers.

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Key Concepts

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

Treatment Variable

In experimental design, the treatment variable is the factor that researchers want to test to see its effects. Here, the treatment variables are the two fertilizers: Fertilizer A and Fertilizer B. These fertilizers are applied to the tomato plants to investigate which one results in a heavier tomato yield. By focusing on the treatment variable, the study aims to determine how each fertilizer impacts tomato growth.

• Fertilizer A
• Fertilizer B

Understanding the treatment variable helps in setting up the experiment, ensuring only this factor changes while others remain constant.

Response Variable

The response variable is what you measure in an experiment to see the effect of the treatment. In this case, the response variable is the total weight of the tomatoes produced by the plants. This variable shows how effective each fertilizer is in enhancing tomato growth. The response variable is crucial because it provides measurable outcomes, allowing researchers to compare the impacts of Fertilizer A and B.
Thus, in any experiment, clearly defining your response variable will guide your data collection and analysis. It is the key to understanding the effect of the treatment.

Randomized Design

A randomized design is a method used to eliminate bias by randomly assigning treatments to subjects. In the tomato plant experiment, a simple randomized design involves randomly choosing 20 out of the 40 tomato plants to receive Fertilizer A. The remaining 20 plants receive Fertilizer B.

• Number plants from 1 to 40.
• Use a random number generator to pick 20 numbers for Fertilizer A.
• Assign Fertilizer B to the rest.

Randomized designs ensure that each plant has an equal chance of receiving any treatment, helping to control other variables that might affect the results.

Blocked Design

A blocked design is an experiment strategy that groups subjects based on shared characteristics before applying treatments. For this tomato plant study, blocking is done by the greenhouse location—southern or northern sides. Each side has 20 plants with different light exposure, a factor that could influence growth.

• Southern Side: Randomly assign 10 plants Fertilizer A and 10 plants Fertilizer B.
• Northern Side: Do the same assignment.

By blocking, you control variations caused by light differences, allowing clearer observation of the fertilizers' effects. Researchers often prefer blocked designs for more accurate and reliable comparisons.