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An agriculture researcher wants to compare the yield of 5 corn varieties: A, B, C, D, and E. The field in which the experiment will be carried out increases in fertility from north to south. The researcher therefore divides the field into 25 plots of equal size, arranged in 5 east–west rows of 5 plots each, as shown in the diagram. (a) Explain why a randomized block design would be better than a completely randomized design in this setting. (b) Should the researcher use the rows or the columns of the field as blocks? Justify your answer. (c) Use technology or Table D to carry out the random assignment required by your design. Explain your method clearly.

Short Answer

Expert verified
A randomized block design reduces fertility-related variability. Rows should be used as blocks to match fertility gradient. Randomly assign varieties within each row.

Step by step solution

01

Understanding Randomized Block Design

A randomized block design is used to account for variability that arises from different conditions in different parts of a study area. By grouping similar experimental units (plots in this case) together into blocks, extraneous variation is controlled and variability among treatment effects becomes more evident. In fields where fertility changes from north to south, a randomized block design can more effectively compare corn varieties by eliminating fertility as a confounding variable.
02

Deciding Between Rows or Columns for Blocking

Given that the fertility gradient runs from north to south, it means the difference in fertility across the field is primarily from one side to another, not top to bottom. Therefore, using rows as blocks is more appropriate because each block (row) will experience similar fertility conditions. This ensures that differences in yield can be more confidently attributed to the corn variety rather than differences in soil fertility.
03

Random Assignment within Blocks

Random assignment within each block (row) ensures each corn variety is placed randomly within that block to control for any minor soil variation. Use Table D or a random number generator to assign the varieties (A, B, C, D, E) to the 5 plots in each row, ensuring each variety appears exactly once in each row. This can be done by generating random permutations for numbers 1 through 5 and mapping each to a variety.

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Key Concepts

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

Agricultural Experimentation
Agricultural experimentation plays a pivotal role in the continuous enhancement of farming practices and crop yield. It involves systematically testing various agricultural methods or varieties to determine the most efficient, productive options. In the context of the exercise, the researcher is testing different varieties of corn to ascertain which yields best results under specific field conditions.

To ensure the reliability of results, it is essential to consider the environment where the experiment is carried out. Factors like field fertility and weather conditions can significantly influence outcomes. Consequently, agricultural experiments like this one are designed with consideration for these environmental influences to ensure findings accurately reflect the performance of the tested variables rather than natural variations.

By using a random block design, the researcher takes into account the natural north-to-south fertility gradient of the field, which could otherwise skew results if not appropriately controlled.
Experimental Design
Experimental design is a cornerstone of scientific inquiry, and in agricultural research, it ensures that the study is structured to yield reliable conclusions. The choice of design is crucial in managing variables that could affect the results. In this exercise, a Randomized Block Design is chosen over a Completely Randomized Design.

  • The randomized block design groups similar experimental units into blocks (here, rows) to neutralize variability within the block.
  • It enhances the ability to detect the true effects of the treatments by reducing the noise created by potential confounding variables, such as soil fertility.
  • The alignment of blocks with rows in this context helps control variability due to the known fertility gradient across the field.
This thoughtful arrangement within the experimental design improves the accuracy of comparing the corn varieties, leading to more conclusive results about which variety performs best in each block.
Confounding Variable Control
Confounding variables are extraneous factors that could influence the outcome of an experiment. In agricultural studies, these might include sunlight, soil fertility, or irrigation differences. Proper control of these variables is vital to ensure that the observed effect can confidently be attributed to the experimental treatment and not to other influences.

In the given scenario, soil fertility is a significant confounding variable because it varies predictably from north to south. To mitigate this, the researcher opts for a randomized block design, which aims to control this variation by:
  • Dividing the field into blocks (rows) that are more uniform in terms of fertility.
  • Randomly assigning treatments within these blocks to ensure that each treatment appears once in every block.
By doing this, the impact of soil fertility is controlled across treatments, allowing the researcher to more accurately assess the effect of different corn varieties on yield. Successfully controlling for confounding variables ensures the integrity of experimental results and the validity of the conclusions drawn.

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Most popular questions from this chapter

Identify the experimental units or subjects, the explanatory variables (factors), the treatments, and the response variables. How can we reduce the rate of refusals in telephone surveys? Most people who answer at all listen to the interviewer’s introductory remarks and then decide whether to continue. One study made telephone calls to randomly selected households to ask opinions about the next election. In some calls, the interviewer gave her name, in others she identified the university she was representing, and in still others she identified both herself and the university. For each type of call, the interviewer either did or did not offer to send a copy of the final survey results to the person interviewed. Do these differences in the introduction affect whether the interview is completed?

A department store mails a customer satisfaction survey to people who make credit card purchases at the store. This month, 45,000 people made credit card purchases. Surveys are mailed to 1000 of these people, chosen at random, and 137 people return the survey form. Identify the population and the sample.

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The Brigham Young University (BYU) statistics department is performing experiments to compare teaching methods. Response variables include students’ final-exam scores and a measure of their attitude toward statistics. One study compares two levels of technology for large lectures: standard (overhead projectors and chalk) and multimedia. There are 8 lecture sections of a basic statistics course at BYU, each with about 200 students. There are four instructors, each of whom teaches two sections.\(^{44}\) Suppose the sections and lecturers are as follows: (a) Suppose we randomly assign two lecturers to use standard technology in their sections and the other two lecturers to use multimedia technology. Explain how this could lead to confounding. (b) Describe a better design for this experiment.

At a party there are 30 students over age 21 and 20 students under age 21. You choose at random 3 of those over 21 and separately choose at random 2 of those under 21 to interview about attitudes toward alcohol. You have given every student at the party the same chance to be interviewed: what is the chance? Why is your sample not an SRS?

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