91影视

The changing climate will probably bring more rain to California, but we don鈥檛 know whether the additional rain will come during the winter wet season or extend into the long dry season in spring and summer. Kenwyn Suttle of the University of California at Berkeley and his coworkers carried out an experiment to study the effects of more rain in either season. They randomly assigned plots of open grassland to 3 treatments: added water equal to 20% of annual rainfall either during January to March (winter) or during April to June (spring), and no added water (control). Thirty-six circular plots of area 70 square meters were available (see the photo), of which 18 were used for this study. One response variable was total plant biomass, in grams per square meter, produced in a plot over a year.\(^{35}\) (a) Outline the design of the experiment. What is this type of design called? (b) Explain how you would randomly assign the experimental units to the three treatments. Then carry out your random assignment.

Step by step solution

01

Understand the Experimental Design

The experiment involves three treatments: added water in the winter (January to March), added water in the spring (April to June), and a control group with no added water. The experiment aims to examine the effect of these treatments on plant biomass in grassland plots. This design is a completely randomized design, as plots are randomly assigned to treatments.

02

Determine the Number of Plots per Treatment

Since there are 18 plots used for the study and 3 treatments, each treatment will be assigned one-third of these plots. Dividing 18 plots by 3 treatments gives 6 plots per treatment.

03

Assign Plots Randomly

To randomly assign plots to each of the three treatments, one method is to number the plots from 1 to 18 and use a random number generator or a table of random numbers to assign them to each treatment. First, assign 6 plots to the 'winter' treatment, then 6 to the 'spring' treatment, and finally 6 to the 'control' group.

04

Carry Out the Random Assignment

Using a random number generator, suppose we select the numbers: 1, 3, 5, 7, 9, and 11 for the winter treatment; 2, 4, 6, 8, 10, and 12 for the spring treatment; and 13, 14, 15, 16, 17, and 18 for the control group. Assign these plots to the respective treatments based on these numbers.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Completely Randomized Design

In an experiment, researchers often need to decide how to assign treatments to subjects or experimental units. A completely randomized design is one of the simplest experimental designs. In this setup, all experimental units have an equal chance of receiving any treatment. This randomness ensures that variability in the treatment effect is minimized due to other factors.

This design suits situations where experimental units can be assumed to be similar or where their differences are not critical. It is especially useful when the number of units is evenly divisible by the number of treatments, as seen in the grassland plot study.

• All experimental units (plots in this case) are treated equally, with random allocation to three different water treatments.
• The strength of this design lies in its simplicity and fairness.

This type of design is often contrasted with blocked designs that account for known or suspected sources of variability by grouping similar experimental units.

Random Assignment

Random assignment is a core element of a completely randomized design. It involves randomly allocating experimental units to the available treatments, in this case, different water rainfall patterns.

Why do we randomize? It's crucial to ensure that any differences observed in the results can be attributed to the treatments themselves and not some underlying bias. In the case of the grassland plots, each of the 18 plots has an equal chance of being subjected to any of the three treatments:

• Added water in winter
• Added water in spring
• No added water, which serves as a control

This randomization can be easily achieved using methods like a random number generator, where plots are assigned numbers, and numbers are selected at random for treatment assignment.

Treatment Groups

Within an experimental design, treatment groups are the categories into which subjects are divided to receive different conditions of the experiment. In Kenwyn Suttle's study, there were three treatment groups:

• Winter water addition group
• Spring water addition group
• Control group with no added water

Each group or treatment is designed to test one variable, which in this experiment is the timing of water addition. This helps researchers understand the variable's effect on the response variable, which is the total plant biomass in this scenario.

Treatment groups are essential as they help isolate the specific impact of the experimental conditions.

Response Variable

The response variable is what researchers measure to determine the effect of the treatment. In simpler terms, it's what changes as a result of the treatment being applied. In this experimental context, the response variable is the total plant biomass produced per plot.

Why is plant biomass chosen? It serves as an indicator of how well plants grow under different water addition scenarios. By measuring the biomass, researchers can detect variations induced by the timing and presence of extra water.

• This variable reveals potential differences in growth.
• It helps link the treatment to observable, measurable outcomes.

Understanding the response variable is key for interpreting any experiment, as it provides measurable insights into the effectiveness of the treatments.