Question

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

Randomly assign 24 plants to 6 treatments, ensuring each has 4 plants.

Step-by-step solution

Understanding the Problem

We have 24 tomato plants and need to assign them to six different treatments. Each treatment is a combination of OptiGro fertilizer and watering routines, resulting in 4 plants per treatment.

Listing All Treatments

Identify the treatments by combining the factors. For this problem, assume there are 2 levels of fertilizer (e.g., OptiGro and no fertilizer) and 3 levels of watering routines (e.g., Routine A, Routine B, Routine C). This totals 6 unique treatments.

Preparing for Random Assignment

Create a list or a table to keep track of both the plant numbers (1 to 24) and the six treatments. Each treatment should be represented equally, four times, for the 24 plants.

Using Randomization

Use a method of randomization, such as a random number generator or drawing numbers from a hat, to randomly assign one of the six treatments to each plant number. Ensure that exactly 4 plants end up in each treatment group.

Verification of Random Assignment

After assigning all plants, double-check that each treatment has the correct number of plants (4 plants per treatment). Adjust if necessary to ensure proper randomization and balance.

Key concepts

Two-Factor Experiment

A two-factor experiment is a setup where we investigate the effects of two different factors on a specific outcome. In this particular case, the factors are the use of OptiGro fertilizer and varying watering routines. The primary goal is to see how these two factors interact and influence the growth of the plants. Each factor can have different levels. For example, fertilizer can be applied or not applied, and watering can be done in three distinct routines. This results in several combinations of the two factors, and each unique combination is known as a treatment. Conducting a two-factor experiment helps researchers understand not just the individual impact of each factor, but also how they might work together to affect the outcome. In the exercise, figuring out these combinations, or treatments, is an essential step before moving on to their random assignment.

Random Assignment

Random assignment is a crucial step in experimental design that ensures each subject in the study has an equal chance of being placed into any one of the treatment groups. To achieve this, subjects (in this case, tomato plants) are assigned to their treatments via a method that relies on chance, such as a random number generator or drawing names from a hat. The process works to eliminate researcher biases and other systematic differences. In the context of the exercise, random assignment ensures that the distribution of plants to each of the six treatments is fair and unbiased. It's important because it helps provide a reliable comparison between the treatments without other unforeseen variables affecting the results.

Treatment Groups

Treatment groups are the different combinations of factors that are tested in an experiment, and each group receives a specific combination of the experiment's factors. In the experiment described, there are six treatment groups derived from two levels of fertilizer and three watering routines. Each treatment group receives a unique combination, like OptiGro fertilizer with Watering Routine A. Having well-defined treatment groups allows researchers to observe how specific factor combinations affect the growth of plants. Comparisons between these groups enable conclusions about which combinations are most effective, highlighting possible interactions between factors. For this experiment, ensuring each group has the same number of plants further maintains the study's balance and validity.