Question

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.

Short answer

Randomly assign 8 plants to each of the three groups using a random number generator, ensuring no plants are repeated across groups.

Step-by-step solution

Understand the Problem

We have 24 tomato plants that need to be split into three equal groups for a completely randomized single factor test of OptiGro fertilizer. This means we will give one group OptiGro A, another group OptiGro B, and the last group no fertilizer.

Determine Group Sizes

Since there are 24 tomato plants and three groups, each group will need to have 8 plants. Thus, our task is to randomly allocate 8 plants per group.

Assign Unique Identifiers

Label each of the 24 tomato plants with a unique number from 1 to 24. This helps in randomizing and tracking to ensure that each selected plant is only assigned to one group.

Random Selection for Grouping

Use a random selection method, such as a random number generator, to select 8 numbers from 1 to 24. Assign the first set of 8 randomly selected numbers to Group 1 (OptiGro A).

Continue Random Selection

Continue with the random selection process to choose another set of 8 numbers from the remaining 16 numbers for Group 2 (OptiGro B).

Finalize Remaining Group

Assign the remaining 8 unselected numbers to Group 3 (No fertilizer). This group will automatically take the last set of numbers not chosen for Groups 1 or 2.

Verify Randomization

Ensure no overlaps between groups and that each plant has been assigned to one and only one group. This verification step ensures complete randomness and coverage of all plants.

Key concepts

Completely Randomized Design

One of the fundamental types of experimental designs is the Completely Randomized Design. This concept revolves around ensuring that every subject or experimental unit has an equal chance of being assigned to any of the treatment groups. In a completely randomized design, like the one used in the tomato plant experiment, randomization is key. The objective is to minimize biases and create comparable groups.

By applying this design to our scenario with tomato plants, we aim to achieve unbiased results when testing the effectiveness of OptiGro fertilizers. The process involves distributing the plants into groups in a manner that's truly random, unconstrained by prior conditions. This blanket randomization means every tomato plant has an identical probability of receiving any of the three treatments, leading to a robust and reliable outcome. Such a design serves as a straightforward yet powerful tool in ensuring the validity of experimental results.

Single Factor Experiment

A Single Factor Experiment investigates the impact of one variable while controlling for others. In essence, it tests how changes in one factor influence the results in an experiment. In our exercise, the single factor under investigation is the type of fertilizer used: OptiGro A, OptiGro B, or no fertilizer. The aim is to observe how each of these treatments affects the growth of tomato plants.

This approach allows for a focused analysis on the specific factor without interference from other variables. By holding all other conditions constant except for the fertilizer type, researchers can confidently attribute differences in plant growth to the fertilizer alone. Hence, a single factor experiment provides a clear view of the effect one specific change has in an otherwise stable environment.

Such a design is particularly advantageous when only a few treatment levels are necessary and is commonly employed in agricultural research to fine-tune crop treatments for optimal growth.

Group Assignment

Group Assignment in experimental design involves distributing subjects into different groups for receiving various treatments. This crucial step ensures that the study's findings are statistically valid and applicable. In the case of the tomato plant experiment, the assignment is executed by labeling each plant with a unique identifier and using a random selection method to allocate them to groups.

There are several ways to ensure effective group assignment. One common practice is:

• Using random number generators to ensure truly random allocation
• Dividing the total number of subjects equally among groups
• Verifying that each subject is only placed in one group

These steps collectively help maintain the integrity of randomization and make certain that the groups are comparable.

Proper group assignment is vital because it prevents selection bias, which can skew results. It ensures that any observed differences between groups can be confidently attributed to the treatment rather than pre-existing conditions.