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Suppose you want to compare the effectiveness of the flu vaccine in preventing the flu using one of two different forms: nasal spray versus injection. Suppose you have 60 subjects available of different ages, and you suspect that age might have an effect on the outcome. Assume there are 20 children aged 2 to 15,20 people aged 16 to 30, and 20 people aged 31 to 49 . a. Identify the treatment variable and the response variable. b. Describe a simple randomized design (no blocking) to test the whether the injection or the nasal spray is more effective. Explain in detail how to assign people to treatment groups. c. Describe a blocked design (blocking by age) to test whether the injection or the nasal spray is more effective. Explain in detail how you will assign people to treatment groups. d. What advantage does the blocked design have?

Step by step solution

01

Identify the variables

In this experiment, the treatment variable is the form of the flu vaccine - either nasal spray or injection. The response variable is whether or not the subject contracts the flu after vaccination.

02

Describe a simple randomized design

In a simple randomized design, subjects are randomly assigned to treatment groups. In this case, we can number the participants from 1 to 60, and then use a random number generator to assign each participant to receive either the nasal spray or the injection. We should aim for an equal number of participants for both treatment groups, i.e., 30 participants for the nasal spray and 30 for the injection.

03

Describe a blocked design

In a blocked design, the subjects are divided into blocks or groups before assigning treatments. Here, we can divide the participants into three age groups (blocks): 2-15, 16-30, and 31-49. Then, randomly assign treatments within each block. For example, within the 2-15 age group, 10 children could randomly get the spray and 10 get the injection. Repeat for the other two age groups.

04

Benefits of the blocked design

Block design helps control the variability within each block. In this case, age is a suspected factor that might affect the outcomes of the study. Therefore, blocking by age will control for differences in response due to age, making the comparison between the nasal spray and injection more clear and reliable.

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Key Concepts

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

Randomized Design

In statistics, a randomized design is a fundamental method used to compare treatments under investigation. The primary goal of such a design is to reduce bias and ensure that the treatment groups only differ by the treatment being tested.

When implementing a simple randomized design, each subject is assigned to a treatment group purely by chance. This approach helps to ensure that each group is comparable in terms of unknown or uncontrollable variables. In the context of evaluating flu vaccines, subjects would be randomly divided into two groups: one for the nasal spray and another for the injection treatment.

To execute this effectively in the experiment:

• Assign a unique identifier, such as a number, to each subject.
• Utilize a random number generator to divide subjects into two groups.
• Aim to have an equal number of subjects in each group to maintain balance.

This randomness is crucial as it helps to mitigate the effect of confounding variables that might otherwise skew the results.

Blocked Design

A blocked design is a type of experimental design that groups subjects into 'blocks' based on certain inherent characteristics before treatments are assigned. This method is utilized when there is a known variable, which is likely to influence the response variable, and this variable can be controlled by grouping.

In the context of the flu vaccine study, subjects are grouped into blocks based on age ranges (2-15, 16-30, and 31-49). By blocking subjects by age, researchers can:

• Control for age-related differences that might affect vaccine effectiveness.
• Compare the effectiveness within each age group, thereby reducing age-related variability.
• Enhance the accuracy of comparing the two forms of vaccines by minimizing confounding effects of age.

Within each age block, subjects would then be randomly assigned to receive either the nasal spray or the injection. The randomization continues to play a key role, but within more homogeneous groups.

Treatment Variable

In any scientific study, a treatment variable, also known as an independent variable, refers to the element of the study that is manipulated or changed to observe its effect on the response variable. It's the condition given to the experimental group, while the control group receives the standard condition or a placebo.

In our flu vaccine study, the treatment variable is the form of the vaccine provided — nasal spray or injection. The study is designed to:

• Independently vary the form of the vaccine between subjects.
• Monitor and measure the outcome (response) based on the specific treatment administered.

Identifying the treatment variable is crucial as it sets the stage for the entire experiment and serves as the basis for any causal conclusions drawn.

Response Variable

The response variable, also known as the dependent variable, is the outcome that researchers are trying to explain or predict. It's the effect or result that is observed as a consequence of the treatment variable.

In the flu vaccine example, the response variable is whether or not the subject contracts the flu after being vaccinated. An ideal experimental design will:

• Allow for an unbiased observation of the response variable related to the treatment.
• Enable a clear comparison between different treatment groups.

Documenting the response to the treatment accurately is essential for evaluating the effectiveness of the treatment and for the validity of the experiment's results.