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Chapter 11: Problem 36

On April \(12,1955,\) Dr. Jonas Salk released the results of clinical trials for his vaccine to prevent polio. In these clinical trials, 400,000 children were randomly divided in two groups. The subjects in group 1 (the experimental group) were given the vaccine, while the subjects in group 2 (the control group) were given a placebo. Of the 200,000 children in the experimental group, 33 developed polio. Of the 200,000 children in the control group, 115 developed polio. (a) What type of experimental design is this? (b) What is the response variable? (c) What are the treatments? (d) What is a placebo? (e) Why is such a large number of subjects needed for this study? (f) Does it appear to be the case that the vaccine was effective?

Short Answer

Expert verified
(a) Randomized controlled trial (RCT). (b) Whether a child develops polio. (c) Polio vaccine and placebo. (d) A placebo is a substance with no therapeutic effect. (e) Ensures statistical significance. (f) Yes, fewer cases in the vaccinated group.

Step by step solution

01

Define the Type of Experimental Design

This is a randomized controlled trial (RCT). In an RCT, subjects are randomly assigned to either a treatment group (experimental group) or a control group, allowing researchers to isolate the effects of the treatment.
02

Identify the Response Variable

The response variable in this study is whether a child develops polio or not. It measures the outcome of interest that the study aims to investigate.
03

Determine the Treatments

The treatments in this study are the polio vaccine and the placebo. The experimental group received the polio vaccine, while the control group received a placebo.
04

Explain What a Placebo Is

A placebo is a substance with no therapeutic effect, used as a control in testing new drugs. In this study, the placebo group did not receive the actual vaccine to allow a comparison of outcomes between the two groups.
05

Reason for the Large Sample Size

A large number of subjects are needed to ensure statistical significance. With more subjects, the study results are more likely to be reliable and generalizable to the larger population.
06

Assess the Effectiveness of the Vaccine

To determine if the vaccine was effective, compare the number of polio cases in both groups. In the experimental group, 33 out of 200,000 children developed polio. In the control group, 115 out of 200,000 children developed polio. The lower incidence in the experimental group suggests the vaccine was effective.

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Key Concepts

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

Experimental Design
An experimental design refers to the structured plan for conducting an experiment. It helps researchers to determine the cause-and-effect relationships by manipulating certain variables while keeping others constant. In this context, we鈥檙e looking at a randomized controlled trial (RCT). In an RCT, participants are randomly allocated into different groups to receive varied treatments.
This randomization ensures that the groups are comparable and that any differences observed are due to the treatment itself, minimizing biases. For instance, in Jonas Salk's polio vaccine trial, children were randomly divided into the experimental group, which received the vaccine, and the control group, which received a placebo.
This clear separation allows researchers to isolate the variables and confidently attribute results to the treatment.
Response Variable
The response variable is the main outcome that the study aims to measure. It indicates the impact of the experimental treatment. In the context of the polio vaccine study, the response variable is whether a child develops polio or not.
This binary (yes or no) measurement captures the efficacy of the vaccine. By comparing the response variable across different groups, researchers can assess the effectiveness of the treatment.
For example, if fewer children in the treatment group develop polio compared to the control group, it suggests the vaccine is effective.
Placebo
A placebo is a substance with no therapeutic effect, used as a control in an experimental study. It helps researchers measure the actual effect of the treatment by comparing it to the placebo group.
In Salk's study, the placebo group received a harmless substance instead of the polio vaccine. This group acts as a baseline to measure the vaccine's effectiveness accurately.
If the experimental group (those who got the vaccine) shows significantly better outcomes compared to the placebo group, researchers can confidently attribute those outcomes to the vaccine.
Without a placebo, it would be difficult to distinguish the actual effect of the treatment from other factors.
Treatment Groups
Treatment groups in an experimental study are the groups that receive the different treatments being tested. This is essential for comparing the effects of the treatments under investigation.
In the polio vaccine trial, there are two primary treatment groups: the experimental group and the control group.
鈥� The experimental group receives the new treatment (the polio vaccine, in this case).
鈥� The control group receives the placebo.
By comparing health outcomes between these groups, such as the incidence of polio, researchers can determine the treatment's efficacy.
This careful structuring ensures that the results are valid and reliable, free from external biases.

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Most popular questions from this chapter

Clifford Adelman, a researcher with the Department of Education, followed a cohort of students who graduated from high school in \(1992,\) monitoring the progress the students made toward completing a bachelor's degree. One aspect of his research was to compare students who first attended a community college to those who immediately attended and remained at a four-year institution. The sample standard deviation time to complete a bachelor's degree of the 268 students who transferred to a four-year school after attending community college was \(1.162 .\) The sample standard deviation time to complete a bachelor's degree of the 1145 students who immediately attended and remained at a four-year institution was \(1.015 .\) Assuming the time to earn a bachelor's degree is normally distributed, does the evidence suggest the standard deviation time to earn a bachelor's degree is different between the two groups? Use the \(\alpha=0.05\) level of significance.

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To illustrate the effects of driving under the influence (DUI) of alcohol, a police officer brought a DUI simulator to a local high school. Student reaction time in an emergency was measured with unimpaired vision and also while wearing a pair of special goggles to simulate the effects of alcohol on vision. For a random sample of nine teenagers, the time (in seconds) required to bring the vehicle to a stop from a speed of 60 miles per hour was recorded. $$ \begin{array}{lccccccccc} \text { Subject } & \mathbf{1} & \mathbf{2} & \mathbf{3} & \mathbf{4} & \mathbf{5} & \mathbf{6} & \mathbf{7} & \mathbf{8} & \mathbf{9} \\ \hline \text { Normal, } X_{i} & 4.47 & 4.24 & 4.58 & 4.65 & 4.31 & 4.80 & 4.55 & 5.00 & 4.79 \\ \hline \text { Impaired, } Y_{i} & 5.77 & 5.67 & 5.51 & 5.32 & 5.83 & 5.49 & 5.23 & 5.61 & 5.63 \\ \hline \end{array} $$ (a) Whether the student had unimpaired vision or wore goggles first was randomly selected. Why is this a good idea in designing the experiment? (b) Use a \(95 \%\) confidence interval to test if there is a difference in braking time with impaired vision and normal vision where the differences are computed as "impaired minus normal." Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.
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