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Marijuana and traffic accidents \((1.1)\) Researchers in New Zealand interviewed 907 drivers at age \(21 .\) They had data on traffic accidents and they asked the drivers about marijuana use. Here are data on the numbers of accidents caused by these drivers at age \(19,\) broken down by marijuana use at the same age: \(^{23}\) $$ \begin{array}{llll}{\text { Drivers }} & {452} & {229} & {70} & {156} \\\ {\text { Accidents caused }} & {59} & {36} & {15} & {50} \\ \hline\end{array} $$ (a) Make a graph that displays the accident rate for each class. Is there evidence of an association between marijuana use and traffic accidents? (b) Explain why we can't conclude that marijuana use causes accidents.

Step by step solution

01

Calculate the Accident Rate for Each Group

First, let's compute the accident rate for each group of drivers. The accident rate can be calculated by dividing the number of accidents by the number of drivers in each group. This will help us understand how frequently accidents occur in each class.1. First group: \( \frac{59}{452} \approx 0.1305 \)2. Second group: \( \frac{36}{229} \approx 0.1572 \)3. Third group: \( \frac{15}{70} \approx 0.2143 \)4. Fourth group: \( \frac{50}{156} \approx 0.3205 \)

02

Create a Graph of Accident Rates

To visualize the differences, plot these accident rates on a bar graph. Each bar will represent one group, showing the accident rate for that specific marijuana use category. This visual representation allows us to compare the proportions easily: - Group 1, which had an accident rate of 0.1305. - Group 2, with an accident rate of 0.1572. - Group 3, having an accident rate of 0.2143. - Group 4, exhibiting the highest rate at 0.3205.

03

Analyze the Graph for Association

Examine the graph to determine if there is a pattern or trend that suggests an association between marijuana use and traffic accidents. As we can observe from the graph, the accident rate increases as we move from group 1 to group 4, suggesting a potential association between higher marijuana use and more frequent accidents.

04

Clarify Association vs Causation

Despite observing an association where increased marijuana use correlates with a higher accident rate, we cannot conclude causation. Several factors could influence this relationship, such as reckless behavior, lifestyles, or other substances that might not be controlled in this study. Therefore, association does not imply causation.

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Key Concepts

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

Traffic Accidents

Traffic accidents are unexpected events that can cause damage or injury on the road. They often involve collisions between vehicles or between a vehicle and a pedestrian or object. Understanding traffic accidents is crucial because it helps in developing safety measures.

Several factors contribute to traffic accidents.
These include:

• Driver behavior
• Road conditions
• Vehicle malfunctions

Studying accident rates among different groups of drivers allows us to identify potential risk factors and develop targeted intervention strategies. By collecting data on traffic accidents, we can analyze patterns to find out more about how and why these incidents occur.

Marijuana Use

Marijuana use refers to the consumption of cannabis, a plant-based substance that is often used for recreational or medicinal purposes. The substance is known for its psychoactive effects, which can alter perception, mood, and cognitive function.

When considering marijuana use, it is important to understand its potential impacts on an individual's ability to perform tasks that require attention and coordination, such as driving.

Possible effects of marijuana use include:

• Impaired judgment
• Slower reaction times
• Altered perception of time and distance

These effects can potentially increase the risk of traffic accidents when combined with driving activities.

Association vs Causation

In research, it is important to distinguish between association and causation. An association occurs when two variables seem to be related, or move together in some way, whereas causation implies that one variable directly affects the other. The mistake of assuming causation from an observed association is common.

Here's why you should be cautious:

• **Confounding variables**: Other variables may influence the relationship between your variables of interest.
• **Directionality problem**: You cannot always tell which variable influences the other.
• **Third-variable problem**: A third factor might be affecting both variables in question.

Without thorough research and controlled studies, it is inappropriate to assert that one factor causes another directly. For example, while there might be an association between marijuana use and traffic accidents, we cannot claim that marijuana use causes accidents without considering other factors.

Accident Rate Calculation

Accident rate calculation is a statistical method used to determine the frequency of accidents in a specific group. It helps identify how often accidents occur relative to the number of individuals in the group. Calculating accident rates allows easier comparison across different groups and assessment of risk levels.

Here's how to calculate an accident rate:

• Divide the number of accidents by the total number of drivers in the group.

Using the New Zealand study as an example:

• First group rate: \( \frac{59}{452} \approx 0.1305 \)
• Second group rate: \( \frac{36}{229} \approx 0.1572 \)
• Third group rate: \( \frac{15}{70} \approx 0.2143 \)
• Fourth group rate: \( \frac{50}{156} \approx 0.3205 \)

This method reveals patterns and potential risk factors by highlighting differences in accident rates. Understanding how to compute these rates is pivotal in behavioral studies and policy-making.