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Chapter 1: Problem 77

Describe an association between two variables. Give a confounding variable that may help to account for this association. People with shorter hair tend to be taller.

Short Answer

Expert verified
The observed association is that people with shorter hair tend to be taller - indicating a negative association between hair length and height. A potential confounding variable in this case could be 'gender' - as generally, men tend to have shorter hair and are typically taller.

Step by step solution

01

Understanding the Variables

Analyze the given statement: 'People with shorter hair tend to be taller.' Here, two variables are given - hair length and height. These are the two variables to be analyzed.
02

Describe the Association

Based on the provided statement, the observed association could be described as: as hair length decreases (or the shorter the hair), the height tends to increase (or people tend to be taller). This indicates a negative relationship or association between the two variables - hair length and height.
03

Give a Confounding Variable

A confounding variable is an external factor that might influence the outcome of the study, or 'confound' the results, hence the name. In this case, a potential confounding variable could be 'gender'. In many societies, men, who tend to be taller on average, also tend to have shorter hair. Therefore, the association that people with shorter hair tend to be taller might actually be influenced by this confounding variable - gender.

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Key Concepts

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

Confounding Variable
A confounding variable is an unseen factor that can distort the perceived relationship between two variables. It acts like an invisible character in a story, quietly influencing the plot without being the main focus. For example, in the association between hair length and height, gender serves as a confounding variable. This is because gender influences both hair length and height independently.

  • Men generally have shorter hair and are taller on average.
  • Women, tend to have longer hair and can vary in height.
Recognizing a confounding variable is crucial, as it helps avoid inaccurate conclusions. It ensures that the real connections are identified, rather than attributing relationships to direct causes that don't exist. It reminds us that underlying factors must always be considered for a thorough analysis.
Negative Relationship
Negative relationship describes a situation where an increase in one variable tends to be associated with a decrease in another. In simpler terms, as one thing goes up, the other comes down. This is seen in the statement, "People with shorter hair tend to be taller".

In our example:
  • As hair length decreases, height seems to increase.
This inverse relationship can occur for various reasons, often highlighting a complex interaction between the variables. But beware! Causation isn't always implied, as seen with the confounding variable here: gender. Hence, understanding negative relationships requires careful examination to avoid misconceptions.
Two Variables
In statistics, two variables are often examined to identify and describe relationships. Variables are characteristics or properties that can take on different values or categories. In our example, the two variables are hair length and height. By observing these variables, we try to find patterns or associations.

  • Hair length could range from short to long.
  • Height could range from short to tall.
Understanding these two variables helps us pose questions about the observed behaviors. Why might shorter hair associate with greater height? What factors might link these observations? By exploring the variables, we work towards finding meaningful connections and insights.

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Most popular questions from this chapter

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