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Chapter 9: Problem 9

Over the past 50 years, there has been a strong negative correlation between average annual income and the record time to run 1 mile. In other words, average annual incomes have been rising while the record time to run 1 mile has been decreasing. (a) Do you think increasing incomes cause decreasing times to run the mile? Explain. (b) What lurking variables might be causing the increase in one or both of the variables? Explain.

Short Answer

Expert verified
(a) No, rising incomes likely don't cause faster mile times. (b) Lurking variables include sports science advancements and economic growth, affecting both variables.

Step by step solution

01

Define the Relationship

A negative correlation between average annual income and record time to run 1 mile indicates that as one variable increases, the other decreases. Hence, as incomes have risen, the time to run a mile has reduced.
02

Assess Causation

Correlation does not imply causation. Just because there is a pattern between rising incomes and decreasing mile times, it doesn't mean increasing income causes faster mile times.
03

Identify Lurking Variables

Lurking variables that might explain both phenomena include improvements in sports science and healthcare, leading to better athletic performance, and broader economic growth, leading to higher incomes. Other potential variables include advancements in training techniques and increased funding for athletic programs, which can influence both income and performance.
04

Conclude Analysis

Given the identified lurking variables, the decrease in mile times and rise in incomes likely happen concurrently due to overall societal improvements rather than one causing the other.

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Key Concepts

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

Correlation vs Causation
In statistics, understanding the difference between correlation and causation is crucial. Correlation refers to a relationship or connection between two variables where they tend to occur together. For instance, in our exercise, average annual incomes and mile running times have a strong negative correlation. This means as income has increased, the time it takes to run a mile has decreased.

However, this doesn't mean one causes the other. This is where causation comes in. Causation implies that one event is the result of the occurrence of the other event; in simple terms, it means one event is a consequence of another. Just because two variables show a consistent pattern together, it doesn鈥檛 guarantee that one directly influences the other.
  • Correlation = Association
  • Causation = Cause-and-Effect
Think of this as a reminder that statistics require careful interpretation, and not all relationships are direct or causal.
Lurking Variables
Lurking variables can sometimes obscure the real story behind the data. These are hidden variables that affect both the independent and dependent variables in a study, leading observers to a false conclusion.

In the discussed exercise, there might be several lurking variables influencing the changes in both average incomes and mile-running times. Advances in sports science, better healthcare, and improved athletic training are just a few examples of factors that could lead to better athletic performance and economic prosperity simultaneously. These variables improve people鈥檚 capacity to earn more while also enhancing physical capabilities by offering better training and nutrition.
Understanding these hidden variables can help to avoid incorrect assumptions that one variable necessarily causes changes in another.
Statistical Analysis
Statistical analysis involves gathering, reviewing, and interpreting data to uncover patterns and trends. It's essential for drawing valid conclusions and making informed decisions.

For our scenario of annual incomes and mile-running times, proper statistical analysis would involve identifying factors beyond the obvious. This includes looking for patterns over time, considering data collection methods, and accounting for additional context like economic trends and societal developments.
Statistical analysis helps clarify whether correlations might represent causation or are simply coincidental. By scrutinizing a broader dataset and considering all potential variables, analysts can provide evidence-based conclusions and avoid misleading results.

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Most popular questions from this chapter

What is the symbol used for the population correlation coefficient?

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