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Chapter 1: Problem 64

We give a headline that recently appeared online or in print. State whether the claim is one of association and causation, association only, or neither association nor causation. Daily exercise improves mental performance.

Short Answer

Expert verified
The claim in the headline 'Daily exercise improves mental performance' implies both association and causation. Therefore, the correct answer is 'association and causation'. Note that whether this claim is scientifically accurate is another matter that would require further evidence and understanding.

Step by step solution

01

Identify the Events in the Claim

In the headline 'Daily exercise improves mental performance', there are two events - 'daily exercise' and 'improved mental performance'.
02

Evaluate the Presence of Association

The claim suggests that these two events occur together. That is, when daily exercise happens, mental performance improves. So there is an association between the two events.
03

Assess if there is Causation

The headline implies that the 'daily exercise' causes the 'improved mental performance'. This means, according to the claim, the improved mental performance is a result of the daily exercise. Therefore, there is causation as per the claim.

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Key Concepts

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

Statistical Analysis
Statistical analysis involves examining a dataset as a whole to identify relationships and trends. In the context of the headline 'Daily exercise improves mental performance', statistical analysis would mean collecting data on individuals who exercise daily and those who do not, then comparing their mental performance outcomes.
To do this effectively, researchers can use methods like:
  • Averages: Determine the average mental performance scores across groups.
  • Variance: Analyze the variability in mental performance within each group.
  • Regression analysis: Examine how daily exercise statistically predicts mental performance, controlling for other variables.
This analysis helps identify whether a significant pattern or trend exists between daily exercise and mental performance.
Data Interpretation
Data interpretation is about making sense of data results, drawing logical conclusions about what's likely happening in the real world. When interpreting data on daily exercise and mental performance, we look beyond numbers to understand the practical significance.
For example, if statistical analyses show higher mental performance scores among those who exercise daily, the interpretation might suggest benefits related to physical activity. However, several factors can influence these results:
  • Sample size: Larger samples improve confidence in the findings.
  • Confounding variables: Other factors (e.g., diet, sleep) might affect mental performance.
  • Measurement accuracy: Ensuring accurate and reliable measures of exercise and performance.
Proper interpretation considers such factors, leading to a deeper understanding of the relationship between exercise and mental performance.
Causal Relationship
A causal relationship is a direct link where one event causes another to happen, beyond coincidental association. In the example provided, the claim suggests daily exercise leads to improved mental performance, implying a causal link.
However, establishing causation requires more than observing association:
  • Controlled experiments: Randomized controlled trials explicitly determine causality by eliminating confounding variables.
  • Temporal precedence: Exercise must be shown to occur before improvements in mental performance.
  • Consistency: Repeated studies across various settings should find similar results.
Without these rigorous tests, a headline like this remains an association at best. Only through careful study can researchers confidently assert that daily exercise truly causes enhanced mental performance.

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Most popular questions from this chapter

In Exercise \(1.17,\) we ask whether experiences of parents can affect future children, and describe a study that suggests the answer is yes. A second study, described in the same reference, shows similar effects. Young female mice were assigned to either live for two weeks in an enriched environment or not. Matching what has been seen in other similar experiments, the adult mice who had been exposed to an enriched environment were smarter (in the sense that they learned how to navigate mazes faster) than the mice that did not have that experience. The other interesting result, however, was that the offspring of the mice exposed to the enriched environment were also smarter than the offspring of the other mice, even though none of the offspring were exposed to an enriched environment themselves. What are the two main variables in this study? Is each categorical or quantitative? Identify explanatory and response variables.

What Percent of Young Adults Move Back in with Their Parents? The Pew Research Center polled a random sample of \(n=808\) US residents between the ages of 18 and 34 . Of those in the sample, \(24 \%\) had moved back in with their parents for economic reasons after living on their own. \(^{26}\) Do you think that this sample of 808 people is a representative sample of all US residents between the ages of 18 and \(34 ?\) Why or why not?

State whether or not the sampling method described produces a random sample from the given population. The population is all people who visit the website CNN.com. All visitors to the website are invited to take part in the daily online poll.

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.

State whether or not the sampling method described produces a random sample from the given population. Take a random sample of one type of printer and test each printer to see how many pages of text each will print before the ink runs out. Use the average from the sample to estimate how many pages, on average, all printers of this type will last before the ink runs out.
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