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Chapter 1: Problem 107

Causation does not necessarily mean that there is no confounding variable. Give an example of an association between two variables that have a causal relationship AND have a confounding variable.

Short Answer

Expert verified
An example of a causal relationship influenced by a confounding variable is the association between exercise and lifespan, where the exercise (independent variable) seems to cause a longer lifespan (dependent variable). However, the individuals' diet is a confounding variable that could be affecting both the amount they exercise and their lifespan.

Step by step solution

01

Understand Key Terms

An association refers to a relationship between two variables where changes in one variable coincide with changes in the other. Causation implies that one variable is influencing the other, not just associated with it. A confounding variable is an external variable that may be causing the changes in both dependent and independent variables.
02

Identify an Example of Causal Relationship

Let's consider an example where it is observed that individuals who exercise more (independent variable) tend to live longer (dependent variable). This seems to be a causal relationship as exercise is credited with longer lifespan due to its health benefits.
03

Identify a Confounding Variable

In this scenario, a confounding variable could be the individuals' diet. A healthy diet could be a common cause affecting both the individuals' exercise habits and lifespan. This means that while there is an observed association between exercise and lifespan, diet can be a confounding factor influencing both.

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Key Concepts

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

Causation and Association in Statistics
When exploring the dynamics of variables within the realm of statistics, it's crucial to discern the difference between causation and association. These concepts are foundational to understanding how variables interact in a variety of scenarios, such as in scientific research or data analysis.

Causation is a notion that implies a direct influence of one variable on another, demonstrating that changes in the cause lead to effects in the outcome. For example, taking medication (cause) to lower blood pressure (effect) is an illustrative case of causation if scientific research supports that the medication directly leads to the lowering of blood pressure.

Association, on the other hand, simply identifies relationships where variables move together in some pattern, but this linkage does not necessarily infer that one causes the other. Think about the relationship between ice cream sales and drowning incidents: they both tend to rise during the summer months, illustrating an association due to the season, not that one causes the other.
Identifying Confounding Variables
To identify confounding variables, it is essential to look beyond the direct relationship between an independent (predictor) and dependent (outcome) variable. A confounding variable is an outsider that can influence both the independent and dependent variables, thus muddling the perceived association. This external factor may pose as a hidden element that impacts the study, creating the illusion of a direct causal link when there might be none, or it might over- or underestimate the true relationship.

For instance, consider a study investigating the relationship between the amount of time spent studying (independent variable) and scores on an exam (dependent variable). Socio-economic status could be a confounding variable if it influences both how much time a person can dedicate to studying (more resources could translate into more available study time) and the likelihood of scoring higher (access to additional educational resources and environments conducive to learning).
Relationship Between Variables
Delving into the relationship between variables is akin to untangling a web of interconnections where each thread may affect the outcome in different ways. To properly analyze these relationships, one needs to consider the potential for direct and indirect interactions, as well as the impact of confounding variables.

Statisticians use various methods to examine relationships, including correlation coefficients to measure the strength and direction of an association, regression analysis to predict the outcome of a dependent variable based on one or more independent variables, and controlled experiments to isolate and test for causation. It is fundamental, however, to remain cautious, as correlation does not equate to causation, and the presence of lurking variables may obscure the true nature of the relationship.

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Most popular questions from this chapter

Employment statistics in the US are often based on two nationwide monthly surveys: the Current Population Survey (CPS) and the Current Employment Statistics (CES) survey. The CPS samples approximately 60,000 US households and collects the employment status, job type, and demographic information of each resident in the household. The CES survey samples 140,000 nonfarm businesses and government agencies and collects the number of payroll jobs, pay rates, and related information for each firm. (a) What is the population in the CPS survey? (b) What is the population in the CES survey? (c) For each of the following statistical questions, state whether the results from the CPS or CES survey would be more relevant. i. Do larger companies tend to have higher salaries? ii. What percentage of Americans are selfemployed? iii. Are married men more or less likely to be employed than single men?

Spiders regularly engage in spider foreplay that does not culminate in mating. Male spiders mature faster than female spiders and often practice the mating routine on not-yet-mature females. Since male spiders run the risk of getting eaten by female spiders, biologists wondered why spiders engage in this behavior. In one study, some spiders were allowed to participate in these near-matings, while other maturing spiders were isolated. When the spiders were fully mature, the scientists observed real matings. They discovered that if either partner had participated at least once in mock sex, the pair reached the point of real mating significantly faster than inexperienced spiders did. (Mating faster is, apparently, a real advantage in the spider world.) Describe the variables, indicate whether each variable is quantitative or categorical, and indicate the explanatory and response variables.

State whether or not the sampling method described produces a random sample from the given population. The population is adults between the ages of 18 and 22. A sample of 100 students is collected from a local university, and each student at the university had an equal chance of being selected for the sample.

It is well-known that lack of sleep impairs concentration and alertness, and this might be due partly to late night food consumption. A 2015 study \(^{54}\) took 44 people aged 21 to 50 and gave them unlimited access to food and drink during the day, but allowed them only 4 hours of sleep per night for three consecutive nights. On the fourth night, all participants again had to stay up until 4 am, but this time participants were randomized into two groups; one group was only given access to water from \(10 \mathrm{pm}\) until their bedtime at \(4 \mathrm{am}\) while the other group still had unlimited access to food and drink for all hours. The group forced to fast from \(10 \mathrm{pm}\) on performed significantly better on tests of reaction time and had fewer attention lapses than the group with access to late night food. (a) What are the explanatory and response variables? (b) Is this an observational study or a randomized experiment? (c) Can we conclude that eating late at night worsens some of the typical effects of sleep deprivation (reaction time and attention lapses)?

About \(60 \%\) of a child's growth hormone is secreted during sleep, so it is believed that a lack of sleep in children might stunt growth. \(^{63}\) (a) What is the explanatory variable and what is the response variable in this association? (b) Describe a randomized comparative experiment to test this association. (c) Explain why it is difficult (and unethical) to get objective verification of this possible causal relationship.
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