Directed Acyclic Graph (DAG)

Example of a Spurious Correlation: Chocolate and Nobel Prizes

What term describes a situation where two variables appear to be directly influencing each other, but in reality, their relationship is an illusion usually caused by a confounding variable?

A researcher discovers a strong positive correlation between the number of hours students spend on social media and their reported levels of anxiety. However, further analysis reveals that a third variable—academic workload—independently increases both social media use (as a coping mechanism) and anxiety levels. In this scenario, the original correlation between social media use and anxiety is best described as a spurious correlation.

A researcher discovers a strong positive correlation between a child's vocabulary size and their shoe size. However, further investigation reveals that this relationship exists because older children tend to have both larger vocabularies and larger feet. Match each component of this research scenario to the role it plays in illustrating a spurious correlation.

A researcher discovers a strong correlation between 'Time Spent Gardening' and 'Lower Stress Levels' but suspects the relationship is not causal. Arrange the logical steps of the analysis required to identify if this is a spurious correlation.

A researcher is critiquing a claim that 'Reading Fiction' directly causes 'Increased Empathy.' Upon evaluating the study's Directed Acyclic Graph (DAG), the researcher identifies that 'Openness to Experience' is a common cause for both reading habits and empathy levels. To accurately judge the validity of the original causal claim, the researcher must characterize the observed relationship as a(n) _____ correlation.

Match each term to its correct role in the context of identifying relationships between variables.

When two variables, $X$ and $Y$, have a spurious correlation caused by a confounding variable, $Z$, which of the following best describes the underlying relationship between these variables?

A clinical researcher uses a Directed Acyclic Graph (DAG) to map out a study on the use of a wellness app and reported sleep quality. The DAG indicates that 'baseline health consciousness' is a confounding variable that independently increases both the likelihood of using the app and the practice of good sleep hygiene. Because the app usage and sleep quality are only related through this third variable rather than directly influencing each other, the researcher must identify the unadjusted statistical association between them as a ________ correlation.

A researcher maps a Directed Acyclic Graph (DAG) illustrating that a student's level of parental income independently increases both their access to tutoring and their standardized test scores. If a multiple regression analysis shows that access to tutoring and test scores are strongly correlated before controlling for parental income, but this correlation drops to zero once parental income is included in the model, the researcher must conclude that the initial correlation between tutoring and test scores was a spurious correlation.

A peer reviewer is evaluating a manuscript that claims a direct causal link between a new psychological therapy and reduced depression, based solely on a strong positive correlation. Arrange the logical steps the reviewer should take to critique this claim using a Directed Acyclic Graph (DAG) and ultimately judge the relationship as a spurious correlation.