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Finding the Lurking Variable:  Statistics and Causal Relationships

Finding the Lurking Variable: Statistics and Causal Relationships

Description:

This exercise encourages you to examine a situation or a designed study and identify the "lurking variable" - that is, a factor that might have been overlooked but is important to understanding how it might impact the results.  A variable that is not well accounted for might be confounding - leading those who are studying the issue to be distracted from a better or fuller perspective overall. This is an important skill in inferential reasoning that aids in proper interpretation (and cautious use) of results.  The overarching goal is not only for you to be able to interpret conclusions reported in scholarly and popular literature, but also to be able to explain them clearly to other people.

A confounding factor is a variable not accounted for that correlates with both the independent and the dependent variable in an experiment or study's design.  Identifying possible confounding factors can be very important when designing a study, as they can usually be accounted for. Additionally, as a good statistical consumer, it's important to be able to look at a study that intends to show causation and think about possible lurking variables that distract you from the facts.

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Tutorial

Acknowledgements

Woody Burchett, University of KentuckyThis exercise was  developed by  Woody Burchett,  graduate student and teaching assistant in the Statistics Department, University of Kentucky. A similar activity has been used in STA210: Introduction to Statistical Reasoning which is a component of the University's general education program, UK Core (see more at http://www.uky.edu/UGE/documents/Templates/Statistical.pdf). Successful students who complete this course at UK should be able to articulate how statistical science can be used to address uncertainty in many of our everyday decisions and decide whether a statistical argument (that is used, for example, in the mainstream media) is valid.

Introduction

A causal relationship is very difficult to conclude in anything but a randomized controlled experiment, and one of the reasons is the possible existence of confounding factors or lurking variables.  A confounding factor is a variable not accounted for that correlates with  both the independent and the dependent variables in an experiment of study's design. For example, researchers observe that there is a definite correlation between sale of sunglasses and instances of  drowning deaths.  The researchers conclude that the sale of sunglasses is causing more drowning deaths because people who wear sunglasses sometimes have difficulty seeing and could fall into a pool of water. 

Obviously the researchers' conclusion is not valid.  During the warm seasons, more people purchase sunglasses. Additionally, during the warm seasons more people go swimming, which in turn will lead to more instances of drowning deaths.  The confounding factor or lurking variable in this case is the temperature.

A Freakonomics Movie: Correlation vs Causality:

Watch this short video to see how confounding factors can get in the way. Search the Freakonomics website for other, sometimes hard to believe examples of lurking variable.

Source: http://www.freakonomics.com/videos/#originals search "correlation vs causality"

Activity

In a small group setting or in a virtual group (using  Facebook, Twitter or other social media), discuss the following research study summaries. Brainstorm with your fellow group members the possible confounding factors that could  be present that the researchers did not  take into consideration.

Study #1:  Researchers found that women who don't work during pregnancy tend to have healthier babies.  The conclude that going to work while pregnant can have a harmful impact on the health of the child.

Study #2:  Researchers found that adults going out to eat after 9:00 PM tend to wake up the next morning with headaches more often.  They conclude that restaurants lower theirs standards as the night get later and as a result the consumers don't feel well the next morning.

Study #3:  Researchers looked at countries around the world and found a positive correlation between CO2 emissions and life expectancy. They concluded that carbon dioxide emissions are good for your health.

Study #4:  Researchers found that students who eat breakfast tend to have better test scores than students who don't.  They conclude that eating breakfast makes students better learners.

Conclusion

Inference is the act or process of deriving logical conclusions from premises known (or assumed) to be true. Using critical thinking skills to review and examine that process is an important part of learning in college, and ultimately is an important life-long skill. If you can successfully discuss inference results in the context of an issue at hand, you serve a valuable role in your workplace, your community and the world.

Additional Resources

"Fallacy: Composition" The Nizkor Project. http://www.nizkor.org/features/fallacies/composition.html

Kurland, D. "Inference: The Process." How Language Really Works: The Fundamentals of Critical Reading and Effective Writing. http://www.criticalreading.com/inference_process.htm

Ma, D. "A Case of Restaurant Arson and the Reasoning of Statistical Inference." Introductory Statistics. http://introductorystats.wordpress.com/2011/10/25/a-case-of-restaurant-arson-and-the-reasoning-of-statistical-inference.

Mohanan, K.P. "Rules of Inference," Critical Thinking and Pedagogy. National University of Singapore. http://www.cdtl.nus.edu.sg/ctp/rules.htm.