Freshman Statistics Seminar

Week 3: Correlation and Causation
Ray Dybzinski

Objective:

  • Get students to think deeply about the correlation and causation without necessarily going into their relationship to experimentation, randomization, etc. (that will come in subsequent weeks).

Article Summary:

  • Anon 2006 Breitbart.Com “Alcohol Use Helps Boost Income – Study” Researchers found a “significant” correlation between alcohol consumption (yes/no) and income. Drinkers earned more. What’s interesting is that the majority of the article goes beyond this correlation to posit causation (notice that even the title suggests causation). But the science in this particular study stops at the correlation; all the rest is thinly veiled speculation. The upshot of the speculation is that drinkers tend to socialize more and thus gather “social capital” that they can use to benefit their business transactions.
  • Burgess 2006 Yahoo News “Wealth And Westernisation Drives China To Drink – Expert”

Over the last 20 years, there has been a 10% rise in drinking rates in China. Again, this correlation is the only statistical fact presented; the rest is thinly veiled speculation regarding causation and associated correlations. The upshot of the speculation is that wealth has created disposable income, some of which tends to get spent on alcohol, and that the Chinese are adopting western behaviors (e.g. drink without food).

Suggested Lesson Structure:

  • Students should have read the articles before class.
  • Discuss the papers.
  • Experiment with the Gap Minder website (see Active Learning Modules below).

Discussion Points:

  • Except for one line in the China article (“Economic development was also leading to cultural changes. ‘In business, alcohol can be used to improve the relationship — so it forces you to drink a lot,’ he said”), the two articles look at the same correlation and posit causation in opposite ways. The Income articles posits “drinking leads to wealth” while the China article posits “wealth leads to drinking”. This should give students pause!
  • Encourage students to speculate further – what other reasons might underlie the observed correlations? In each of the cases presented in the two articles, can they make a case for causation going the other way?
  • Importantly, in both cases the drinking and the wealth may be caused by some other factor. The classic example of this is that the murder rate goes up with average daily temperature and ice cream sales go up with average daily temperature. Thus, there is a correlation between the murder rate and ice cream sales even though they have no direct causal relationship! In the case of drinking and wealth, ask students to come up with other unmeasured factors that might explain the correlation.

Active Learning Modules:
Gap Minder website: http://www.gapminder.org/

  • The Gap Minder website allows students to instantly correlate a host of interesting statistics among nations. Web-savvy students should probably have little trouble figuring out how to “work” it, but you may want to point out the difference between linear and log scales. A correlation may be apparent with one scale but not the other.
  • On the board, make categories for students to record interesting findings. Suggestions would be,
    • “unexpected, but likely not causal correlation” (e.g. number of girls compared to boys in school versus life expectancy)
    • “unexpected, but plausibly causal correlation” (e.g. number of girls compared to boys in school versus children per woman)
    • “notable outliers” (e.g. in a graph of child mortality versus life expectancy, watch Rwanda from 1988 to 1998 – its outlier status stems from the genocide there.)

Perhaps allow student to add their own categories if they want to! Explain that you will leave some time at the end of class to discuss their findings.

  • During the wrap-up discussion, continue to separate the phenomenon of correlation with that of causation using the correlations that they wrote on the board. As in the alcohol versus wealth discussion, have then try to make a case for causation in either direction or for correlation with some unmeasured third factor. Leave them with the mantra – “correlation does not imply causation!”

Additional Links:

Alcohol use helps boost income – A study

Wealth and Westernization Drives China to Drink