Lesson 8: Monsters That Hide in Observational Studies

Lesson 8: Monsters that Hide in Observational Studies

Objective:

Students will learn about confounding factors that may impact the results of an observational study, which is why causation can never be concluded with observational studies, only associations between variables.

Materials:

  1. Computers

  2. Spurious Correlations website (tylervigen.com)

Vocabulary:

cause, confounding factors, associated

Essential Concepts:

Essential Concepts:

Confounding factors/variables make it difficult to determine a cause-and-effect relation between two variables.

Lesson:

  1. Ask students to recall that they looked at the relationship between a student’s GPA and the number of friends that person has on social media during lesson 6. It seemed that students with higher GPAs had more friends than students with lower GPAs. But did this mean that the cause of a person’s GPA is the amount of friends they have? NO!

  2. They also identified other variables that could have contributed to the relationship, these outside variables are called confounding factors. Confounding factors are variables that are related to both the explanatory variable and the response variable in an observational study.

  3. Propose the following statement to students: “Research suggests that a rise in umbrella sales leads to decreased crime rates.”

  4. Allow the students to work in teams to think about possible confounding factors. They should choose a variable that is related to umbrella sales, and that might be lead to decreased crime rates. After they’ve come up with a few possibilities, use the following diagram progression to further explain the impact of confounding factors.

    1. Step 1: Draw an arrow showing that “a rise in umbrella sales leads to decreased crime rates” since that is what researchers have stated.

    2. Step 2: Include the variable that might be related to people buying more umbrellas (i.e., the confounding factor). For example, when the weather is rainy, people buy more umbrellas.

    3. Step 3: Draw an additional arrow from “Weather” to “Crime Rates Down” because it is well known that when the weather is bad, people are less likely to be outside committing crimes.

    4. Step 4: Remind students that the original claim was that “a rise in umbrella sales leads to decreased crime rates”.” However, we’ve now shown that maybe buying umbrellas is not the only thing that could be contributing to a decrease in crime, which makes us question the link between the two variables.

    5. Step 5: Therefore, we have found a confounding factor with the variable “crime rates.” This means we can erase the original “link” between a rise in umbrella sales and decreased crime rates since there are outside variables interfering. We can’t say buying umbrellas causes decreased crime rates, but we can say that a rise in umbrella sales are associated with decreased crime rates.

  5. Once the students grasp what confounding factors are and how to identify them, introduce them to the website Spurious Correlations by Tyler Vigen. This site shows many explanatory and response variables that are randomly associated with each other. Spurious Correlations can be found at: http://www.tylervigen.com/spurious-correlations.

  6. For the example given above, we see that as the US spends more money on science, space, and technology, more people are dying by way of suicide. Clearly, it does not make sense that if the US keeps spending money on science, then more people are going to commit suicide. It simply happened by chance (or a bizarre chain of confounding factors) that the two variables are related to each other.

  7. Allow the students to explore the website on their own (Note: there are multiple pages of graphs, so they are not restricted to simply the homepage). They should choose a graph that interests them and answer the following questions in their DS journals:

    1. What are the two variables shown in your graph?

    2. Is there a positive association or a negative association between the variables?

    3. Write an interpretation of this plot in the context of the data.

    4. Write the data points in a "spreadsheet format" in a form that RStudio could read. Each row should represent a point on the graph, and each column one of the two variables.

    5. By hand, make a scatterplot of the association. Describe whether the association seems strong or weak or moderate to you.

    6. Do you think that the explanatory variable causes the response variable? Explain.

    7. If you answered 'no' to f, then draw a diagram like in #4 with possible confounding factors.

      Note: this can be difficult, depending on the graph chosen. Some factors to consider: weather, economy, fashion trends.

  8. Example answers to Step 7 are given below:

    1. What are the two variables shown in your graph? Total revenue generated by arcades in the US and the number of computer science doctorates awarded.

    2. Is there a positive association or a negative association between the variables? There is a direct relationship because the lines have the same shape (they follow the same pattern).

    3. Write an interpretation of this plot in the context of the data. It seems that as more doctorates are awarded to computer scientists, arcades are generating more revenue.

      Arcade Revenue     CS doctorates

                          1196     861

                          1176     830

      etc.

    4. Answers will vary.

    5. Can you conclude that the one variable causes the other? No. Although the two variables are associated with one another, we do not have evidence to say that more doctorate awards cause arcades to make more money because the data do not come from a controlled experiment.

    6. Draw a diagram like the one we did together earlier (in step 4 of lesson) with possible confounding factors. Student’s diagram should look like the one below:

  9. Once all students have selected a graph and have answered the above questions, have them share their responses with a partner. They should explain why they thought their particular graph was interesting, how the two variables are related (directly or inversely), and whether or not there is a causal link between the variables.

  10. At the end of this lesson, students should understand that causation can only be concluded when an experiment is performed, but associations can be concluded for observational studies.

Class Scribes:

One team of students will give a brief talk to discuss what they think the 3 most important topics of the day were.

Next Day

LAB 3B: Confound it all!

Complete Lab 3B prior to Lesson 9.