Correlation Versus Causation

The Lesson Activities will help you meet these educational goals:

·  Mathematical Practices—You will construct viable arguments and analyze the reasoning of others.

·  21st Century Skills—You will use critical-thinking and problem-solving skills , assess and validate information, and communicate effectively.

Directions

You will evaluate some of these activities yourself, and your teacher may evaluate others. Please save this document before beginning the lesson and keep the document open for reference during the lesson. Type your answers directly in this document for all activities.

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Self-Checked Activities

Read the instructions for the following activities and type in your responses. At the end of the lesson, click the link to open the Student Answer Sheet. Use the answers or sample responses to evaluate your own work.

1.  Interpreting Statements

As a part of your training, your editor has asked you to analyze these news headlines:

1.  Does your neighborhood cause schizophrenia?

2.  Keeping a food diary doubles weight loss, study says

3.  Mother’s diet can help determine the sex of child

4.  TV raises blood pressure in obese kids

5.  A surprising secret to long life: Stay in school

6.  Chocolate really does make us feel better

7.  Facebook users get worse grades in college

a.  Identify the causal variable and the response variable in each statement. The first statement has been analyzed as an example.

Sample answer:

Causal Variable / Response Variable
1.  the neighborhood you live in / getting (or not getting) schizophrenia
2.  maintaining a food diary / doubling weight loss
3.  mother’s diet / sex of the child
4.  time obese kids spend watching TV / a rise in blood pressure
5.  time spent at school / having a long life
6.  eating chocolate / positive health or mood effect
7.  time student spends on Facebook / student’s grades

b.  List some of the categorical variables in the statements and the values they might take.

Sample answer:

Variable: the neighborhood you live in; Values: high-income, middle-income, low-income or urban, suburban, exurban, rural

Variable: getting schizophrenia; Values: yes, no

Variable: maintaining a food diary; Values: yes, no

Variable: Doubling weight loss (or increased weight loss); Values: yes, no

Variable: mother’s diet; Values: low-energy, high-energy

Variable: sex of the child; Values: male, female

Variable: eating chocolate; Values: yes, no

Variable: mood; Values: positive, neutral, negative

c.  List some of the possible quantitative variables in the statements and the units that can be used to measure them.

Sample answer:

Variable: time spent watching TV; Unit: hours

Variable: time spent at school; Unit: years

Variable: time spent on Facebook; Unit: hours

Variable: rise in blood pressure; Unit: millimeters of mercury (mmHG).

Variable: having a long life; Unit: years

2.  Analyzing and Evaluating Statements

In the second step in your training, your editor asks you to evaluate news articles so you can summarize and include them in your publication. Read these articles, and then answer the questions that follow:

·  dogs and their behavior

·  food allergies

a.  List three relationships between pairs of variables in the article on dog behavior.

Sample answer:

Relationships include:

·  between a dog’s behavior and age

·  between a dog’s behavior and sex or size

·  between a dog’s behavior and the owner’s sex

·  between a dog’s behavior and the use of a leash

b.  Compare what the data in the article on dog behavior says and what the article seems to imply. If you can, propose an alternative reason to explain the results found in the study.

Sample answer:

The article presents evidence that dogs walked by men are more aggressive. It implies that being walked by a man causes the dogs to be more aggressive. However, another variable that could be correlated to the two variables in the statement is the type of dog selected by men. These owners then walk their dogs (as you would expect them to). So, we can’t infer that dogs become aggressive if they’re walked by men. A dog owned by a woman might not suddenly become more aggressive if it’s walked by a man.

c.  Based on your analysis, write an alternative headline for the article on dog behavior. Remember, a headline should grab the reader’s attention without overstating the results.

Sample answer:

Aggressive dogs and men go together

d.  Identify the variables being related in the article about allergies.

Sample answer:

The article identifies two variables: education and food allergies.

e.  Discuss whether you think this statement from the article is justified: “Education is the cause of food allergies.”

Sample answer:

Even without reading the article, we can be pretty certain that more education doesn’t cause food allergies. What the results show is correlation, not causation. It’s possible, for instance, that better-educated people visit doctors more often and are more likely to identify an allergy rather than just live with feeling bad for unknown reasons.

3.  Correlation Versus Causality

In this activity, you will read articles to be included in the “Research and Results” section of your magazine and then write your own headlines based on your analysis of the relationships between the variables involved. Read these articles, and then answer the questions that follow:

·  foods and diabetes

·  infants’ health and safety

a.  In the diabetes article, what variables did the researchers try to control for in the study because they might affect the risk of diabetes?

Sample answer:

Other variables that may have contributed to reducing the risk of diabetes are consumption of fruits and vegetables, consumption of red meat and trans fats, physique, physical activity level, and smoking.

b.  Does the story support the headline for the diabetes article? Why or why not?

Sample answer:

Yes, the story supports the headline, which implies a causal relationship between eating brown rice and reduced risk of diabetes. In addition to pointing toward a correlation, the article documents supporting studies indicating that certain constituents of brown rice reduce the risk of diabetes through biochemical reactions. The study was also large (thousands of subjects) and seemed to have been well controlled for other variables. This study may not prove causation, but it seems like strong support for the hypothesis that eating brown rice could help prevent diabetes.

c.  Write an alternative headline for the diabetes article.

Sample answer:

Brown rice might help prevent diabetes

or

Brown rice healthier than white rice

d.  In the article on sudden infant death syndrome (SIDS), what are some other variables that may have reduced the number of deaths?

Sample answer:

Variables that can reduce the risk of SIDS include the use of a fan, sleeping posture, type of bedding, and the use of a pacifier.

e.  Does the story support the headline? Why or why not?

Sample answer:

The information provided in the article indicates that the use of a fan and the risk of SIDS are correlated: when fans are used, the incidence of SIDS is lower. We can’t conclude, though, that using fans reduces the number of deaths. There are other variables in this scenario that could be more significant in affecting the number of deaths. Most important is this statement at the end of the article: “…the trend was not statistically significant.”

Given that there is no supporting evidence beyond correlation and that the correlation is not statistically significant, the headline is misleading.

f.  Write an alternative headline for the second article.

Sample answer:

Could fans reduce crib deaths?

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