3.6.3 Using the Term Causal Relationship
3.6.3 • Using the Term Causal Relationship
Activity
The phrases “correlation, not causation” or “association, not causation” are often used to refer to situations in which there is a relationship, but it is not a causal relationship. While correlation used to describe the strength of the relationship between variables, a causal relationship means that a change in one of the variables actually causes a change in the other variable.
Describe a pair of variables with each condition. Be prepared to show your reasoning.
Two variables have a causal relationship.
Compare your answer:
Your answer may vary, but here is a sample.
Length of a person’s feet in inches and their men’s shoe size. Increased foot size would cause someone to purchase larger shoe sizes.
Two variables have an association in which the variables are strongly related, but a third factor might be the cause for the changes in the variables.
Compare your answer:
Your answer may vary, but here is a sample.
Amount of power produced by solar panels and the percentage of people wearing sunglasses while driving. These factors are probably strongly, positively related, but the cause is the amount of sunlight getting through to the ground for each variable rather than either one of the variables causing the other to increase directly.
The variables are not related.
Compare your answer:
Your answer may vary, but here is a sample.
The number of hits by a certain baseball player per game for a season and the price of a barrel of oil on the day of the games. There is no reasonable relationship between the variables, and they are very unlikely to be related even by external causes.
How are associations and causal relationships similar?
Compare your answer:
Your answer may vary, but here is a sample. Associations and causal relationships indicate that two data sets or variables are related in some way.
How are associations and causal relationships different?
Compare your answer:
Your answer may vary, but here is a sample. Causal relationships involve variables that interact in a way that one causes the other. Associations may have other factors that impact the relationship or they simply have a correlation, but one does not cause the other.
How are associations and causal relationships different from data sets representing data that are not related?
Compare your answer:
Your answer may vary, but here is a sample. Associations and causal relationships have some type of relationship or interaction between the variables. Unrelated data my just be random numbers or pairings of data sets.
Are you ready for more?
Extending Your Thinking
For questions 1 – 4, use the following instructions.
Look through news articles or advertisements for claims of causation or correlation. Find 2 or 3 claims and read or watch the articles or the advertisements. Answer these questions for each of the claims.
What is the claim?
Compare your answer:
Your answer may vary, but here is a sample.
- Claim 1: Green tea lowers blood pressure.
- Claim 2: Chocolate improves health.
- Claim 3: Soda helps with heartburn.
What evidence is provided for the claim?
Compare your answer:
Your answer may vary, but here is a sample.
- Claim 1: Study groups were given either green tea or a drink that was colored like green tea for several weeks, and their blood pressure was taken before and after the study.
- Claim 2: They analyzed the number of antioxidants in chocolate as compared to fruit.
- Claim 3: No evidence was provided other than that it seemed to work for some people.
Does there appear to be evidence for causation or correlation? Explain your thinking.
Compare your answer:
Your answer may vary, but here is a sample.
- Claim 1: There appears to be evidence for correlation because there was a control group, and the blood pressure was taken before and after drinking tea. However, there was no mention of how the groups were randomized or selected, so I am not sure if there is evidence for causation.
- Claim 2: The only evidence provided is the quantity of antioxidants chocolate contains, so a study would need to be done on antioxidants and health to show correlation or causation.
- Claim 3: There is no evidence for correlation or causation because only a testimonial is provided.
Choose the claim with the least or no evidence. Describe an experiment or other way that you could collect data to show correlation or causation.
Compare your answer:
Your answer may vary, but here is a sample.
To show that heartburn relief is correlated with or caused by drinking soda, I would have to randomly assign subjects to different treatment groups. One group would get soda, and the other would get a placebo. I would then need to collect and compare data about their heartburn symptoms to determine if there is correlation or causation.
Self Check
Additional Resources
Is It Causation?
Correlation means there is a relationship or pattern between the values of two variables. A scatter plot displays data about two variables as a set of points in the -plane and is a useful tool for determining if there is a correlation between the variables.
Causation means that one event causes another event to occur. Causation can only be determined from an appropriately designed experiment. In such experiments, similar groups receive different treatments, and the outcomes of each group are studied. We can only conclude that a treatment causes an effect if the groups have noticeably different outcomes.
Why doesn’t correlation mean causation?
Even if there is a correlation between two variables, we cannot conclude that a change in one variable causes a change in the other. This relationship could be coincidental, or a third factor may be causing both variables to change.
Example
Liam collected data on the sales of ice cream cones and air conditioners in his hometown. He found that when ice cream sales were low, air conditioner sales tended to be low, and that when ice cream sales were high, air conditioner sales tended to be high.
Liam can conclude that sales of ice cream cones and air conditioners are positively correlated.
Liam can’t conclude that selling more ice cream cones causes more air conditioners to be sold. It is likely that the increases in the sales of both ice cream cones and air conditioners are caused by a third factor, an increase in temperature!
Try it
Is It Causation?
Vivek notices that students in his class with larger shoe sizes tend to have higher grade point averages. Based on this observation, what is the best description of the relationship between shoe size and grade point average?
Compare your answer: The relationship has a positive correlation because as shoe size increases, grade point average tends to increase. There is not a causal relationship.