CAUSE & EFFECT, AND OTHER RELATIONSHIPS“Correlation does not mean Causation”

Examining Relationships

• The main reason for a correlation study is to find evidence of a cause-and-effect relationship. Perhaps we want to know if calculators help students learn math or even mild exercise reduces heart disease.

• A strong correlation doesn’t prove that the changes in one variable cause changes in the other. There are other types of relationships that exist. We call these causal relationships.

Note: It’s not casual, it’s causal.

Consider this graph…Initial conclusions from this graph might lead someone to believe that the higher level of math one takes causes them to have a better chance at employment.

Often, this is NOT a cause & effect relationship, there is a correlation, but other factors are needed to be considered.

From the article where the graph was taken…

The fact that advancing in math is tied to better labor outcomes could mean all sorts of things, including, but not limited to:

(1) It's causation, plain and simple: Math totally makes you rich. 

(2) Taking lots of math is a sign that you're a smart student, and smart students tend to earn more money, whether or not they love math. As Peter Coy puts it:

“It could be that people take more math in high school because they’re smarter than classmates who go equally far in their education, are harder working, or both.“

(3) Students who show an interest in math and related fields are often drawn into an orbit of higher-paying job opportunities, like finance and consultinghttp://m.theatlantic.com/business/archive/2013/11/will-studying-math-make-you-richer/281104/

Cause & Effect Relationships

Cause-and-effect relationships are when a change in X produces a change in Y.

For example, increasing the height a ball is dropped increases the bounce height. Also, increasing production line speed increases the number of items produced each day.

Common-Cause Factor

Common-Cause factor is an external variable that causes two variables to change in the same way.

For example, a town finds the revenue from parking fees at the beach each summer correlates to the tomato harvest. Here, good weather is a common-cause factor that increases the tomato crop and the number of people at the beach.

Reverse Cause & Effect Relationships

Reverse cause-and-effect relationships are when the dependent and independent variables are reversed in the process of establishing a relationship.

For example, a researcher hypothesizes that drinking coffee causes nervousness, but discovers it’s the reverse (nervousness causes people to drink more coffee).

Accidental Relationships

Accidental relationships are relationships that exist without any causal relationship between variables.

For example, suppose one states that there is a strong correlation between the number of cell phone users and global warming over the past 10 years. They have a positive correlation, but the relationship is merely a coincidence.

Presumed Relationships

Presumed relationships are when a correlation does not seem to be accidental even though no cause-and-effect relationship or common-cause factor is apparent.

For example, say a correlation exists between people’s fitness level and the number of adventure movies seen. It seems logical, but it would be difficult to find a common-cause or prove one variable affects the other.

How do I identify these relationships?

These relationships can be identified and discussed using a scatter plot for quantitative data, or a split-bar graph for qualitative data.

Examples

Classify the relationships in the following situations.

 • The rate of a chemical reaction increases with

temperature.• Leadership ability has a positive correlation with academic

achievement.• The prices of butter and motorcycles have a strong

positive correlation over many years.• Sales of cellular phones has a strong positive correlation

with ozone levels in the atmosphere over the decade.• Traffic congestion and the number of urban expressways.