9.05 Associations in bivariate data
Concept summary
When looking at bivariate data, it can often appear that the two variables are correlated.
It is important to be able to distinguish between causal relationships (when changes in one variable cause changes in the other variable) and non-causal relationships.
To do so, we make sure to look at all aspects of an association between two variabels.
For categorical data, we can describe an association as positive or negative, as well as whether the association is strong or weak (or if there is no association).
There are more ways to describe an association for numerical data, since we can measure and perform calculations on this type of data. Descriptions can include whether a relationship is linear or nonlinear, whether a relationship is positive or negative (whether one variable is increasing or decreasing compared to the other), as well as whether an association is strong or weak (or if there is no association).
Worked examples
Example 1
Determine whether the following statement is true or false:
"There is a causal relationship between number of cigarettes a person smokes and their life expectancy"
Approach
Solution
Reflection
Example 2
Mayra surveyed some people on their way into Adventure Island Water Park. She asked the participants whether they arrived in a carpool or drove alone to the park, and whether they preferred the Lazy River or Raging Rapids.
| Lazy River | Raging Rapids | Total | |
|---|---|---|---|
| Carpooled to water park | 25 | 16 | 41 |
| Drove alone to water park | 25 | 20 | 45 |
| Total | 50 | 36 | 86 |
Describe the association, if any, between how people arrived to the water park and their preferred water park attraction activity. Justify your response.