Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Categorical Data
- Numerical Data
Purpose and Instructional Strategies
In grade 8, students first analyzed bivariate numerical data using scatter plots. In Algebra I, students study association between variables in bivariate data and learn that there is a difference between two variables being strongly associated and one of them having a causative effect on the other. In later courses, students will learn how to design statistical experiments that can show causation.
- The intent of this benchmark includes the ability to informally draw conclusions about whether causation is justified when two variables are correlated.
- Correlation and causation are often misunderstood. It is important for students to understand their relationship. Causation and correlation can exist at the same time; however, correlation does not imply causation. Causation explicitly applies to cases where an action causes an outcome. Correlation is simply a relationship observed in bivariate data. One action may relate to the other, but that action doesn’t necessarily cause the other to happen, because both of them may be the result of a third “hidden variable.”
- Causation is possible, but it is also possible that correlation occurs from a third variable.
- For example, if one states, “On days when I drink coffee, I feel more productive.” it may be that one feels more productive because of the
caffeine (causation) or because they spent time in the coffee shop drinking coffee where there are fewer distractions (third variable). Since one cannot determine whether the causation or the third variable results in correlation, then causation is not confirmed.
- Causation seems unlikely and a third variable seems likely.
- For example, there is a strong correlation between the number of Nobel prizes won by country and the per capita chocolate consumption by country. However, there are many possibilities a third variable, such as a strong economy, that can result in this correlation so causation can be ruled out.
- Causation is likely because there is a reasonable explanation for the causation.
- For example, if one states, “After I exercise, I feel physically exhausted.” it is reasonable to consider this to be a cause-and-effect. Causation can be confirmed by the explanation that because one is purposefully pushing their body to physical exhaustion when doing exercise, the muscles used to exercise are exhausted (effect) after they exercise (cause).
- When correlation is apparent in a bivariate data set, students are encouraged to seek a reasonable explanation that either identifies a hidden variable or a reasonable explanation for causation. Further investigation may be required to confirm or disconfirm causation.
- In Algebra I, the term correlation is used to describe an association between two variables and does not necessarily imply a linear relationship.
- Instruction includes asking the following questions while students investigate correlation and causation.
- Does this correlation make sense? Is there an actual connection between these variables? Will the correlation hold if I look at some new data that I haven’t used in my current analysis?
- Is the relationship between these variables direct, or are they both a result of some other variable?
Common Misconceptions or Errors
- Even though students may not be able to reasonably explain why a causal relationship exists, they may assume that correlation implies causation.
Strategies to Support Tiered Instruction
- Instruction includes co-creating and discussing examples and non-examples of causal relationships in numerical and categorical data.
- For example, a non-causal relationship could be a person’s shoe size and approximate number of vocabulary words they know.
- For example, a causal relationship could be a person’s shoe size and their age.
- Teachers provides instruction to increase understanding the relationship between correlation and causation. Teachers provides students with context that demonstrates when both correlation and causation are present. They may also provide context when only correlation is represented in the given context.
Instructional Task 1 (MTR.3.1, MTR.4.1)
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.
- Data from a certain city shows that the size of an individual’s home is positively correlated with the individual's life expectancy. Which of the following factors would best explain why this correlation does not necessarily imply that the size of an individual’s home is the main cause of increased life expectancy?
Larger homes have more safety features and amenities, which lead to increased life
The ability to afford a larger home and better healthcare is a direct effect of having
The citizens were not selected at random for the study.
There are more people living in small homes than large homes in the city. Some
responses may have been lost during the data collection process.
Instructional Item 1
- Dr. Larry has noticed that when he carries around his lucky rock, his students seem to be nicer to him. Can one conclude that this positive correlation shows a causal relationship?
Yes, because Larry decides whether or not to put his lucky rock in his pocket before
he encounters people during the day.
Yes, because it is not a negative correlation.
No, because lucky rocks only work for children.
No, because it is possible that people are nice to Larry because of another factor that
also causes him to put the rock in his pocket.