## Association Algebra

Determine whether arguments based on data confuse association with causation.

#### Causation

Definition: Causation in Algebra has a lot to do with correlation. For example, there is a common phrase which states that “correlation does not imply causation,” and which means that a clear relationship between two variables doesn’t automatically mean that one leads to the other.

Any correlation tends to mean a “linear” relationship. As we have already learned in Algebra, there are linear equations that can use data to prove a theory. The problem with arguments based on data is that they might confuse “association” with causation.

#### Association

Definition: Association is a relationship between two measurable quantities that leaves them statistically independent. This is a much broader way of viewing data than causation, and says that one event might make it either more or less probable that another occurs.

The example of the teacher assuming that daily homework led to improved quiz and test scores is a good way to understand that validation through an algebraic expression would be the only way to ensure that the scores really did improve (causation) due to the homework assignments.

#### Try these questions

1. Which of the following, in algebra, has a lot to do with correlation?
1. inductive reasoning
2. validation
3. causation
4. association

2. There is a common phrase which states that “correlation does not imply causation”. True or False?

3. Any correlation tends to mean which type of relationship?
1. linear
2. associative
3. exponential
4. both A and C

4. The problem with arguments based on data is that they might confuse which of the following with causation?
1. inductive reasoning
2. validation
3. causation
4. association

5. Which of the following is a relationship between two measurable quantities that leaves them statistically independent?
1. inductive reasoning
2. validation
3. causation
4. association

1. C.A clear relationship between two variables doesn’t automatically mean that one leads to the other.
2. True. This also means that a clear relationship between two variables doesn’t automatically mean that one leads to the other
3. A. As we have already learned in Algebra, there are linear equations that can use data to prove a theory.
4. D. The problem with arguments based on data is that they might confuse “association” with causation.
5. D. This is a much broader way of viewing data than causation, and says that one event might make it either more or less probable that another occurs.

#### Final Questions

1. Which of the following, in algebra, has a lot to do with correlation?
1. inductive reasoning
2. validation
3. causation
4. association

2. There is a common phrase which states that “correlation does not imply causation,” and which means that a clear relationship between two variables doesn’t automatically mean that one leads to the other. True or False?

3. Any correlation tends to mean which type of relationship?
1. linear
2. associative
3. exponential
4. both A and C

4. The problem with arguments based on data is that they might confuse which of the following with causation?
1. inductive reasoning
2. validation
3. causation
4. association

5. Which of the following is a relationship between two measurable quantities that leaves them statistically independent?
1. inductive reasoning
2. validation
3. causation
4. association

6. Which of the following is a much broader way of viewing data than causation, and says that one event might make it either more or less probable that another occurs?
1. inductive reasoning
2. association
3. causation
4. validation