Cumulative Assessment
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We have been given four situations and want for each one determine if the variables are correlated.
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A correlation exists between to variables when a change in one is associated with a change in the other. |
If there is correlation, we also want to know if there is a causal relationship.
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A causal relationship exists when one variable causes a change in another variable. |
Let's look at each of the given statements.
The first situation described is about pricing of pants.
This situation has a negative correlation. We can illustrate this by describing the likely outcome if the price of pants is increased in a store and compare with the outcome of a decrease in price.
| Change in Price | Result |
|---|---|
| Price is increased | Sales go down |
| Price is decreased | Sales go up |
There is also a causal relationship between price and sales. If the price is lowered more people can afford them, which will result in more being sold.
The next situation is about cell phones and urban transport.
These variables definitely have a strong positive correlation, as both are related to how many people live in the city.
| Size of City | Size of Population | Number of Taxis and Cell Phones |
|---|---|---|
| Large city | Large population | More taxis and cell phones |
| Small city | Small population | Fewer taxis and cell phones |
However, they do not have a causal relationship. Putting more taxis on the streets does not make people go and buy cell phones. Also, distributing 1000 free cell phones among the population does not result in the number of taxis getting higher.
The third situation is comparing intelligence quotient and qualities as a sprinter.
There is no correlation between these two variables. There are fast runners with low IQ and there are fast runners with high IQ. There are highly intelligent people who can run fast and there are highly intelligent people who run slow.
The last situation is comparing study time and result in tests.
The more time a person studies and prepares for an exam, the more likely they are to score well on that exam. The score earned has a strong, positive correlation with the amount of time spent studying. This is also a causal relationship, since one directly influences the other.
| Situation | Correlation | Causation | ||
|---|---|---|---|---|
| Yes | No | Yes | No | |
| A. | X | X | ||
| B. | X | X | ||
| C. | X | X | ||
| D. | X | X | ||