Correlation vs. Causation

Correlation vs. Causation

Correlation vs Causation:

Many studies and surveys consider data on more than one variable. For example, suppose a study finds that, over the years, the prices of burgers and fries have both increased. Does this mean that an increase in the price of burgers causes the increase in the price of fries? To answer questions like this, we need to understand the difference between correlation and causation.

Correlation:

​Correlation means there is a relationship or pattern between the values of two variables.

A scatterplot displays data about two variables as a set of points in the xy-plane and is a useful tool for determining if there is a correlation between the variables.

Causation:

Causation means that one event causes another event to occur.

Causation can only be determined from an appropriately designed experiment. In such experiments, similar groups receive different treatments, and the outcomes of each group are studied. We can only conclude that a treatment causes an effect if the groups have noticeably different outcomes.

What do these Experiments Test?

• Describing a relationship between variables

• Identifying statements consistent with the relationship between variables

• Identifying valid conclusions about correlation and causation for data shown in a scatterplot

• Identifying a factor that could explain why a correlation does not imply a causal relationship

How can we Determine if two Things are Correlated?

If there is a correlation between two variables, a pattern can be seen when the variables are plotted on a scatterplot. If this pattern can be approximated by a line, the correlation is linear. Otherwise, the correlation is non-linear.

Does Correlation Imply Causation?

Even if there is a correlation between two variables, we cannot conclude that one variable causes a change in the other. This relationship could be coincidental, or a third factor may be causing both variables to change.

Example:

For example, Liam collected data on the sales of ice cream cones and air conditioners in his hometown. He found that when ice cream sales were low, air conditioner sales tended to be low and that when ice cream sales were high, air conditioner sales tended to be high.

Example:

For example, Liam collected data on the sales of ice cream cones and air conditioners in his hometown. He found that when ice cream sales were low, air conditioner sales tended to be low and that when ice cream sales were high, air conditioner sales tended to be high.

• Liam can conclude that sales of ice cream cones and air conditioner are positively correlated.

Example:

For example, Liam collected data on the sales of ice cream cones and air conditioners in his hometown. He found that when ice cream sales were low, air conditioner sales tended to be low and that when ice cream sales were high, air conditioner sales tended to be high.

• Liam can conclude that sales of ice cream cones and air conditioner are positively correlated.

• Liam can't conclude that selling more ice cream cones causes more air conditioners to be sold. It is likely that the increases in the sales of both ice cream cones and air conditioners are caused by a third factor, an increase in temperature!

Multiple Choice

Daniel notices that, on average, students in his class that are involved in extracurricular activities tend to have higher grade point averages. Is this an example of correlation or causation?

• Correlation

• Causation

Multiple Choice

Doug wants to determine if a lack of sleep impacts test performance. Doug carries out a study where he ha ten students take a test. The next day the students took another test where five of them slept for seven or more hours the night before and five students slept for less than seven hours. Doug then compared students performance on the first test and second test. He found that on average students who slept seven hours or less performed worse on the second test than they had on the first, whereas students who slept seven or more hours performed about the same. Is this an example of correlation or cauation?

• Correlation

• Causation

Fill in the Blanks

Jim notices that as temperatures increase, so do ice cream sales at his ice cream shop. Is this an example of correlation or causation?

Fill in the Blanks

Vivek notices that students in his class with larger shoe sizes tend to have higher grade point averages. Is this an example of correlation or causation?