Data Analysis Causation Goal: I can distinguish between correlation and causation. (S-ID.9)

Correlation  Describes the relationship between two variables in a scatterplot. Data can have a positive correlation, a negative correlation, or no correlation.

You try…  Identify the type of correlation.

You try…  Identify the type of correlation.

You try…  Identify the type of correlation.

Causation  We've seen several examples of data that display a strong linear relationship between variables. But does that mean that one variable is the cause of the other?  Causation is a relationship in which the change in the value of one variable “x” causes a change in the value of the other variable “y”.  You can think of causation as an "cause-and-effect" relationship between x and y. (Example: I earned an A in math and it cause my parents to be happy.)  A strong correlation between variables doesn't always mean causation.  However if there is not a strong correlation between the variables, there cannot be causation.

Causation vs Correlation  A strong correlation between variables doesn't always mean causation.

Example #1  HOW CAN I TELL IF THERE’S CAUSATION?  Scientists who study crickets have found that their chirps are affected by air temperature.  Let's examine this data set to see if the two variables are correlated and whether changes in one variable (temperature) causes changes in the other (chirps).  The scatterplot shows a positive correlation for the average number of cricket chirps at a given temperature. y = x – r = 0.836

Example #1  Let's consider the crickets. We know there's a strong correlation between air temperature and the average number of cricket chirps. Crickets are cold-blooded, which means that their body temperatures change in response to environmental temperatures.  As air temperature increases, body temperature increases. As body temperature increases, the cricket's heart rate, respiration rate, and metabolism increase. So it makes sense that the rate at which crickets chirp would also increase.  Given the strong correlation we've seen a cause-and-effect relationship between air temperature and the average number of cricket chirps makes sense.  Therefore, it is likely that an increase in air temperature causes an increase in the average number of cricket chirps.

Example #2  The scatterplot below shows the daily closing price of stocks. Investors use the daily closing price of stocks to monitor how well their portfolios are performing.  Does this show correlation or causation?  According to the correlation coefficient, there is a very strong correlation between the days since purchase and the closing price of this stock.

Example #2  Does the correlation imply a causal relationship between days since purchase and closing price?  Even though there is a very strong correlation between the variables, days since purchase would not necessarily cause closing prices to increase. The stock market fluctuates from one day to the next and stock prices rise and fall at different points in time. Although the trend appears to be decreasing, the stock price could increase at any time.

 As we saw in example 2, a strong correlation between variables doesn't always mean causation.  The only way to determine causation with certainty is to conduct a controlled experiment.  In controlled experiments, changes are made to the independent variable and changes in the dependent variable are observed or measured. All other variables are kept constant (controlled). Causation vs Correlation

Confounding Variable  A confounding variable is a extraneous variable that interferes or skews your results.  A confounding variable can also make to variables seem like they are related when they are not like the previous example of ice cream sales and murders, temperature was the connection between ice cream sales and murders, which is skewing your results.  A confounding variable is sometimes called a lurking variable. Causation vs Correlation

Example #3  Which statement best describes the relationship between extra studying and SAT scores?  A. Extra studying does not cause SAT math scores to improve.  B. Extra studying may cause SAT math scores to improve.  C. Extra studying causes SAT math scores to improve.  Answer: B While there may be a strong correlation between SAT scores and extra studying, we cannot say with certainty that extra studying will cause an increase in SAT scores. Since there may be other variables to consider, it is better to say that there may be a causal relationship.

Your turn…  Determine whether each situation likely represents a correlation or causation. Aggression in teens depends on the consumption of foods high in sugar. Correlation? Or Causation?  Answer: Correlation.  There may be a correlation between aggression in teens and the consumption of foods high in sugar, but we cannot say with certainty there is a causal relationship. A controlled experiment is needed to determine if this is a true causal relationship. There may be a confounding variable connecting the two variables.

Your turn…  Determine whether each situation likely represents a correlation or causation. The number of cavities teens have depends on the consumption of foods high in sugar. Correlation? Or Causation?  Answer: Causation.  Since studies have shown a strong correlation between the number of cavities and the consumption of foods high in sugar has been linked to causes cavities, it is likely there is a causal relationship.

Your turn…  Determine whether each situation likely represents a correlation or causation. The number of broken bones for skiers depends on the total snowfall per day. Correlation? Or Causation?  Answer: Correlation.  There may be a correlation between the number of broken bones for skiers and the total snowfall per day, but we cannot say with certainty there is a causal relationship. More people go skiing when it snows but snow might not be the only cause of broken bones there may be a confounding variable linking the two. A controlled experiment is needed to determine if this is a true causal relationship.

Your turn…  Determine whether each situation likely represents a correlation or causation. The number of days a ski resort is open depends on the total snowfall per day. Correlation? Or Causation?  Answer: Causation.  It is likely there is a causal relationship since snow is needed to ski.