Correlation vs Causation

Correlation vs Causation

by Lauren Wisehart

​Correlation

​Two sets of data can have a relationship called correlation. It can be positive or negative.

• Positive Correlation- the values  INCREASE  together.

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• Negative Correlation- when one value INCREASES the other DECREASES.

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• Linear Correlation- the correlation resembles a LINE

​Correlation Coefficient (r)

Correlation Coefficient ​(r) describes the strength and direction of the correlation.

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​r values can not be less than -1 or greater than +1. This can be written as the inequality  -1 < r < 1

Multiple Choice

Number of steps taken per day and number of kilometers walked per day. $$r=.92$$  

• strong positive

• strong negative

• weak positive

• weak negative

Multiple Choice

Average time spent listening to music per day and average time spent watching TV per day.  $$r=-.17$$  

• strong positive

• strong negative

• weak positive

• weak negative

Multiple Choice

Car weight and distance traveled using a full tank of gas.  $$r=-.86$$  

• strong positive

• strong negative

• weak positive

• weak negative

Multiple Choice

Estimate the correlation coefficient for this scatterplot.

• A) r = 1.2

• B) r = 0.89

• C)r = 0

• D) r = -0.89

Multiple Choice

Estimate the correlation coefficient for this scatterplot.

• A) r = -0.9

• B) r = 1

• C) r = 0.9

• D) r = -1

Multiple Choice

Estimate the correlation coefficient

• r = 1

• r = -1

• r ≈ -0.8

• r ≈ 0.8

• r ≈ -0.5

Multiple Choice

Describe the relationship between the variables.

• Weak positive correlation
• Weak negative correlation
• Strong positive correlation
• Strong negative correlation

Multiple Choice

Amount of Education and Amount of income

• Positive Correlation

• Negative Correlation

• No Correlation

Multiple Choice

Number of days absent from school vs. math average

• Positive Correlation

• Negative Correlation

• No Correlation

Multiple Choice

Test scores vs. shoe sizes

• Positive Correlation

• Negative Correlation

• No Correlation

Multiple Choice

Distance traveled vs. amount of gas in the car

• Positive Correlation

• Negative Correlation

• No Correlation

​Correlation vs. Causation

​Causation means that x makes y happen. For example, the more cash you spend, the less cash you will have. This example has a correlation AND causation.

BUT… Correlation ≠ Causation.

Example: There may be a correlation between the number of glue sticks in a classroom and the number of students in a classroom. However, adding glue sticks to a classroom does not make more students be in the classroom.

Multiple Choice

Which one of these examples is NOT an example of CAUSATION?

• Kryptonite causes Superman to lose all his powers.

• Temperatures of less than 32˚F cause water to freeze.

• Umbrellas cause rainstorms.

• Stepping on the gas pedal causes a car to move faster.

Multiple Choice

Which example shows CAUSATION? (Which one CAUSED the other to happen.)

• High social media usage and reduced grades.

• Car ran out of gas and being stranded on the side of the road.

• Recess time and number of friends.

Multiple Choice

Which example shows CAUSATION? (Which one CAUSED the other to happen.)

• Rainfall and time spent reading.

• Eating more butter and increased divorce rates.

• It started raining and the baseball game was delayed.

Multiple Choice

Which example shows CORRELATION? (The events show correlation, but one thing does NOT cause the other thing to happen.)

• I put water in the freezer and now I have ice.

• The alarm clock went off and I woke up.

• Temperature and the amount of people at the beach.

Multiple Choice

Which example shows a CORRELATION? (The events show correlation, but one thing does NOT cause the other thing to happen.)

• It rained and the ground is wet.

• Ice cream sales increase as temperature increases.