The phrase “**correlation does not imply causation**” is often used in statistics to point out that correlation between two variables does not necessarily mean that one variable causes the other to occur.

To better understand this phrase, consider the following real-world examples.

**Example 1: Ice Cream Sales & Shark Attacks**

If we collect data for monthly ice cream sales and monthly shark attacks around the United States each year, we would find that the two variables are highly correlated.

Does this mean that consuming ice cream causes shark attacks?

Not quite. The more likely explanation is that more people consume ice cream and get in the ocean when it’s warmer outside, which explains why these two variables are so highly correlated.

Although ice cream sales and shark attacks are highly correlated, one does not cause the other.

**Example 2: Master’s Degrees vs. Box Office Revenue**

If we collect data for the total number of Master’s degrees issued by universities each year and the total box office revenue generated by year, we would find that the two variables are highly correlated.

Does this mean that issuing more Master’s degrees is causing the box office revenue to increase each year?

Not quite. The more likely explanation is that the global population has been increasing each year, which means more Master’s degrees are issued each year and the sheer number of people attending movies each year are both increasing in roughly equal amounts.

Although these two variables are correlated, one does not cause the other.

**Example 3: Pool Drownings vs. Nuclear Energy Production**

If we collect data for the total number of pool drownings each year and the total amount of energy produced by nuclear power plants each year, we would find that the two variables are highly correlated.

Does this mean that increased pool drownings are somehow causing more nuclear energy to be produced?

Not exactly. The more likely explanation is that global population has been increasing, which means more people are drowning in pools and nuclear energy production is becoming more viable each year which explains why it has increased.

Although these two variables are highly correlated, one does not cause the other.

**Example 4: Measles Cases vs. Marriage Rate**

If we collect data for the total number of measles cases in the U.S. each year and the marriage rate each year, we would find that the two variables are highly correlated.

Does this mean that reduced measles cases is causing lower marriage rates?

Not exactly. Instead, the two variables are independent – modern medicine is causing measles cases to drop and fewer people are getting married due to various reasons each year.

Although these two variables are highly correlated, one does not cause the other.

**Example 5: High School Graduates vs. Pizza Consumption**

If we collect data for the total number of high school graduates and total pizza consumption in the U.S. each year, we would find that the two variables are highly correlated.

Does this mean that an increased number of high school graduates is leading to more pizza consumption in the United States?

Not quite. The more likely explanation is that U.S. population has been increasing over time, which means that the number of people receiving a high school degree and the total pizza being consumed are both increasing as population increases.

Although these two variables are correlated, one does not cause the other.

**Additional Resources**

The following tutorials provide additional information about correlation:

An Introduction to the Pearson Correlation Coefficient

Does Causation Imply Correlation?

Correlation vs. Association: What’s the Difference?

What is Considered to Be a “Strong” Correlation?

When Should You Use Correlation?

It seems the statistics in the examples are made up. For instance, the first nuclear reactor was built in 1942 (the Chicago pile). Nuclear power wasn’t used for electricity production until the 1950s (Obninsk; Calder Hall, Windscale). I would have liked to see some real-world examples.

can you send me pizza when i graduate highschool

Lots of things vary with time so it is easy to find examples of things that appear to be correlated but are merely a reflection of time. Ot would be far more convincing if you used examples where time was not involved – eg height versus weight.

I said to 2 friends, one female and one male, that the female should make a decision based on numbers because girls are better at math.

She replied that she is better at math, but that her & I are going to have a little chat soon.

I need to know if there is a phrase that is basically the opposite of “correlation does not equal causation”, i.e. if she says girls are not better at math, but she is better at math, how can that be said succinctly, so as to help me soften the blow of the butt chewing she appears to be ready to give me when we next meet, which will probably be tomorrow?