Ice Cream and Drowning: Why Correlation Is Not Causation (and How to Test It Properly)

In statistics lectures, there is one classic example that never gets boring. Researchers collect monthly data and find that when ice cream sales rise, the number of drowning cases rises too. The correlation is strong. The chart is pretty, two lines moving up and down together like two dancers who have rehearsed.

The question: should we ban ice cream at the beach?

Of course not. And you have probably guessed why. Hot weather makes people buy more ice cream, and hot weather also makes more people swim. More people swimming means more people drowning. Ice cream and drowning both rise because of a third cause. Statisticians call it a confounder.

The example is funny, but the same mistake happens every day in the real world: in company reports, in the news, and, most often, in theses. Let us take it apart so you do not get fooled.

What exactly is correlation?

Correlation measures how strongly two variables move together. Its value (the correlation coefficient) ranges between −1 and +1. Close to +1 means both tend to rise together, close to −1 means one rises when the other falls, and around 0 means there is no clear linear pattern.

The method depends on the measurement scale of the variables. For two numeric variables with a linear relationship, we use Pearson correlation. For ranked data or data that does not meet the assumptions, we use Spearman or Kendall. For two categorical variables (for example gender and product choice), we use measures of association such as Phi or Cramer’s V. These tools are useful, but they all answer the same question: “do the two move together?” Not: “does one cause the other?”

Four reasons two things can correlate without causing each other

1. A confounder (a third cause). Like ice cream and drowning. Another example: people who carry matches in their pockets are more likely to get lung cancer. It is not the matches that cause it, but the smoking habit that makes them carry matches.

2. Reversed direction of cause and effect. We suppose A causes B, when B actually causes A. For example, you find that employees who attend training more often perform better. Maybe training improves performance, but maybe managers more often send already high-performing employees to training.

3. Coincidence. If you search enough pairs of variables, some pairs will appear correlated by chance alone. There are websites that collect silly correlations, such as per capita cheese consumption tracking the number of people who died by becoming tangled in their bedsheets. The correlation is high, the meaning is zero. The more hypotheses you test, the greater the chance of finding a false relationship.

4. A deceptive pattern because data is combined (Simpson’s paradox). A trend visible in the combined data can reverse when the data is split into groups. For example, a hospital looks worse than another overall, but when viewed by patient severity, it is actually better at every level. The reason: that hospital receives more patients in serious condition. Combining data without thinking about its composition hides the truth.

So how can we claim cause and effect?

Establishing cause and effect is harder than computing a correlation, and it demands design, not just formulas. There are several approaches, from the strongest:

• Randomized controlled experiments. Researchers randomly assign subjects to treatment and control groups. Because assignment is random, known and unknown confounders tend to be balanced between groups. This is the gold standard, but it is not always possible or ethical.
• Natural experiments and quasi-experimental designs. When we cannot randomize, we look for natural situations that resemble randomization, or compare changes before and after a policy between affected and unaffected groups (for example a difference-in-differences design).
• Statistical control. We include known confounders in a regression model to “remove” their influence. This is useful, but only as good as the list of confounders you know and measure. Unobserved confounders remain dangerous.
• Theoretical reasoning and layered evidence. In fields that are hard to experiment in (for example epidemiology), cause-and-effect conclusions are built from many studies, plausible mechanisms, a clear time order, and consistency of findings.

For a thesis with a one-time survey, the practical message is this: use language proportionate to your design. Write “is related to” or “is associated with”, not “causes” or “has an impact on”, unless your design truly supports it. And state plainly that you cannot rule out other explanations.

An example from the workplace

Suppose the HR department finds that employees who joined a mentoring program have a lower turnover rate. The tempting conclusion: “Mentoring lowers turnover, let’s extend it to all employees.” But before deciding, ask:

• Who joined mentoring? If more motivated employees are more likely to sign up, the difference may reflect motivation, not the effect of mentoring.
• Are there other differences between participants and non-participants (division, tenure, salary)?
• Can we test it through a limited pilot with random selection?

Those questions may seem to slow things down, but they actually save money. Expanding a program whose effect is illusory costs far more than running a careful small pilot.

A quick way to detect misleading claims

Whenever you hear a claim that “A causes B”, ask these five questions:

1. Could B be causing A?
2. Is there a third thing causing both?
3. Could the relationship arise purely by chance (how many other relationships were tried)?
4. Is there a fair comparison, meaning a group that is similar except for A?
5. Is there a plausible mechanism explaining how A affects B?

If the claim fails three of the five questions, treat it as a hypothesis, not a fact.

Ice cream does not make people drown. But the habit of drawing conclusions from two lines that move together has “drowned” a lot of business decisions and research.

How to report a correlation properly

A well-reported correlation includes five things: the coefficient (for example r = 0.42), the number of observations, the confidence interval, the p-value as a supplement, and a scatterplot. The scatterplot matters because the same number can come from very different patterns. There is a classic example called Anscombe’s quartet: four datasets with nearly identical means, variances, and correlations, but with completely different shapes, some a straight line, some curved, some driven by a single outlier. Without looking at the chart, we can conclude the wrong thing.

To interpret the strength of a relationship, a commonly used guideline (which is rough and depends on the field) calls an absolute value of about 0.10 weak, 0.30 moderate, and 0.50 and above strong. But in the social sciences, a correlation of 0.30 is often already considered meaningful. So the context of the field needs to be considered.

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