When it comes to finance, ‘normal’ data is actually pretty weird

When business researchers analyze data^[1], they often rely on assumptions^[2] to help make sense of what they find. But like anyone else, they can run into a whole lot of trouble if those assumptions turn out to be wrong – which may happen more often than they realize. That’s what we found in a recent study looking at financial data from about a thousand major U.S. companies.

One of the most common assumptions in data analysis is that the numbers will follow a normal distribution^[3] – a central concept in statistics often known as the bell curve^[4]. If you’ve ever looked at a chart of people’s heights, you’ve seen this curve: Most people cluster near the middle, with fewer at the extremes. It’s symmetrical and predictable, and it’s often taken for granted in research.

But what happens when real-world data doesn’t follow that neat curve?

We are professors^[5] who study business^[6], and in our new study^[7] we looked at financial data from public U.S. companies^[8] – things like firm market value, market share, total assets and similar financial measures and ratios. Researchers often analyze this kind of data to understand how companies work and make decisions.

We found that these numbers often don’t follow the bell curve. In some cases, we found extreme outliers, such as a few large firms being thousands of times the size of other smaller firms. We also observe distributions that are “right-skewed^[9],” which means that the data is bunched up on the left side of the chart. In other words, the values are on the lower end, but there are a few really high numbers that stretch the average upward. This makes sense, because in many cases financial metrics can only be positive – you won’t find a company with a negative number of employees, for example.

Why it matters

If business researchers rely on flawed assumptions, their conclusions – about what drives company value, for example – could be wrong. These mistakes can ripple outward, influencing business decisions, investor strategies or even public policy.

Take stock returns, for example. If a study assumes those returns are normally distributed, but they’re actually skewed or full of outliers, the results might be distorted. Investors hoping to use that research might be misled.

Researchers know their work has real-life consequences, which is why they often spend years refining a study, gathering feedback and revising the article before it’s peer-reviewed and prepared for publication. But if they fail to check whether data is normally distributed, they may miss a serious flaw. This can undermine even otherwise well-designed studies.

In light of this, we’d encourage researchers to ask themselves: Do I understand the statistical methods I’m using? Am I checking my assumptions – or just assuming they’re fine?

What still isn’t known

Despite the importance of data assumptions, many studies fail to report tests for normality. As a result, it’s unclear how many findings in finance and accounting research rest on shaky statistical grounds. We need more work to understand how common these problems are, and to encourage best practices in testing and correcting for them.

While not every researcher needs to be a statistician, everyone using data would be wise to ask: How normal is it, anyway?

References

1. ^{^} analyze data (hstalks.com)
2. ^{^} rely on assumptions (doi.org)
3. ^{^} normal distribution (www.mathsisfun.com)
4. ^{^} bell curve (www.merriam-webster.com)
5. ^{^} We are professors (www.business.msstate.edu)
6. ^{^} who study business (business.wvu.edu)
7. ^{^} new study (link.springer.com)
8. ^{^} public U.S. companies (www.sec.gov)
9. ^{^} right-skewed (www.statology.org)