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

Business researchers often rely on assumptions when analyzing financial data, but these assumptions can be flawed, leading to incorrect conclusions.
The normal distribution assumption, a central concept in statistics, may not hold true for real-world financial data, which can lead to distorted results and misleading conclusions.
Researchers found that financial metrics such as firm market value, market share, and total assets often don’t follow the bell curve, with extreme outliers and right-skewed distributions common.
Flawed assumptions in data analysis can have significant consequences, influencing business decisions, investor strategies, and public policy, making it essential to verify statistical methods and assumptions.
More research is needed to understand how common these problems are and to encourage best practices in testing and correcting for flawed assumptions in financial data analysis.

When business researchers analyze data, they often rely on assumptions 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 – a central concept in statistics often known as the bell curve. 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.

A one-minute introduction to the concept of the bell curve.

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

We are professors who study business, and in our new study we looked at financial data from public U.S. companies – 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,” 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?

The authors do not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and have disclosed no relevant affiliations beyond their academic appointment.

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Q. What is the concept of “normal” data in finance?

A. In finance, ‘normal’ data refers to a central concept in statistics known as the bell curve or normal distribution, which assumes that numbers follow a symmetrical and predictable pattern.

Q. Why do business researchers rely on assumptions when analyzing data?

A. Business researchers often rely on assumptions to help make sense of what they find, but these assumptions can turn out to be wrong if not checked.

Q. What did the authors of the study find in their analysis of financial data from U.S. companies?

A. The authors found that financial data from public U.S. companies does not follow a normal distribution, with some cases showing extreme outliers and distributions that are “right-skewed”.

Q. Why is it important to check for normality in data analysis?

A. It’s essential to check for normality because flawed assumptions can lead to distorted conclusions about what drives company value or other business decisions.

Q. What are the consequences of failing to check for normality in data analysis?

A. Failing to check for normality can undermine even well-designed studies and mislead investors, policymakers, or others who rely on those findings.

Q. Why do researchers often spend years refining their studies before publication?

A. Researchers know that their work has real-life consequences and therefore spend time gathering feedback, revising the article, and ensuring its accuracy before peer-review and publication.

Q. What is a common problem in finance and accounting research?

A. Many studies fail to report tests for normality, leaving it unclear how many findings rest on shaky statistical grounds.

Q. How can researchers ensure that their data analysis is accurate?

A. Researchers should ask themselves if they understand the statistical methods they’re using and check their assumptions before making conclusions.

Q. What does “right-skewed” mean in the context of financial data distribution?

A. In finance, a “right-skewed” distribution means that the values are bunched up on the left side of the chart, with fewer extreme outliers on the right side.

Q. Why is it essential for researchers to be aware of their assumptions and methods?

A. It’s crucial for researchers to be aware of their assumptions and methods because they can have significant real-life consequences, influencing business decisions, investor strategies, or public policy.