A visual representation of OLS regression struggling with outliers compared to a robust solution.

Beyond the Average: Why Traditional Statistics Miss the Mark and How to Fix It

Mira Elwood in Tech & Innovation September 2025 • 4 min read.

"Uncover the limitations of ordinary least squares and explore robust alternatives for a clearer, more accurate view of your data."

In today's data-driven world, statistical analysis is the bedrock of informed decision-making. From predicting market trends to understanding customer behavior, businesses and researchers alike rely on statistical models to extract meaningful insights from raw data. However, the accuracy and reliability of these insights hinge on the suitability of the chosen statistical methods.

Traditional statistical techniques, such as Ordinary Least Squares (OLS) regression, operate under a set of assumptions about the data. One of the most critical assumptions is that the data is normally distributed and free from outliers. But what happens when these assumptions are violated? What if your data is skewed, contains extreme values, or simply doesn't conform to the idealized normal distribution? In these scenarios, relying solely on OLS can lead to biased results and misleading conclusions.

This article explores the limitations of OLS and introduces robust alternatives that provide a more reliable way to analyze data in the face of real-world complexities. We'll delve into methods that are less sensitive to outliers and non-normality, offering a clearer and more accurate understanding of your data.

The Pitfalls of OLS: When Traditional Methods Fail

A visual representation of OLS regression struggling with outliers compared to a robust solution.

Ordinary Least Squares (OLS) regression is a widely used statistical technique that aims to find the best-fitting linear relationship between a dependent variable and one or more independent variables. OLS works by minimizing the sum of the squared differences between the observed values and the values predicted by the model. However, this method is highly sensitive to extreme values, or outliers, in the data. Even a single outlier can exert a disproportionate influence on the OLS regression line, pulling it away from the true underlying relationship.

Furthermore, OLS assumes that the errors in the model are normally distributed. This assumption is often violated in real-world data, which can exhibit skewness (asymmetry) or heavy tails (more extreme values than a normal distribution). When the normality assumption is violated, the standard errors of the OLS estimates can be unreliable, leading to inaccurate hypothesis tests and confidence intervals.

When to be wary of OLS:

Presence of outliers in the data.
Non-normal distribution of the data.
Small sample sizes, where assumptions are harder to verify.
Data with inherent skewness or potential for extreme values.

To illustrate the limitations of OLS, consider an example of analyzing housing prices in a city. A few exceptionally expensive mansions can skew the OLS regression line, leading to an overestimation of the average home price. Similarly, in studies of income, a few high earners can inflate the average income and distort the relationship between income and other variables like education or experience.

Embracing Robustness for Reliable Insights

While OLS remains a valuable tool in many situations, it's crucial to recognize its limitations and consider robust alternatives when dealing with real-world data. By embracing methods that are less sensitive to outliers and non-normality, researchers and businesses can gain a clearer, more accurate, and more reliable understanding of their data, leading to better decisions and more robust insights.

About this Article -

This article was crafted using a human-AI hybrid and collaborative approach. AI assisted our team with initial drafting, research insights, identifying key questions, and image generation. Our human editors guided topic selection, defined the angle, structured the content, ensured factual accuracy and relevance, refined the tone, and conducted thorough editing to deliver helpful, high-quality information.See our About page for more information.

This article is based on research published under:

DOI-LINK: 10.1007/978-3-319-98926-6_7, Alternate LINK

Title: Interval-Level Variables

Journal: The Measurement of Association

Publisher: Springer International Publishing

Authors: Kenneth J. Berry, Janis E. Johnston, Paul W. Mielke

Published: 2018-01-01

Everything You Need To Know

What is Ordinary Least Squares (OLS) regression, and why isn't it always the best choice for statistical analysis?

Ordinary Least Squares (OLS) regression is a statistical technique used to model the linear relationship between variables by minimizing the sum of squared differences. However, OLS is sensitive to outliers and assumes normally distributed errors. When these assumptions are violated, the results from OLS can be biased and unreliable. Therefore, it's not universally applicable and may require robust alternatives.

Under what conditions should one be cautious when using Ordinary Least Squares (OLS) regression?

When data contains outliers, is not normally distributed, involves small sample sizes, or has inherent skewness, the application of Ordinary Least Squares (OLS) may lead to inaccurate or misleading results. These conditions violate the assumptions underlying OLS, causing the model to misrepresent the true relationships within the data.

What are robust statistical methods, and how do they improve data analysis compared to Ordinary Least Squares (OLS)?

Robust statistical methods are alternatives to Ordinary Least Squares (OLS) that are less sensitive to outliers and deviations from normality. These methods provide a more reliable and accurate understanding of data when the assumptions of OLS are not met, leading to better informed decisions and insights.

How do outliers affect Ordinary Least Squares (OLS) regression, and why is this a problem?

Outliers can significantly distort the Ordinary Least Squares (OLS) regression line because OLS minimizes the sum of squared errors. A single extreme value can disproportionately influence the model, pulling it away from the true underlying relationship and leading to biased estimates. Robust methods are designed to mitigate this influence.

What are the potential consequences of relying on Ordinary Least Squares (OLS) when its assumptions are not met, and why is it important to consider robust alternatives?

Relying solely on Ordinary Least Squares (OLS) when its assumptions are violated can lead to flawed conclusions and poor decision-making. This is because the model may misrepresent the true relationships within the data, leading to inaccurate predictions and interpretations. Embracing robust alternatives can provide a more reliable understanding, especially in complex real-world scenarios, and reduce the risk of acting on misleading information. However, understanding your data is critical. If variance is understood then OLS can be exceptionally useful. Consider if the test you're creating is exploratory or confirmatory.