What is Normal Data and why is it important?

A quick introduction to understanding Normal Data

What is Normal Data and why is it important?

Stockholm, Sweden

1/14/2025

David Leiva

David Leiva

Lean Six Sigma Master Black Belt

Whenever we dive into statistics, one concept that pops up over and over is the Normal Distribution. But what does it really mean? And why is it so important? Let's break it down in simple terms.

What Is A Normal Distribution?

A Normal Distribution is a way to describe how data is spread out. It's often called a “bell curve” because of its shape: the highest point is in the middle, and it gently slopes down on both sides. The idea is that most of your data will cluster around the average (or mean), with fewer values the further you move from it.

Gaussian with limits

For example, let's say you're timing how long it takes to complete a task. Your times might look something like this:

10:15

10:21

10:23

10:17

10:18

10:22

10:21

10:17

If we plot this data on a graph, the majority of your times would stack up around 10.19. That's the mean. If your process is consistent, the graph would look symmetrical—a classic bell curve.

Why does it matter?

The Normal Distribution is everywhere. From the heights of people to IQ scores to how long it takes to bake a cake, natural childbirth, or even gambling in Vegas. Data from countless real-world processes follow this pattern. Here's why it's so useful:

  • Predictability When your data follows a normal distribution, you can use it to make predictions. For example, you can calculate the likelihood of a value falling within a certain range.
  • Reliability A normal distribution often indicates that your process is stable and under control. If the data starts to skew (e.g., the curve becomes lopsided), it's a sign that something might be wrong.

The Role of the Mean and Standard Deviation

Two key players define a normal distribution:

  • Mean μ The average value of your data. It's the center of the bell curve.
  • Standard Deviation σ This measures how spread out the data is. A small standard deviation means most data points are close to the mean, while a larger one means they're more spread out.
Gaussian with limits

Think of it like this: If you're making cookies and your bake times have a small standard deviation, it means almost every batch comes out perfect. A large standard deviation? Well, some cookies might be undercooked, and others might be burnt.

Why Should You Care?

Understanding the Normal Distribution helps you evaluate your processes and make better decisions. It's not just about being “on average” but about being consistently close to that average. The more consistent your process, the more reliable your results will be.

Typically for us to test Normality, we rely on different statistical tests which will tell us if our data points are Normal or not.

To determine if data follows a normal distribution, several statistical tests are commonly used. The Anderson-Darling (AD) test checks how well your data aligns with a specified distribution (commonly normal) by giving more weight to the tails of the distribution, making it sensitive to deviations at the extremes. The Kolmogorov-Smirnov (KS) test compares the cumulative distribution of your data to the expected normal distribution, identifying differences across the entire range, but it may lack sensitivity for smaller datasets. The Shapiro-Wilk (SW) test is particularly effective for small to moderate sample sizes and tests whether the data points can be modeled by a normal distribution. All these tests produce a p-value; if it's below a chosen significance level (like 0.05), you reject the assumption of normality. Each test has strengths, so selecting the right one depends on sample size and the importance of tail behavior.

Scatter correlation

Note: If my data is non-normal, it is not the end of the world! There is always an explanation for this!

What Happens If My Data Points Are Non-Normal?

So, we've talked about how amazing it is to have a Normal Distribution—predictability, stability, and that nice bell curve. But what if your data doesn't follow a normal distribution? Don't worry; this happens more often than you might think. Let's break it down.

What Does Non-Normal Mean?

When your data is non-normal, it means the shape of your data doesn't resemble the symmetrical bell curve of a normal distribution. Instead, it might look skewed.

Skewed distribution

Why does it happen?

Here are a few common reasons your data might be non-normal:

  • Natural Causes Some processes simply don't produce normal data. For example, income levels in a population are usually right-skewed because a few people earn way more than the average. Other examples of these are manufacturing process times or Pull Tests.
  • Process Instability If your process isn't under control, you might see unusual patterns in your data. For instance, machine malfunctions or sudden supply chain disruptions can cause skewed results.
  • Outliers Extreme values can distort the shape of your distribution

Why Should You Care About Non-Normal Data?

Non-normal data can cause problems if you're using statistical tools that assume a normal distribution. Many calculations, like process capability (Cp, Cpk) or hypothesis testing, are based on normality. If your data doesn't follow a bell curve, your results might not be accurate, leading to poor decisions.

What Can You Do About It?

  • Check for Outliers Look for unusual data points that might be throwing off your distribution. If they're errors or anomalies, you can remove them (but make sure you have a good reason!).
  • Transform the Data Sometimes, applying a transformation (like Box-Cox or Johnson) can make the data look more normal.
  • Use Non-Parametric Tests If transforming the data isn't an option, consider using statistical tools that don't assume normality. You can test to see if it resembles another distribution.
  • Understand the Root Cause If your data is non-normal because your process is unstable, you might need to fix the root cause. This could mean adjusting your process, eliminating bottlenecks, or improving consistency.

Regardless of whether you're dealing with Normal or Non-Normal data, the shape of the data is telling you something important about your process. Don't ignore it—learn from it!

I'm David, Lean Six Sigma Master Black Belt

David

With over 15 years of experience in various manufacturing industries, I've gained valuable knowledge and insights. I'm happy to help with any questions or comments you might have about this post or statistics in general—feel free to reach out!

david@dominionspc.com

Dominion

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