If you’ve worked with inferential statistical methods, you’ve likely heard of the normal distribution. Despite how well-known the term “normal distribution” is, there’s a lot of confusion about what it means and why it matters (or doesn’t, depending on your method). In this article, we’ll clear up that confusion so you walk away with a better understanding of normal distribution as it reflects to the methods and processes you’re working with.
What is a Normal Distribution?
Inferential statistical methods are based on the recognition of a pattern of variation and once established and described, comparison of other processes to the pattern. The Normal distribution goes hand in hand with inferential statistical methods as it is a pattern of variation. It plays an essential part in Six Sigma and Statistical Process Control as they both rely on these statistics for their methods and compare variation in a process of interest to a reference distribution (e.g, an established pattern or distribution.)
Diving a bit deeper into what a normal distribution is, it can be defined as a specific pattern or distribution that is described mathematically. These patterns or distributions occur commonly in both natural and manmade (think: manufacturing and nonmanufacturing) processes. Keep in mind that the averages of randomly selected samples from a stable process will naturally follow a normal distribution if the sample sizes are large enough.
But what makes a Normal distribution normal or is it really “normal”? There is disagreement on where the term “Normal” came from, but it was most probably adopted since it is a common distribution, i.e., it occurs often in nature. However, not all patterns are normally Normal. Some process outputs “normally” follow different patterns. Though if you had to rate patterns (distributions) on their importance to statistics, the Normal distribution would surely be number 1!
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Does the “Normalness” of the Distribution Really Matter?
Your next question is probably going to be: “Does it matter if a distribution is normal?” It’s a good question, and the answer is, “It depends.” If the statistical method you’re working with is mostly dependent on you being able to assume that the pattern of variation is “normally” normal, then yes, it matters. But if being able to make that assumption confidently is not central to the method you’re working with, then it may not matter.
So, when you’re working with a statistical method and deciding how to use it, be sure to determine whether or not the method assumes a normal distribution and how sensitive it is to that assumption. If the method is robust to that assumption, the consequences of the distribution not being normal are minimal and therefore, not as important. But if the method is less robust to that assumption, then you must be aware that distribution that is not normal may lead you to an incorrect conclusion.
Finally, an incorrect conclusion could produce a domino effect if you’re making high-level, strategic decisions based on the conclusion drawn. Thus, it’s critical to establish from the beginning how the Normal distribution relates to any and all statistical methods used and the robustness of an assumption before diving into mission-critical projects and processes.
For more insights into normal distribution and other reference distributions, sign up for NWCPE’s upcoming SS 511 Hypothesis Testing for Observational Data today.