Normal Distribution

Blog posts and articles about the role of the normal distribution in statistics, data analysis, and quality improvement.

It’s safe to say that most people who use statistics are more familiar with parametric analyses than nonparametric analyses. Nonparametric tests are also called distribution-free tests because they don’t assume that your data follow a specific distribution. You may have heard that you should use nonparametric tests when your data don’t meet the assumptions of the parametric test, especially the... Continue Reading
In part 1 of this post, I covered how Six Sigma students at Rose-Hulman Institute of Technology cleaned up and prepared project data for a regression analysis. Now we're ready to start our analysis. We’ll detail the steps in that process and what we can learn from our results. What Factors Are Important? We collected data about 11 factors we believe could be significant: Whether the date of... Continue Reading
By Peter Olejnik, guest blogger. Previous posts on the Minitab Blog have discussed the work of the Six Sigma students at Rose-Hulman Institute of Technology to reduce the quantities of recyclables that wind up in the trash. Led by Dr. Diane Evans, these students continue to make an important impact on their community. As with any Six Sigma process, the results of the work need to be evaluated. A... Continue Reading
If you wanted to figure out the probability that your favorite football team will win their next game, how would you do it?  My colleague Eduardo Santiago and I recently looked at this question, and in this post we'll share how we approached the solution. Let’s start by breaking down this problem: There are only two possible outcomes: your favorite team wins, or they lose. Ties are a possibility,... Continue Reading
by Matthew Barsalou, guest blogger.  E. E. Doc Smith, one of the greatest authors ever, wrote many classic books such as The Skylark of Space and his Lensman series. Doc Smith’s imagination knew no limits; his Galactic Patrol had millions of combat fleets under its command and possessed planets turned into movable, armored weapons platforms. Some of the Galactic Patrol’s weapons may be well... Continue Reading
In technical support, we frequently receive calls from Minitab users who have questions about the differences between Cpk and Ppk.  Michelle Paret already wrote a great post about the differences between Cpk and Ppk, but it also helps to have a better understanding of the math behind these numbers. So in this post I will show you how to calculate Ppk using Minitab’s default settings when the... Continue Reading
Have you ever had a probability plot that looks like this? The probability plot above is based on patient weight (in pounds) after surgery minus patient weight (again, in pounds) before surgery. The red line appears to go through the data, indicating a good fit to the Normal, but there are clusters of plotting points at the same measured value. This occurs on a probability plot when there are many... Continue Reading
Last week, thanks to the collective effort from many people, we held very successful events in Guadalajara and Mexico City, which gave us a unique opportunity to meet with over 300 Spanish-speaking Minitab users. They represented many different industries, including automotive, textile, pharmaceutical, medical devices, oil and gas, electronics, and mining, as well as academic institutions and... Continue Reading
I’ve written about the importance of checking your residual plots when performing linear regression analysis. If you don’t satisfy the assumptions for an analysis, you might not be able to trust the results. One of the assumptions for regression analysis is that the residuals are normally distributed. Typically, you assess this assumption using the normal probability plot of the residuals. Are... Continue Reading
The word kurtosis sounds like a painful, festering disease of the gums. But the term actually describes the shape of a data distribution. Frequently, you'll see kurtosis defined as how sharply "peaked" the data are. The three main types of kurtosis are shown below. Lepto means "thin" or "slender" in Greek. In leptokurtosis, the kurtosis value is high. Platy means "broad" or "flat"—as in duck-billed pl... Continue Reading
Do you suffer from PAAA (Post-Analysis Assumption Angst)? You’re not alone. Checking the required assumptions for a statistical  analysis is critical. But if you don’t have a Ph.D. in statistics, it can feel more complicated and confusing than the primary analysis itself. How does the cuckoo egg data, a common sample data set often used to teach analysis of variance, satisfy the following formal... Continue Reading
by Iván Alfonso, guest blogger I'm a huge fan of hot cakes—they are my favorite dessert ever. I’ve been cooking them for over 15 years, and over that time I’ve noticed many variation in textures, flavor, and thickness. Personally, I like fluffy pancakes. There are many brands of hotcake mix on the market, all with very similar formulations. So I decided to investigate which ingredients and inputs... Continue Reading
There is more than just the p value in a probability plot—the overall graphical pattern also provides a great deal of useful information. Probability plots are a powerful tool to better understand your data. In this post, I intend to present the main principles of probability plots and focus on their visual interpretation using some real data. In probability plots, the data density distribution... Continue Reading
Remember "The Little Engine That Could," the children's story about self-confidence in the face of huge challenges? In it, a train engine keeps telling itself "I think I can" while carrying a very heavy load up a big mountain. Next thing you know, the little engine has done it...but until that moment, the outcome was uncertain. It's a wonderful story for teaching kids about self-confidence. But... Continue Reading
These days, my memory isn't what it used to be. Besides that, my memory isn't what it used to be.  But my incurable case of CRS (Can't Remember Stuff) is not nearly as bad as that of the exponential distribution. When modelling failure data for reliability analysis, the exponential distribution is completely memoryless. It retains no record of the previous failure of an item. That might sound like a... Continue Reading
Now that you’ve seen how to automatically import data and run analyses in my previous post, let’s create the Monthly Report! I will be using a Microsoft Word Document (Office 2010) and adding bookmarks to act as placeholders for the Graphs, statistics, and boilerplate conclusions. Let’s go through the steps to accomplish this: Open up an existing report that you have previously created in Microsoft... Continue Reading
One-way ANOVA can detect differences between the means of three or more groups. It’s such a classic statistical analysis that it’s hard to imagine it changing much. However, a revolution has been under way for a while now. Fisher's classic one-way ANOVA, which is taught in Stats 101 courses everywhere, may well be obsolete thanks to Welch’s ANOVA. In this post, I not only want to introduce you to... Continue Reading
by Laerte de Araujo Lima, guest blogger In a previous post (How Data Analysis Can Help Us Predict This Year's Champions League), I shared how I used Minitab Statistical Softwareto predict the 2013-2014 season of the UEFA Champions league. This involved the regression analysis of main critical-to-quality (CTQ) factors, which I identified using the “voice of the customer” suggestions of some... Continue Reading
Transformations and non-normal distributions are typically the first approaches considered when the when the Normality test fails in a capability analysis. These approaches do not work when there are extreme outliers because they both assume the data come from a single common-cause variation distribution. But because extreme outliers typically represent special-cause variation, transformations... Continue Reading