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Normal Distribution

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

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
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
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
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
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
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
We're frequently asked whether Minitab has been validated by the U.S. Food and Drug Administration (FDA) for use in the pharmaceutical and medical device industries. Minitab does extensive testing to validate our software internally, but Minitab’s statistical software is not—and cannot be—FDA-validated out-of-the-box. Nobody's can. It is a common misconception that software vendors can go through a... Continue Reading
Atlanta was a mess on January 28th, 2014.  Thousands were trapped on the roads overnight while others managed to get to roadside stores to camp out. Thousands of students were forced to spend the night in their schools and the National Guard was called in to get them home. Many wondered how less than three inches of snow could cripple the city, particularly when Atlanta had experienced a similar... Continue Reading
In Parts 1 and 2 of Gauging Gage we looked at the numbers of parts, operators, and replicates used in a Gage R&R Study and how accurately we could estimate %Contribution based on the choice for each.  In doing so, I hoped to provide you with valuable and interesting information, but mostly I hoped to make you like me.  I mean like me so much that if I told you that you were doing... Continue Reading
My main objective is to encourage greater use of statistical techniques in the service sector and present new ways to implement them. In a previous blog, I presented an approach you can use  to identify process steps that may be improved in the service sector (quartile analysis). In this post I'll show how nonparametric distribution analysis may be implemented in the service sector to analyze... Continue Reading
For one reason or another, the response variable in a regression analysis might not satisfy one or more of the assumptions of ordinary least squares regression. The residuals might follow a skewed distribution or the residuals might curve as the predictions increase. A common solution when problems arise with the assumptions of ordinary least squares regression is to transform the response... Continue Reading
When I think about the Central Limit Theorem (CLT), bunnies and dragons are just about the last things that come to mind. However, that’s not the case for Shuyi Chiou, whose playful CreatureCast.org animation explains the CLT using both fluffy and fire-breathing creatures. Per the article that accompanied this video in The New York Times: “Many real-world observations can be approximated by, and... Continue Reading
All measurements are rounded to some degree. In most cases, you would not want to reject normality just because the data are rounded. In fact, the normal distribution would be a quite desirable model for the data if the underlying distribution is normal since it would smooth out the discreteness in the rounded measurements. Some normality tests reject a very high percentage of time due to rounding... Continue Reading
Minitab Statistical Software offers three tests for Normality: Anderson-Darling (AD), Ryan-Joiner (RJ), and Kolmogorov-Smirnov (KS). The AD test is the default, but is it the best test at detecting Non-Normality? Let's compare the ability of each of these normality tests to detect non-normal data under three different scenarios.  We'll use simulated data for each, but they reflect common... Continue Reading
Most of the data that one can collect and analyze follow a normal distribution (the famous bell-shaped curve). In fact, the formulae and calculations used in many analyses simply take it for granted that our data follow this distribution; statisticians call this the "assumption of normality." For example, our data need to meet the normality assumption before we can accept the results of a one- or... Continue Reading