Normal Distribution

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

Control charts are a fantastic tool. These charts plot your process data to identify common cause and special cause variation. By identifying the different causes of variation, you can take action on your process without over-controlling it. Assessing the stability of a process can help you determine whether there is a problem and identify the source of the problem. Is the mean too high, too low,... Continue Reading
By Matthew Barsalou, guest blogger A problem must be understood before it can be properly addressed. A thorough understanding of the problem is critical when performing a root cause analysis (RCA) and an RCA is necessary if an organization wants to implement corrective actions that truly address the root cause of the problem. An RCA may also be necessary for process improvement projects; it is... Continue Reading
Since it's the Halloween season, I want to share how a classic horror film helped me get a handle on an extremely useful statistical distribution.  The film is based on John W. Campbell's classic novella "Who Goes There?", but I first became  familiar with it from John Carpenter's 1982 film The Thing.   In the film, researchers in the Antarctic encounter a predatory alien with a truly frightening... Continue Reading
By Matthew Barsalou, guest blogger Teaching process performance and capability studies is easier when actual process data is available for the student or trainee to practice with. As I have previously discussed at the Minitab Blog, a catapult can be used to generate data for a capability study. My last blog on using a catapult for this purspose was several years ago, so I would like to revisit... Continue Reading
How many samples do you need to be “95% confident that at least 95%—or even 99%—of your product is good? The answer depends on the type of response variable you are using, categorical or continuous. The type of response will dictate whether you 'll use: Attribute Sampling: Determine the sample size for a categorical response that classifies each unit as Good or Bad (or, perhaps, In-spec or... Continue Reading
Whatever industry you're in, you're going to need to buy supplies. If you're a printer, you'll need to purchase inks, various types of printing equipment, and paper. If you're in manufacturing, you'll need to obtain parts that you don't make yourself.  But how do you know you're making the right choice when you have multiple suppliers vying to fulfill your orders?  How can you be sure you're... Continue Reading
Ever use dental floss to cut soft cheese? Or Alka Seltzer to clean your toilet bowl? You can find a host of nonconventional uses for ordinary objects online. Some are more peculiar than others. Ever use ordinary linear regression to evaluate a response (outcome) variable of counts?  Technically, ordinary linear regression was designed to evaluate a a continuous response variable. A continuous... Continue Reading
When we take pictures with a digital camera or smartphone, what the device really does is capture information in the form of binary code. At the most basic level, our precious photos are really just a bunch of 1s and 0s, but if we were to look at them that way, they'd be pretty unexciting. In its raw state, all that information the camera records is worthless. The 1s and 0s need to be converted... Continue Reading
The 1949 film A Connecticut Yankee in King Arthur's Court includes the song “Busy Doing Nothing,” and this could be written about the Null Hypothesis as it is used in statistical analyses.  The words to the song go: We're busy doin' nothin'Workin' the whole day through Tryin' to find lots of things not to do And that summarises the role of the Null Hypothesis perfectly. Let me explain why. What's... Continue Reading
by Colin Courchesne, guest blogger, representing his Governor's School research team.   High-level research opportunities for high school students are rare; however, that was just what the New Jersey Governor’s School of Engineering and Technology provided.  Bringing together the best and brightest rising seniors from across the state, the Governor’s School, or GSET for short, tasks teams of... Continue Reading
If you've read the first two parts of this tale, you know it started when I published a post that involved transforming data for capability analysis. When an astute reader asked why Minitab didn't seem to transform the data outside of the capability analysis, it revealed an oversight that invalidated the original analysis.  I removed the errant post. But to my surprise, the reader who helped me... Continue Reading
I don't like the taste of crow. That's a shame, because I'm about to eat a huge helping of it.  I'm going to tell you how I messed up an analysis. But in the process, I learned some new lessons and was reminded of some older ones I should remember to apply more carefully.  This Failure Starts in a Victory My mistake originated in the 2015 Triple Crown victory of American Pharoah. I'm no... Continue Reading
Every now and then I’ll test my Internet speed at home using such sites as http://speedtest.comcast.net  or http://www.att.com/speedtest/.  My need to perform these tests could stem from the cool-looking interfaces they employ on their site, as they display the results using analog speedometers and RPM meters. They could also stem from the validation that I need in "getting what I am paying for,"... Continue Reading
By Matthew Barsalou, guest blogger.   Many statistical tests assume the data being tested came from a normal distribution. Violating the assumption of normality can result in incorrect conclusions. For example, a Z test may indicate a new process is more efficient than an older process when this is not true. This could result in a capital investment for equipment that actually results in higher... Continue Reading
Scientists who use the Hubble Space Telescope to explore the galaxy receive a stream of digitized images in the form binary code. In this state, the information is essentially worthless- these 1s and 0s must first be converted into pictures before the scientists can learn anything from them. The same is true of statistical distributions and parameters that are used to describe sample data. They... Continue Reading
In previous posts, I discussed the results of a recycling project done by Six Sigma students at Rose-Hulman Institute of Technology last spring. (If you’re playing catch up, you can read Part I and Part II.) The students did an awesome job reducing the amount of recycling that was thrown into the normal trash cans across all of the institution’s academic buildings. At the end of the spring... Continue Reading
by Matthew Barsalou, guest blogger.  The old saying “if it walks like a duck, quacks like a duck and looks like a duck, then it must be a duck” may be appropriate in bird watching; however, the same idea can’t be applied when observing a statistical distribution. The dedicated ornithologist is often armed with binoculars and a field guide to the local birds and this should be sufficient. A... Continue Reading
As a Minitab trainer, one of the most common questions I get from training participants is "what should I do when my data isn’t normal?" A large number of statistical tests are based on the assumption of normality, so not having data that is normally distributed typically instills a lot of fear. Many practitioners suggest that if your data are not normal, you should do a nonparametric version of... Continue Reading
A while back, I offered an overview of process capability analysis that emphasized the importance of matching your analysis to the distribution of your data. If you're already familiar with different types of distributions, Minitab makes it easy to identify what type of data you're working with, or to transform your data to approximate the normal distribution. But what if you're not so great with... Continue Reading
In 1898, Russian economist Ladislaus Bortkiewicz published his first statistics book entitled Das Gesetz der keinem Zahlen, in which he included an example that eventually became famous for illustrating the Poisson distribution. Bortkiewicz researched the annual deaths by horse kicks in the Prussian Army from 1875-1984. Data was recorded from 14 different army corps, with one being the Guard... Continue Reading