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Normal Distribution

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

As a person who loves baking (and eating) cakes, I find it bothersome to go through all the effort of baking a cake when the end result is too dry for my taste. For that reason, I decided to use a designed experiment in Minitab to help me reduce the moisture loss in baked chocolate cakes, and find the optimal settings of my input factors to produce a moist baked chocolate cake. I’ll share the... 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

7 Deadly Statistical Sins Even the Experts Make

Do you know how to avoid them?

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T'was the season for toys recently, and Christmas day found me playing around with a classic, the Etch-a-Sketch. As I noodled with the knobs, I had a sudden flash of recognition: my drawing reminded me of the Empirical CDF Plot in Minitab Statistical Software. Did you just ask, "What's a CDF plot? And what's so empirical about it?" Both very good questions. Let's start with the first, and we'll... Continue Reading
In my last post on DMAIC tools for the Define phase, we reviewed various graphs and stats typically used to define project goals and customer deliverables. Let’s now move along to the tools you can use in Minitab Statistical Software to conduct the Measure phase. Measure Phase Methodology The goal of this phase is to measure the process to determine its current performance and quantify the problem.... Continue Reading
by Matthew Barsalou, guest blogger The great Dr. Seuss tells of Mr. Plunger, who is the custodian at Diffendoofer School on the corner of Dinkzoober and Dinzott in the town of Dinkerville. The good Mr. Plunger “keeps the whole school clean” using a supper-zooper-flooper-do. Unfortunately, Dr. Seuss fails to tell us where the supper-zooper-flooper-do came from and if the production process was... Continue Reading
The language of statistics is a funny thing, but there usually isn't much to laugh at in the consequences that can follow when misunderstandings occur between statisticians and non-statisticians. We see these consequences frequently in the media, when new studies—that usually contradict previous ones—are breathlessly related, as if their findings were incontrovertible facts. Similar, though less... Continue Reading
As we enter late December, snow is falling here on the East Coast of the United States. The official start to winter is on December 21, 2016, but it’s certainly not uncommon to see snowflakes flying before this date. If you live in the U.S., you know the winter of 2015 was one for the record books. In fact, more than 90 inches of snow fell in Boston in the winter of 2015! Have you ever wondered how... Continue Reading
If you’re familiar with Lean Six Sigma, then you’re familiar with DMAIC. DMAIC is the acronym for Define, Measure, Analyze, Improve and Control. This proven problem-solving strategy provides a structured 5-phase framework to follow when working on an improvement project. This is the first post in a five-part series that focuses on the tools available in Minitab Statistical Software that are most... Continue Reading
by Matt Barsalou, guest blogger I know that Thanksgiving is always on the last Thursday in November, but somehow I failed to notice it was fast approaching until the Monday before Thanksgiving. This led to frantically sending a last-minute invitation, and a hunt for a turkey. I live in Germany and this greatly complicated the matter. Not only is Thanksgiving not celebrated, but also actual turkeys... Continue Reading
In Part 1 of this blog series, I wrote about how statistical inference uses data from a sample of individuals to reach conclusions about the whole population. That’s a very powerful tool, but you must check your assumptions when you make statistical inferences. Violating any of these assumptions can result in false positives or false negatives, thus invalidating your results.  The common data... Continue Reading
Statistical inference uses data from a sample of individuals to reach conclusions about the whole population. It’s a very powerful tool. But as the saying goes, “With great power comes great responsibility!” When attempting to make inferences from sample data, you must check your assumptions. Violating any of these assumptions can result in false positives or false negatives, thus invalidating... Continue Reading
So the data you nurtured, that you worked so hard to format and make useful, failed the normality test. Time to face the truth: despite your best efforts, that data set is never going to measure up to the assumption you may have been trained to fervently look for. Your data's lack of normality seems to make it poorly suited for analysis. Now what? Take it easy. Don't get uptight. Just let your data... Continue Reading
See if this sounds fair to you. I flip a coin. Heads: You win $1.Tails: You pay me $1. You may not like games of chance, but you have to admit it seems like a fair game. At least, assuming the coin is a normal, balanced coin, and assuming I’m not a sleight-of-hand magician who can control the coin. How about this next game? You pay me $2 to play.I flip a coin over and over until it comes up heads.Your... Continue Reading
Back when I used to work in Minitab Tech Support, customers often asked me, “What’s the difference between Cpk and Ppk?” It’s a good question, especially since many practitioners default to using Cpk while overlooking Ppk altogether. It’s like the '80s pop duo Wham!, where Cpk is George Michael and Ppk is that other guy. Poofy hairdos styled with mousse, shoulder pads, and leg warmers aside, let’s... Continue Reading
Here is a scenario involving process capability that we’ve seen from time to time in Minitab's technical support department. I’m sharing the details in this post so that you’ll know where to look if you encounter a similar situation. You need to run a capability analysis. You generate the output using Minitab Statistical Software. When you look at the results, the Cpk is huge and the histogram in... Continue Reading
In my last post, we took the red pill and dove deep into the unarguably fascinating and uncompromisingly compelling world of the matrix plot. I've stuffed this post with information about a topic of marginal interest...the marginal plot. Margins are important. Back in my English composition days, I recall that margins were particularly prized for the inverse linear relationship they maintained with... Continue Reading
Earlier this month, PLOS.org published an article titled "Ten Simple Rules for Effective Statistical Practice." The 10 rules are good reading for anyone who draws conclusions and makes decisions based on data, whether you're trying to extend the boundaries of scientific knowledge or make good decisions for your business.  Carnegie Mellon University's Robert E. Kass and several co-authors devised... 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
For hundreds of years, people having been improving their situation by pulling themselves up by their bootstraps. Well, now you can improve your statistical knowledge by pulling yourself up by your bootstraps. Minitab Express has 7 different bootstrapping analyses that can help you better understand the sampling distribution of your data.  A sampling distribution describes the likelihood of... Continue Reading
Once upon a time, when people wanted to compare the standard deviations of two samples, they had two handy tests available, the F-test and Levene's test. Statistical lore has it that the F-test is so named because it so frequently fails you.1 Although the F-test is suitable for data that are normally distributed, its sensitivity to departures from normality limits when and where it can be used. Leve... Continue Reading