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Normal Distribution

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

T-tests are handy hypothesis tests in statistics when you want to compare means. You can compare a sample mean to a hypothesized or target value using a one-sample t-test. You can compare the means of two groups with a two-sample t-test. If you have two groups with paired observations (e.g., before and after measurements), use the paired t-test. How do t-tests work? How do t-values fit in? In this... Continue Reading
About a year ago, a reader asked if I could try to explain degrees of freedom in statistics. Since then,  I’ve been circling around that request very cautiously, like it’s some kind of wild beast that I’m not sure I can safely wrestle to the ground. Degrees of freedom aren’t easy to explain. They come up in many different contexts in statistics—some advanced and complicated. In mathematics, they're... Continue Reading

7 Deadly Statistical Sins Even the Experts Make

Do you know how to avoid them?

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Five-point Likert scales are commonly associated with surveys and are used in a wide variety of settings. You’ve run into the Likert scale if you’ve ever been asked whether you strongly agree, agree, neither agree or disagree, disagree, or strongly disagree about something. The worksheet to the right shows what five-point Likert data look like when you have two groups. Because Likert item data are... Continue Reading
In my last post, I discussed how a DOE was chosen to optimize a chemical-mechanical polishing process in the microelectronics industry. This important process improved the plant's final manufacturing yields. We selected an experimental design that let us study the effects of six process parameters in 16 runs. Analyzing the Design Now we'll examine the analysis of the DOE results after the actual... Continue Reading
Like so many of us, I try to stay healthy by watching my weight. I thought it might be interesting to apply some statistical thinking to the idea of maintaining a healthy weight, and the central limit theorem could provide some particularly useful insights. I’ll start by making some simple (maybe even simplistic) assumptions about calorie intake and expenditure, and see where those lead. And then... Continue Reading
There's nothing like a boxplot, aka box-and-whisker diagram, to get a quick snapshot of the distribution of your data. With a single glance, you can readily intuit its general shape, central tendency, and variability. To easily compare the distribution of data between groups, display boxplots for the groups side by side. Visually compare the central value and spread of the distribution for each... Continue Reading
How deeply has statistical content from Minitab blog posts (or other sources) seeped into your brain tissue? Rather than submit a biopsy specimen from your temporal lobe for analysis, take this short quiz to find out. Each question may have more than one correct answer. Good luck! Which of the following are famous figure skating pairs, and which are methods for testing whether your data follow a... Continue Reading
When you work in data analysis, you quickly discover an irrefutable fact: a lot of people just can't stand statistics. Some people fear the math, some fear what the data might reveal, some people find it deadly dull, and others think it's bunk. Many don't even really know why they hate statistics—they just do. Always have, probably always will.  Problem is, that means we who analyze data need to com... Continue Reading
There are many reasons why a distribution might not be normal/Gaussian. A non-normal pattern might be caused by several distributions being mixed together, or by a drift in time, or by one or several outliers, or by an asymmetrical behavior, some out-of-control points, etc. I recently collected the scores of three different teams (the Blue team, the Yellow team and the Pink team) after a laser... Continue Reading
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