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ANOVA

Blog posts and articles with tips for doing ANOVA (Analysis of Variance), especially for quality improvement initiatives.

Suppose you’ve collected data on cycle time, revenue, the dimension of a manufactured part, or some other metric that’s important to you, and you want to see what other variables may be related to it. Now what? When I graduated from college with my first statistics degree, my diploma was bona fide proof that I'd endured hours and hours of classroom lectures on various statistical topics, including l... Continue Reading
Analysis of variance (ANOVA) can determine whether the means of three or more groups are different. ANOVA uses F-tests to statistically test the equality of means. In this post, I’ll show you how ANOVA and F-tests work using a one-way ANOVA example. But wait a minute...have you ever stopped to wonder why you’d use an analysis of variance to determine whether means are different? I'll also show how... Continue Reading

7 Deadly Statistical Sins Even the Experts Make

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by Laerte de Araujo Lima, guest blogger The NBA's 2015-16 season will be one for the history books. Not only was it the last season of Kobe Bryan, who scored 60 points in his final game, but the Golden State Warriors set a new wins record, beating the previous record set by 1995-96 Chicago Bulls. The Warriors seem likely to take this season's NBA title, in large part thanks to the performance of... Continue Reading
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
Mind the gap. It's is an important concept to bear in mind whilst traveling on the Tube in London, the T in Boston, the Metro in Washington, D.C., etc. But how many of us remember to mind the gap when we create an interval plot in Minitab Statistical Software? Not too many of us, I'd wager. And it's a shame, too. When you travel on the subway, minding the gap means giving thoughtful consideration... Continue Reading
What is an interaction? It’s when the effect of one factor depends on the level of another factor. Interactions are important when you’re performing ANOVA, DOE, or a regression analysis. Without them, your model may be missing an important term that helps explain variability in the response! For example, let’s consider 3-point shooting in the NBA. We previously saw that the number of 3-point... Continue Reading
In my last post, I looked at viewership data for the five seasons of HBO’s hit series Game of Thrones. I created a time series plot in Minitab that showed how viewership rose season by season, and how it varied episode by episode within each season.   My next step is to fit a statistical model to the data, which I hope will allow me to predict the viewing numbers for future episodes.    I am going to... Continue Reading
In this post, I’ll address some common questions we’ve received in technical support about the difference between fitted and data means, where to find each option within Minitab, and how Minitab calculates each. First, let’s look at some definitions. It’s useful to have an example, so I’ll be using the Light Output data set from Minitab’s Data Set Library, which includes a description of the sample... Continue Reading
In the world of linear models, a hierarchical model contains all lower-order terms that comprise the higher-order terms that also appear in the model. For example, a model that includes the interaction term A*B*C is hierarchical if it includes these terms: A, B, C, A*B, A*C, and B*C. Fitting the correct regression model can be as much of an art as it is a science. Consequently, there's not always a... 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
Back when I was an undergrad in statistics, I unfortunately spent an entire semester of my life taking a class, diligently crunching numbers with my TI-82, before realizing 1) that I was actually in an Analysis of Variance (ANOVA) class, 2) why I would want to use such a tool in the first place, and 3) that ANOVA doesn’t necessarily tell you a thing about variances. Fortunately, I've had a lot more... 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
As Halloween approaches, you are probably taking the necessary steps to protect yourself from the various ghosts, goblins, and witches that are prowling around. Monsters of all sorts are out to get you, unless they’re sufficiently bribed with candy offerings! I’m here to warn you about a ghoul that all statisticians and data scientists need to be aware of: phantom degrees of freedom. These phantoms... Continue Reading
In Part 5 of our series, we began the analysis of the experiment data by reviewing analysis of covariance and blocking variables, two key concepts in the design and interpretation of your results. The 250-yard marker at the Tussey Mountain Driving Range, one of the locations where we conducted our golf experiment. Some of the golfers drove their balls well beyond this 250-yard maker during a few of... Continue Reading
In Part 3 of our series, we decided to test our 4 experimental factors, Club Face Tilt, Ball Characteristics, Club Shaft Flexibility, and Tee Height in a full factorial design because of the many advantages of that data collection plan. In Part 4 we concluded that each golfer should replicate their half fraction of the full factorial 5 times in order to have a high enough power to detect... Continue Reading
With Speaker John Boehner resigning, Kevin McCarthy quitting before the vote for him to be Speaker, and a possible government shutdown in the works, the Freedom Caucus has certainly been in the news frequently! Depending on your political bent, the Freedom Caucus has caused quite a disruption for either good or bad.  Who are these politicians? The Freedom Caucus is a group of approximately 40... Continue Reading
You've collected a bunch of data. It wasn't easy, but you did it. Yep, there it is, right there...just look at all those numbers, right there in neat columns and rows. Congratulations. I hate to ask...but what are you going to do with your data? If you're not sure precisely what to do with the data you've got, graphing it is a great way to get some valuable insight and direction. And a good graph to... Continue Reading
Repeated measures designs don’t fit our impression of a typical experiment in several key ways. When we think of an experiment, we often think of a design that has a clear distinction between the treatment and control groups. Each subject is in one, and only one, of these non-overlapping groups. Subjects who are in a treatment group are exposed to only one type of treatment. This is the... 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
To make objective decisions about the processes that are critical to your organization, you often need to examine categorical data. You may know how to use a t-test or ANOVA when you’re comparing measurement data (like weight, length, revenue, and so on), but do you know how to compare attribute or counts data? It easy to do with statistical software like Minitab.  One person may look at this bar... Continue Reading