Did Welch’s ANOVA Make Fisher's Classic One-Way ANOVA Obsolete?

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 Welch’s ANOVA, but also highlight some interesting research that we perform here at Minitab that guides the implementation of features in our statistical software.

One-Way ANOVA Assumptions

Like any...

Equivalence Testing for Quality Analysis (Part II): What Difference Does the Difference Make?

My previous post examined how an equivalence test can shift the burden of proof when you perform hypothesis test of the means. This allows you to more rigorously test whether the process mean is equivalent to a target or to another mean.

Here’s another key difference: To perform the analysis, an equivalence test requires that you first define, upfront, the size of a practically important difference between the mean and the target, or between two means.

Truth be told, even when performing a standard hypothesis test, you should know the value of this difference. Because you can’t really evaluate...

Analyzing College Football Overtimes

Two weeks ago Penn State and Michigan played in a quadruple-overtime thriller that almost went into a 5th overtime. Had Penn State coach Bill O’Brien kicked a field goal in the 4th overtime instead of going for it on 4th and 1, the game would have continued. But the Nittany Lions converted the 4th down (which, by the way, wasn’t a gamble) and went on to score the game winning touchdown in the 4th overtime.

Watching this game got me asking a bunch of questions. How many college football overtime games go into 4 overtimes? Did Penn State still have home-field advantage since they were playing at...

Using Hypothesis Tests to Bust Myths about the Battle of the Sexes

In my home, we’re huge fans of Mythbusters, the show on Discovery Channel. This fun show mixes science and experiments to prove or disprove various myths, urban legends, and popular beliefs. It’s a great show because it brings the scientific method to life. I’ve written about Mythbusters before to show how, without proper statistical analysis, it’s difficult to know when a result is statistically significant. How much data do you need to collect and how large does the difference need to be?

For this blog, let's look at a more recent Mythbusters episode, “Battle of the Sexes – Round Two.” I...

When Should NHL Goalies Get Pulled?

Even the best NHL goalies can get pulled several times each season. Do they really have cold streaks, or is a drop in save percentage on a given day part of normal random variation?

My colleague Doug Gorman and I decided to find out using our favorite statistical software package.  

Control Charts for Coaching Decisions

We used a control chart approach to determine if coaching decisions to pull goalies are supported by sound statistical rules, or if they seem to be more emotional reactions.

We generated 3-sigma lower control limits for each of 10 goalies based on their 2011-2012 game-by-game save...

Getting Started with Factorial Design of Experiments (DOE)

When I talk to quality professionals about how they use statistics, one tool they mention again and again is design of experiments, or DOE. I'd never even heard the term before I started getting involved in quality improvement efforts, but now that I've learned how it works, I wonder why I didn't learn about it sooner. If you need to find out how several factors are affecting a process outcome, DOE is the way to go. 

Somewhere in school you probably learned, like I did, that when you do an experiment you need to hold all the factors constant except for the one you're studying. That seems simple...

Using Minitab to Choose the Best Ranking System in College Basketball

Life is full of choices. Some are simple, such as what shirt to put on in the morning (although if you’re like me, it’s not so much of a “choice” as it is throwing on the first thing you grab out of the closet). And some choices are more complex. In the quality world, you might have to determine which distribution to choose for your capability analysis or which factor levels to use to bake the best cookie in a design of experiments. But all of these choices pale in comparison* to the most important decision you have to make each year: which college basketball teams to pick during March...

Will the Weibull Distribution Be on the Demonstration Test?

Over on the Indium Corporation's blog, Dr. Ron Lasky has been sharing some interesting ideas about using the Weibull distribution in electronics manufacturing. For instance, check out this discussion of how dramatically an early first-failure can affect an analysis of a part or component (in this case, an alloy used to solder components to a circuit board). 

This got me thinking again about all the different situations in which the Weibull distribution can help us make good decisions. The main reason Weibull is so useful is that it's very flexible in fitting different types of data, because it...

Understanding Type 1 and Type 2 Errors from the Feline Perspective: All Mistakes Are Not Equal!

Serving cat food? I sure hope you've set your alpha
level high enough.

"Bad kitty!" That's a phrase you almost never hear, but even we cats make the occasional mistake. I was reminded of this recently as I watched my human trying to analyze some data. People frequently make mistakes when they test a hypothesis with data analysis. Specifically, they can make either Type I or Type II errors.   

When I first started reading my human's statistics textbooks a few years ago, this idea seemed awfully silly to me. We cats appreciate being direct, and you either get the answer correct or you don't. I...

Do NFL Teams Have a Greater Home Field Advantage on Thursday Night?

When Alex Smith travels to Seattle, he has to go up against 67,000 screaming Seahawk fans that make Seattle one of the loudest stadiums in football. When Joe Flacco goes into Pittsburgh, he has to overcome 65,000 Steelers fans clad in black and gold and waving Terrible Towels. And when Matt Schaub plays in Jacksonville he has to, well...people do go to football games in Jacksonville, right?

Either way, all three scenarios have one thing in common. The home field advantage is exactly the same.

Whether you have a sold out stadium full of rambunctious fans, or the stadium is half full, the home...

The Stats Cat on Sample Size, Statistical Power, and the Revenge of the Zombie Salmon

Marlowe the Stats Cat here. That guy I share my house with left his laptop unattended again, and I spent the evening searching the web for news about one of my favorite subjects: salmon. Yum. But I wound up getting more than a collection of cool salmon pictures...I also got a better understanding of the role the size of a dataset plays when you're doing a hypothesis test.  

You see, my search led me to this paper that summarized a 2009 analysis of neuroimaging data collected from a frozen salmon. Yes, you did read that correctly: some people with Ph.D.'s actually ran an MRI on a dead fish....

The Problem With P-Charts: Out-of-control Cycle LaneYs!

Since we introduced new control charts in Minitab 16.2, I’ve been waiting to come across some real data I could use to showcase their awesome power. My friends, this day has come! I am about to reveal a perhaps unconventional use of the Laney P' chart to investigate national cycling data in the UK. So we’re not looking at any real process here, which is how the P' chart is usually used, just data from a national study about cycling habits. Why? Because this dataset gives us a prime example (see what I did there…?) of overdispersion issues that can cause problems when we use standard P control...

Gummi Bear DOE: Replicates and Center Points, Part 2

Last time, we talked about center points and replicates in design of experiments. It turns out that both are tools that you can use to increase the probability of finding a statistically significant difference. But what we really want to know is, how many center points and replicates should be in the gummi bear experiment? To answer that question, we have to estimate the standard deviation of the distances the gummi bears go.

Estimating the Standard Deviation When You Do Design of Experiments

I do have an old data set from some students launching gummi bears that I can use. Historical data is a...

Busting the Mythbusters with Statistics: Are Yawns Contagious?

This looks like a typical Mythbusters experiment!

Statistics can be unintuitive. What’s a large difference? What’s a large sample size? When is something statistically significant? You might think you know, based on experience and intuition, but you really don’t know until you actually run the analysis. You have to run the proper statistical tests to know what the data are telling you!

Even experts can get tripped up by their hunches, as we'll see.

In my family, we’re huge fans of the Mythbusters. This fun Discovery Channel show mixes science and experiments to prove or disprove various myths,...

Gummi Bear DOE: Replicates and Center Points, Part 1

Last time, we talked about what resolution means in design of experiments (DOE). After you choose your resolution in Minitab Statistical Software, you need to choose the number of center points and the number of replicates for corner points. We can consider these two questions together because they’ll help determine the total size of the experiment.

Using center points to check your model

I alluded to center points when we talked about 2-level designs previously. Center points are experimental runs with the all of the continuous factor settings set halfway between the low level and the high...

Measuring Up to Prove Accuracy to a Commission

I love talking to people who use data and analysis to improve processes and quality. As I've worked with customers to tell their stories, my definition of "quality" has expanded. In some cases, data has been used not just to improve quality in terms of reducing defects, but even to demonstrate to regulators that a company is already meeting or exceeding regulatory requirements. 
A few years ago, I spoke with some of the quality experts at a large energy company. This company's business included delivering natural gas to 1.2 million customers in a midwestern state.   Remote systems on about...

Presidential Politics, Political Polls, and Statistics!

It’s election year, and the Presidential campaign is picking up! These are exciting times for my buddy and I who are political junkies. Bring on the banners, slogans, rhetoric, and debates. Our TVs will be filled with ads about everything from financial policy to energy prices. Barack Obama and Mitt Romney may be in our living rooms more often than many family members!

We not only follow all of the races but we make small, friendly bets about the outcomes. However, the winnings pale in importance to the bragging rights! Each bet takes on a life of its own and winning the bet almost becomes more...

The Short, Wild Life Of A Lipsticked Pig

The 2012 U.S. presidential campaign is kicking into high gear. And you know what that means.

Political memes will soon be hatching from their electronic eggs, flying through myriad channels of the media, and buzzing annoyingly in your ears.

Memes are kernels of content that spread rapidly across the internet. Love them or hate them, you can’t deny their proliferation or their impact on our mass consciousness.

Remember the 2008 campaign? Lipstick on a pig? Joe the Plumber?

To explore the dynamic life cycle of memes, researchers at Cornell and Stanford tracked the top memes from the 2008...

Large Samples: Too Much of a Good Thing?

The other day I stopped at a fast food joint for the first time in a while.

After I ordered my food, the cashier asked me if I wanted to upgrade to the “Super-Smiley-Savings-Meal” or something like that, and I said, “Sure.”  

When it came, I was astounded to see the gargantuan soda cup. I don’t know how many ounces it was, but you could have bathed a dachshund in it.

If I drank all the Coke that honkin' cup could hold, the megadose of sugar and caffeine would launch me into permanent orbit around Earth.

That huge cup made me think of sample size.

Generally, having more data is a good thing. But if...

How to Identify the Distribution of Your Data using Minitab

I love all data, whether it’s normally distributed or downright bizarre. However, many people are more comfortable with the symmetric, bell-shaped curve of a normal distribution. It is not as intuitive to understand a Gamma distribution, with its shape and scale parameters, as it is to understand the familiar Normal distribution with its mean and standard deviation.

However, it's a fact of life that not all data follow the Normal distribution. Hey, a lot of stuff is just abnormal...er...non-normally distributed. How to understand and present the practical implications of your non-normal...