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...

The Best European Football League: What the CTQ’s and Minitab Can Tell Us

by Laerte de Araujo Lima, guest blogger

In a previous post (How Data Analysis Can Help Us Predict This Year's Champions League), I shared how I used Minitab Statistical Software to predict the 2013-2014 season of the UEFA Champions league. This involved the regression analysis of main critical-to-quality (CTQ) factors, which I identified using the “voice of the customer” suggestions of some friends.

Since that post was published, my friends have stopped discussing the UEFA Champions league—they were convinced by the results I shared.

But now they’ve challenged me to use Six Sigma tools to...

How to Handle Extreme Outliers in Capability Analysis

Transformations and non-normal distributions are typically the first approaches considered when the when the Normality test fails in a capability analysis. These approaches do not work when there are extreme outliers because they both assume the data come from a single common-cause variation distribution. But because extreme outliers typically represent special-cause variation, transformations and non-normal distributions are not good approaches for data that contain extreme outliers.

As an example, the four graphs below show distribution fits for a dataset with 99 values simulated from a...

Is Your Statistical Software FDA Validated for Medical Devices or Pharmaceuticals?

We're frequently asked whether Minitab has been validated by the U.S. Food and Drug Administration (FDA) for use in the pharmaceutical and medical device industries.

Minitab does extensive testing to validate our software internally, but Minitab’s statistical software is not—and cannot be—FDA-validated out-of-the-box.

Nobody's can.

It is a common misconception that software vendors can go through a certification process to achieve FDA software validation. It's simply not true.

Software vendors who claim their products are FDA-validated should be scrutinized. It is up to the software purchaser to...

Are Atlanta's Winters Getting Colder and Snowier?

Atlanta was a mess on January 28th, 2014.  Thousands were trapped on the roads overnight while others managed to get to roadside stores to camp out. Thousands of students were forced to spend the night in their schools and the National Guard was called in to get them home. Many wondered how less than three inches of snow could cripple the city, particularly when Atlanta had experienced a similar storm in 2011?

This traumatic event, the recollection of recent snow storms, and now the current storm prompted some to wonder whether Atlanta has been experiencing more cold and snow than before. How...

Gauging Gage Part 3: How to Sample Parts

In Parts 1 and 2 of Gauging Gage we looked at the numbers of parts, operators, and replicates used in a Gage R&R Study and how accurately we could estimate %Contribution based on the choice for each.  In doing so, I hoped to provide you with valuable and interesting information, but mostly I hoped to make you like me.  I mean like me so much that if I told you that you were doing something flat-out wrong and had been for years and probably screwed somethings up, you would hear me out and hopefully just revert back to being indifferent towards me.

For the third (and maybe final) installment, I...

Using nonparametric analysis to visually manage durations in service processes

My main objective is to encourage greater use of statistical techniques in the service sector and present new ways to implement them.

In a previous blog, I presented an approach you can use  to identify process steps that may be improved in the service sector (quartile analysis). In this post I'll show how nonparametric distribution analysis may be implemented in the service sector to analyze durations until a task is completed.

Knowing how much time you need to complete a task may be very useful when assessing process efficiency, and is an important factor in many businesses.

Consider a...

See How Easily You Can Do a Box-Cox Transformation in Regression

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 variable so that the data do meet the assumptions. Minitab makes the transformation simple by including the Box-Cox button. Try it for yourself and see how easy it is!

The government in Queensland,...

Explaining the Central Limit Theorem with Bunnies & Dragons

When I think about the Central Limit Theorem (CLT), bunnies and dragons are just about the last things that come to mind. However, that’s not the case for Shuyi Chiou, whose playful CreatureCast.org animation explains the CLT using both fluffy and fire-breathing creatures.

Per the article that accompanied this video in The New York Times:

“Many real-world observations can be approximated by, and tested against, the same expected pattern: the normal distribution. In this familiar symmetric bell-shaped pattern, most observations are close to average, and there are fewer observations further from...

Normality Tests and Rounding

All measurements are rounded to some degree. In most cases, you would not want to reject normality just because the data are rounded. In fact, the normal distribution would be a quite desirable model for the data if the underlying distribution is normal since it would smooth out the discreteness in the rounded measurements.

Some normality tests reject a very high percentage of time due to rounding when the underlying distribution is normal (Anderson-Darling and Kolmogorov-Smirnov), while others seem to ignore the rounding (Ryan-Joiner and chi square).

As an extreme example of how data that is...

Anderson-Darling, Ryan-Joiner, or Kolmogorov-Smirnov: Which Normality Test Is the Best?

Minitab Statistical Software offers three tests for Normality: Anderson-Darling (AD), Ryan-Joiner (RJ), and Kolmogorov-Smirnov (KS). The AD test is the default, but is it the best test at detecting Non-Normality? Let's compare the ability of each of these normality tests to detect non-normal data under three different scenarios.  We'll use simulated data for each, but they reflect common situations you're likely to encounter if you're analyzing data for quality improvement.

Scenario 1 – The manufacturing process produces large outliers from time-to-time. In this simulation, 29 values are...

A correspondence table for non parametric and parametric tests

Most of the data that one can collect and analyze follow a normal distribution (the famous bell-shaped curve). In fact, the formulae and calculationsused in many analyses simply take it for granted that our data follow this distribution; statisticians call this the "assumption of normality."

For example, our data need to meet the normality assumption before we can accept the results of a one- or two-sample t (Student) or z test. Therefore, it is generally good practice to run a normality test before performing the hypothesis test.

But wait...according to the Central Limit Theorem, when the...

The Gentleman Tasting Coffee: A Variation on Fisher’s Famous Experiment

by Matthew Barsalou, guest blogger

In the 1935 book The Design of Experiments, Ronald A. Fisher used the example of a lady tasting tea to demonstrate basic principles of statistical experiments. In Fisher’s example, a lady made the claim that she could taste whether milk or tea was poured first into her cup, so Fisher did what any good statistician would do—he performed an experiment.

The lady in question was given eight random combinations of cups of tea with either the tea poured first or the milk poured first. She was required to divide the cups into two groups based on whether the milk or...

A Brief Illustrated History of Statistics for Industry

by Matthew Barsalou, guest blogger

The field of statistics has a long history and many people have made contributions over the years. Many contributors to the field were educated as statisticians, such as Karl Pearson and his son Egon Pearson. Others were people with problems that needed solving, and they developed statistical methods to solve these problems.

The Standard Normal Distribution

One example is Karl Gauss and the standard normal distribution, which is a key element in statistics. The distribution was used by Gauss to analyze astronomical data in the early nineteenth century and is...

Seven Basic Quality Tools to Keep in Your Back Pocket

Here are seven quality improvement tools I see in action again and again. Most of these quality tools have been around for a while, but that certainly doesn’t take away any of their worth!

The best part about these tools is that they are very simple to use and work with quickly in Minitab Statistical Software or Quality Companion, but of course you can use other methods, or even pen and paper.

1. Fishbone Diagram

Fishbones, or cause-and-effect diagrams, help you brainstorm potential causes of a problem and see relationships among potential causes. The fishbone below identifies the...

Normal: The Kevin Bacon of Distributions

When you learned statistics, most of what you learned was centered around the Normal distribution.  Maybe you became close friends and you later found out his birth name was Gaussian, but either way you probably just call him Normal.

You might know Normal’s a pretty popular guy with plenty of relationships with other distributions.  There are some obvious connections, like how eNormal is Lognormal, but I thought I’d share some less obvious ones. 

You probably already know that by subtracting his mean and dividing by his standard deviation you get Standard Normal.

What if you squared Standard...

Truth, Beauty, Nonparametrics & Symmetry Plots

  “Shall I compare thee to a standard normal distribution?
  Thou art more symmetric and more bell-shaped…”  — Melvin Shakespeare (William’s lesser-known statistician brother)

The Greek philosopher Aristotle believed that symmetry was one of the primary elements of the universal ideal of beauty. Over 2000 years later, emerging research seems to bear him out. 

Studies suggest we tend to be more attracted to people with symmetrical bodies. Using motion-capture technology to record the movements of people dancing to a popular song, one recent study concluded that we even prefer those who dance...

When Should I Use Confidence Intervals, Prediction Intervals, and Tolerance Intervals

In statistics, we use a variety of intervals to characterize the results. The most well-known of these are confidence intervals. However, confidence intervals are not always appropriate. In this post, we’ll take a look at the different types of intervals that are available in Minitab, their characteristics, and when you should use them.

I’ll cover confidence intervals, prediction intervals, and tolerance intervals. Because tolerance intervals are the least-known, I’ll devote extra time to explaining how they work and when you’d want to use them.

What are Confidence Intervals?

A confidence...

Using Binary Logistic Regression to Investigate High Employee Turnover

Human resources might not be a business area where you’d typically expect to conduct a Six Sigma project. However, Jeff Parks, Lean Six Sigma master black belt, found the opportunity to apply Six Sigma to human resources while leading quality improvement efforts at a large manufacturer of aerospace engine parts.

The manufacturer was suffering from high employee attrition, or turnover, and struggled to understand why. With a DMAIC Six Sigma project, Parks set out to work with the HR department to investigate and reduce the high turnover rates.

In 2009, the manufacturer had normal attrition rates...

The Glass Slipper Story: Analyzing the Madness in the 2013 NCAA Tournament

Cinderella showed up early and often during the first weekend of the 2013 NCAA Tournament. Florida Gulf Coast stole the show with their glass slippers, becoming the first ever 15 seed to reach the Sweet 16. But don’t let that overshadow what happened in the West Region: Wichita St and La Salle both arrived in a pumpkin-turned-carriage, and now the Shockers are a game away from the Final Four! And don’t forget about Harvard just because the clock struck midnight on them first. They were at the ball, too! Madness indeed.

In the world of statistics, we have another word for this “madness.” It’s...