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How to Correctly Interpret P Values

The P value is used all over statistics, from t-tests to regression analysis. Everyone knows that you use P values to determine statistical significance in a hypothesis test. In fact, P values often determine what studies get published and what projects get funding.

Despite being so important, the P value is a slippery concept that people often interpret incorrectly. How do you interpret P values?

In this post, I'll help you to understand P values in a more intuitive way and to avoid a very common misinterpretation that can cost you money and credibility.

What Is the Null Hypothesis in Hypothesis...

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...

Equivalence Testing for Quality Analysis (Part I): What are You Trying to Prove?

With more options, come more decisions.

With equivalence testing added to Minitab 17, you now have more statistical tools to test a sample mean against target value or another sample mean.

Equivalence testing is extensively used in the biomedical field. Pharmaceutical manufacturers often need to test whether the biological activity of a generic drug is equivalent to that of a brand name drug that has already been through the regulatory approval process.

But in the field of quality improvement, why might you want to use an equivalence test instead of a standard t-test?

Interpreting Hypothesis...

Revisiting the Relationship between Rushing and NFL Wins with Binary Fitted Line Plots

Back in November, I wrote about why running the football doesn’t cause you to win games in the NFL. I used binary logistic regression to look at the relationship between rush attempts (both by the lead rusher and by the team) and wins. The results showed that the model for rush attempts by the lead rusher and wins fit the data poorly. But the model for team rush attempts and wins did fit the data well (although we went on to show that the team rushing attempts wasn’t causing the winning).

We were able to conclude this by looking at the p-value and goodness-of-fit tests. But what if we wanted...

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...

Five Ways to Make Your Control Charts More Effective

Have you ever wished your control charts were better?  More effective and user-friendly?  Easier to understand and act on?  In this post, I'll share some simple ways to make SPC monitoring more effective in Minitab.

Common Problems with SPC Control Charts

I worked for several years in a large manufacturing plant in which control charts played a very important role. Virtually thousands of SPC (Statistical Process Control) charts were used to monitor processes, contamination in clean rooms, monitor product thicknesses and shapes as well as critical equipment process parameters. Process engineers...

(We Just Got Rid of) Three Reasons to Fear Data Analysis

Today our company is introducing Minitab 17 Statistical Software, the newest version of the leading software used for quality improvement and statistics education.    So, why should you care? Because important people in your life -- your co-workers, your students, your kids, your boss, maybe even you -- are afraid to analyze data.    There's no shame in that. In fact, there are pretty good reasons for people to feel some trepidation (or even outright panic) at the prospect of making sense of a set of data.

I know how it feels to be intimidated by statistics. Not long ago, I would do almost...

Applying Six Sigma to a Small Operation

Using data analysis and statistics to improve business quality has a long history. But it often seems like most of that history involves huge operations. After all, Six Sigma originated with Motorola, and became adopted by thousands of other businesses after it was adopted by a little-known outfit called General Electric.

There are many case studies and examples of how big companies used Six Sigma methods to save millions of dollars, slash expenses, and improve quality...but when they read about the big dogs getting those kind of results, a lot of folks hear a little voice in their heads...

Use the Minitab Assistant to Choose a Graph

Everyone loves Minitab’s Assistant. My favorite bit, as I’ve shown with the Gage R&R Study, is the way that the Assistant puts all the results you need into reports that are easy to understand and present. But it’s also pretty neat that before you ever choose what to do in Minitab, the Assistant is ready to help you. Let’s take a closer look at the Assistant's Graphical Analysis tools.

Help Me Choose

Choose Assistant > Graphical Analysis and the most prominent thing you’ll see is a question:

But you’re not left with just the three objectives. Select "graph variables over time," and before you...

R-Squared: Sometimes, a Square is just a Square

If you regularly perform regression analysis, you know that R2 is a statistic used to evaluate the fit of your model. You may even know the standard definition of R2: the percentage of variation in the response that is explained by the model.

Fair enough. With Minitab Statistical Software doing all the heavy lifting to calculate your R2 values, that may be all you ever need to know.

But if you’re like me, you like to crack things open to see what’s inside. Understanding the essential nature of a statistic helps you demystify it and interpret it more accurately.

R-squared: Where Geometry Meets...

Regression Analysis Tutorial and Examples

I’ve written a number of blog posts about regression analysis and I think it’s helpful to collect them in this post to create a regression tutorial. I’ll supplement my own posts with some from my colleagues.

This tutorial covers many aspects of regression analysis including: choosing the type of regression analysis to use, specifying the model, interpreting the results, determining how well the model fits, making predictions, and checking the assumptions. At the end, I include examples of different types of regression analyses.

If you’re learning regression analysis right now, you might want to...

Understanding ANOVA by Looking at Your Household Budget

by Arun Kumar, guest blogger

One of the most commonly used statistical methods is ANOVA, short for “Analysis of Variance.” Whether you’re analysing data for Six-Sigma styled quality improvement projects, or perhaps just taking your first statistics course, a good understanding of how this technique works is important.

A lot of concepts are involved in any analysis using ANOVA and its subsequent interpretation. You’re going to have to grapple with terms such as Sources of Variation, Sum of Squares, Mean Squares, Degrees of Freedom, and F-ratio—and you’ll need to understand what statistical...

Applied Regression Analysis: How to Present and Use the Results to Avoid Costly Mistakes, part 2

Applied regression analysis can be a great decision-making tool because you can predict the average outcome given input values. However, predictions are not as simple as plugging numbers into an equation. In my previous post I showed how a majority of experts vastly underestimated the variability around the predicted outcome in a manner that can lead to costly mistakes.

We also saw how graphing the data is a simple way to avoid these mistakes because it highlights the uncertainty. In this post, I'll explore other techniques that you can use in Minitab statistical software to facilitate good...

Making a Difference in How People Use Data

A colleague of mine at Minitab, Cheryl Pammer, was recently featured in "A Statistician's Journey," a monthly feature that appears in the print and online versions of the American Statistical Association's AMSTAT News magazine.  

Each month, the magazine asks ASA members to talk about the paths they took to get to where they are today. Cheryl is a "user experience designer" at Minitab. In other words, she's one of the people who help determine how our statistical softwaredoes what it does, and tries to make it as helpful, useful, and beneficial as possible. Cheryl is always looking for ways to...

Optical Illusions, Zen Koans, and Simpson’s Paradox

What do you see when you look at the image at right?

Do you see a bulging sphere that stretches the checkerboard pattern in the center, causing its lines to curve?

Are you sure? Look again. This time, test any “curved” line by holding a straightedge next to it.

The image is actually composed of small squares and straight lines. Yet, when perceived as a composite whole, it creates a completely different  impression.

A similar “illusion” can occur when you analyze your data.  It’s called the Yule-Simpson effect—or Simpson’s paradox for short.

When you look at the overall results of all your data, you...

Use Analysis of Means to Classify Baseball Parks

When I first got interested in looking at baseball park factors, I only wanted to know which parks benefited hitters and which benefited pitchers. Once I got started, I got interested in the difference between ESPN's published formula and its results and whether there were obvious reasons for the variation in park factors from year-to-year.

But today I’m returning to the original question: which parks are hitters’ parks, and which are pitchers’ parks?

We already know that the mean and median are inadequate by themselves. For example, consider AT&T Park, where the mean suggests a pitchers’...

Itchy, Sneezy, Stuffy: Delivering Relief with Nasal Spray and DOE

Recently, a customer called our Technical Support team about a Design of Experiment he was performing in Minitab Statistical Software. After they helped to answer his question, the researcher pointed our team to an interesting DOE he and his colleagues conducted that involved using nasal casts to predict the drug delivery of nasal spray.

The study has already been published, and you can read more about it here, but I wanted to highlight this use of the DOE tools in Minitab in this blog post.

Using Nasal Casts to Predict Nasal Spray Drug Delivery

The nose is a convenient route of administration...

How much do different scoring systems affect fantasy football rankings?

Ever start a fantasy football draft and realize that passing touchdowns are worth 6 points, not 4? Or how about realizing at the last minute that the commissioner of your league decided to have a point per reception (PPR) league. We know that this year running backs are going to be going early in the draft. But if your league is a PPR or gives 6 points for a passing touchdown, should you be focusing on quarterbacks and receivers instead?

Sounds like a perfect question for a data analysis in a statistical software package like Minitab!

Getting Six Points for Passing Touchdowns

My first reaction to...