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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...

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...

Creating a Custom Report using Minitab, part 2

Now that you’ve seen how to automatically import data and run analyses in my previous post, let’s create the Monthly Report!

I will be using a Microsoft Word Document (Office 2010) and adding bookmarks to act as placeholders for the Graphs, statistics, and boilerplate conclusions.

Let’s go through the steps to accomplish this:

  • Open up an existing report that you have previously created in Microsoft Word.
  • Highlight a section of the document where you would like to place the created Minitab graph or statistic.
  • Go to the Insert tab, click the Bookmark link, and type in the name of what you will be...

Creating a Custom Report using Minitab, part 1

As a member of Minitab’s Consulting and Custom Development Services team, I get to help companies across a variety of industries create a many different types of reports for management. These reports often need to be generated weekly or monthly. I prefer to automate tasks like this whenever possible, so that new or updated reports can be created without much effort. A little investment up front can save a lot of time by eliminating the need to recreate the wheel every time management wants a current report. 

I’m going to tell you how to use Minitab Statistical Softwareto automatically generate...

Introducing the Bubble Plot

When you're evaluating a dataset, graphical analysis can be very important. While an analysis like a regression or ANOVA can be backed up by numbers, being able to visualize how your dataset is behaving can be even more convincing than a group of p-values—especially to those who aren’t trained in statistics.

For example, let’s look at a few variables we think may be correlated. In this specific example, we will take the Unemployment Rate and the Crime Rate for each state in the U.S. We have 3 columns of data in Minitab: C1, which contains the State Name; C2, which contains the Crime Rate; and...

Analyzing “Luck” in College Basketball: Part II

Two months ago, I used Ken Pomeroy’s luck statistic to analyze the “luckiest” and “unluckiest” teams in college basketball. What Ken’s luck statistic is really looking at is close games. If you win most of your close games, you'll have a high luck statistic in the Pomeroy Ratings. Lose most of your close games, and your luck statistic will be low.

I looked at the winning percentages in close games of the 20 luckiest teams, 20 unluckiest teams, and 20 teams right in the middle. Sure enough the lucky group won most of their close games, the unlucky group lost most, and the middle group won just...

Re-analyzing Wine Tastes with Minitab 17

In April 2012, I wrote a short paper on binary logistic regression to analyze wine tasting data. At that time, François Hollande was about to get elected as French president and in the U.S., Mitt Romney was winning the Republican primaries. That seems like a long time ago…

Now, in 2014, Minitab 17 Statistical Software has just been released. Had Minitab 17, been available in 2012, would have I conducted my analysis in a different way?  Would the results still look similar?  I decided to re-analyze my April 2012 data with Minitab 17 and assess the differences, if there are any.

There were no...

Opening Ceremonies for Bubble Plots and Poisson Regression

By popular demand, Release 17 of Minitab Statistical Software comes with a new graphical analysis called the Bubble Plot.

This exploratory tool is great for visualizing the relationships among three variables on a single plot.

To see how it works, consider the total medal count by country from the recently completed 2014 Olympic Winter Games. Suppose I want to explore whether there might be a possible association between the number of medals a country won and its maximum elevation. For that, I could use a simple scatterplot, right?

But say I want to throw a third variable into the mix, such as...

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...

Busting a Myth about the NHL and Olympic Games

In the sports world, it is generally accepted that the NHL players who participate in the Olympics (approximately 20%) put their NHL team at a disadvantage for the remainder of the season.

The NHL season does stop during the Olympic Games, but the thought is that the best NHL players leave their team to play the extra games, which will tire them out for the remainder of the NHL regular season and playoffs.

But do the data really support that conventional wisdom?

Relationship Between NHL Performance and Olympic Selection

First, I want to mention there is a relationship between the number of players...

(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...

How High Should R-squared Be in Regression Analysis?

Just how high should R2 be in regression analysis? I hear this question asked quite frequently.

Previously, I showed how to interpret R-squared (R2). I also showed how it can be a misleading statistic because a low R-squared isn’t necessarily bad and a high R-squared isn’t necessarily good.

Clearly, the answer for “how high should R-squared be” is . . . it depends.

In this post, I’ll help you answer this question more precisely. However, bear with me, because my premise is that if you’re asking this question, you’re probably asking the wrong question. I’ll show you which questions you should...

Does Peyton Manning Play Worse in Cold Weather?

If you’re a believer that Peyton Manning plays worse in cold weather, the last few weeks have only strengthened your resolve. In 3 of his last 4 games, he’s played in temperatures below 40 degrees, and come out with a record of 1-2. In his other “warm weather” games this season, Manning has a record of 10-1. This continues a theme that has plagued Manning his entire career, that he underperforms when the temperature goes south.

But will the statistics support that theory?

Peyton’s Statistics in Cold Weather Games

Thanks to an article by the Mile High Report, I was able to obtain data on every...

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...

Correlation Is not Causation: Why Running the Football Doesn’t Cause You to Win Games in the NFL

I know we lost by 2 touchdowns, but if only you had given Peterson 3 more carries we would have won!

Last week, ESPN ran an article about why the running game still matters. They used statistics to show that the more you run the football in the NFL, the more likely you are to win the game. Specifically, if you have a running back who gets at least 20 carries, you win about 70% of the time. Statistics from different eras all had the same result: it appears that the more you run the football, the better your odds of winning the football game are.

If only it were that simple.

There is no doubt that...

Interpreting Halloween Statistics with Binary Logistic Regression

As Halloween is almost here, I'm ready to check out some Halloween statistics. You can have a lot of fun with Minitab on Halloween.

The National Retail Foundation (NRF) released the results of their Halloween Consumer Spending Survey last month. The basics are easy to summarize:

Because we have Minitab, we can dig a little deeper into the data. The NRF gives some information about the proportion of respondents who participate and the proportion of participators who will celebrate with different activities. The proportions for participators are broken down by different age groups. There’s...

Four Tips on How to Perform a Regression Analysis that Avoids Common Problems

In my previous post, I highlighted recent academic research that shows how the presentation style of regression results affects the number of interpretation mistakes. In this post, I present four tips that will help you avoid the more common mistakes of applied regression analysis that I identified in the research literature.

I’ll focus on applied regression analysis, which is used to make decisions rather than just determining the statistical significance of the predictors. Applied regression analysis emphasizes both being able to influence the outcome and the precision of the predictions.

Tip...