T for 2. Should I Use a Paired t or a 2-sample t?

Boxers or briefs.

Republican or Democrat.

Yin or yang.

Why is it that life often seems to boil down to two choices?

Heck, it even happens when you open the Basic Stats menu in Minitab. You’ll see a choice between a 2-sample t-test and a paired t-test:

Which test should you choose? And what’s at stake?

Ask a statistician, and you might get this response: "Elementary, my dear Watson. Choose the 2-sample t-test to test the difference in two means: H0: µ1 – µ2 = 0 Choose the paired t-test to test the mean of pairwise differences H0: µd = 0."

You gaze at your two sets of data values, mystified. Do you...

What Is a t-test? And Why Is It Like Telling a Kid to Clean Up that Mess in the Kitchen?

A t-test is one of the most frequently used procedures in statistics.

But even people who frequently use t-tests often don’t know exactly what happens when their data are wheeled away and operated upon behind the curtain using statistical software like Minitab.

It’s worth taking a quick peek behind that curtain.

Because if you know how a t-test works, you can understand what your results really mean. You can also better grasp why your study did (or didn’t) achieve “statistical significance.”

In fact, if you’ve ever tried to communicate with a distracted teenager, you already have experience with...

Get Your Way, Every Time: 7 Default Settings in Minitab You Didn’t Know You Could Change

Unless you’re 3 years old, you probably can’t have things just the way you want them all the time.  

You can’t always have peanut butter and ranch dressing on your toast. Or ketchup on your pineapple. Or sugar sprinkles on your peas.

But there is one small arena in life over which you can still exert your control. 

Tools > Options in Minitab's statistical software allows you to change selected default settings in the software, without having to throw a temper tantrum first.

This powerful, underutilized feature in Minitab may save you from the inconvenience of having to change a default setting...

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...

Benthic Invertebrates Gone Wild!

Using a Survey of Aquatic Bugs to Estimate Stream Quality

As we click, flip, and scroll through hundreds of sites and channels, cruising for our daily dose of e-thrills, it’s easy to forget there’s a beautiful, wild, creative universe right in our backyards.

I had the chance to experience a tiny part of that universe on a recent Saturday afternoon, when a couple of friends, Yolanda and Monika, asked me if I wanted to join them to monitor the water quality of the stream that runs in back of our house.

Yolanda and Monika are part of a large grassroots network of volunteers who selflessly give their...

How to Prove You're (a) Case Using Statistics

by Patrique Roonquel, guest blogger
Institut Sacre Bleu

I enjoy using Minitab Statistical Software to uncover the vast causal relationships unfolding in the universe all around me. 

What kind of novel things have I proven with Minitab? Almost anything you can imagine, mon petite shoe.

For example, the fitted line plot below clearly shows one thing:  it’s time for our political parties to stop all the bickering and finally give Americans what we really want…

…a much taller president!

(See the dot way up at the top of the plot? That’s George Washington, the Father of our Country.  He was one of...

Rethinking the Obvious: How Data Analysis and Diagrams Can Upend Conventional Wisdom

Has it happened to you?  

You organize a brainstorming session to begin analyzing your process.

At the kick-off meeting, several people sit with arms crossed, lips pursed, eyes cast downward. Frequently, they’re the ones who’ve worked at the process for most of their professional lives.

Here we go again. Wasting time to prove the obvious,” their faces say. “I’ve done my job for years. You’re not going to show me anything I don’t already know.”

Yet you bravely push forward. Every now and then you see someone roll their eyes. “When can I get back to my desk and do some real work?!!!”  they seem to...

What Makes Great Presidents and Good Models?

If the title of this post made you think you’d be reading about Abraham Lincoln and Tyra Banks, you’re only half right. 

A few weeks ago, statistician and journalist Nate Silver published an interesting post  on how U.S. presidents are ranked by historians. Silver showed that the percentage of electoral votes that a U.S. president receives in his 2nd term election serves as a rough predictor of his average ranking of greatness.

Here’s the model he came up with, which I’ve duplicated in Minitab using the scatterplot with regression and groups (Graph > Scatterplot ):

Silver divided the data into...

Violations of the Assumptions for Linear Regression: Closing Arguments and Verdict

  Lionel Loosefit has been hauled to court for violating the assumptions of regression analysis. On the last day of the trial, the prosecution and defense present their closing arguments. And the fate of Mr. Loosefit is decided by judge and jury...

The Prosecution's Summary

Prosecutor: Ladies and gentlemen, we’ve presented a slew of evidence in this trial. You’ve seen, with your own eyes, every possible heinous violation of the assumptions for regression in the defendant’s model. Here’s what we’ve shown, in a nutshell:

Prosecutor: We’ve carefully delineated each violation with specific graphic...

Violations of the Assumptions for Linear Regression: Residuals versus the Fits (Day 3)

Lionel Loosefit has been hauled to court for violating the assumptions of linear regression. On Day 3 of the trial, the court examines the allegation that the residuals in Mr. Loosefit's model exhibit nonconstant variance. The defendant’s mother, Mrs. Lottie Loosefit, has taken the stand on behalf of her son.

Defense Attorney: So, Mrs. Loosefit, from what you’ve described to us, your son, Lionel, appears to have been a model child.

Lottie Loosefit [eyes watering]: He was every mother’s dream. He brushed his teeth every morning and every night, made his bed, folded his socks, picked up all his...

Violations of the Assumptions for Linear Regression (Day 2): Independence of the Residuals

Recap: Lionel Loosefit has been arrested and hauled to court for violating the assumptions of regression analysis. In the previous court session, the prosecution presented evidence to show that the errors in Mr. Loosefit’s model were not normally distributed. Today, the prosecution addresses the second alleged violation: namely, that the errors in the defendant’s regression model are not independent. Dr. Minnie Tabber, a world-renowned statistician, is on the witness stand.

Prosecutor: Let me remind the members of the jury that a residual is simply the difference between the data value...

Violations of the Assumptions for Linear Regression: The Trial of Lionel Loosefit (Day 1)

Bailiff: All Rise. The Honorable Judge Lynn E. R. Peramutter presiding.

Judge: Please be seated. Bailiff, please read the charges.

Bailiff: Your honor, this is the case of the State vs. Lionel Loosefit. The defendant is charged with creating a model that violated the legal requirements for regression. The infractions include:

  • Producing grossly nonnormal errors
  • Producing errors that lack independence
  • Exhibiting nonconstant variance
  • Violating the linearity assumption

Judge: Thank you, bailiff. Let’s hear the opening statement by the prosecutor.

Prosecutor: Your honor, ladies and gentlemen of the jury....

Probit Analysis: Down Goes the Meathouse!

Whenever something suddenly fell apart, my grandfather used to exclaim “Down goes the meat house!” I don’t know where that expression came from—as a child I often pictured a flabby house of raw meat caving in on itself. (This was decades before Lady Gaga made wearing raw meat dresses...uh...er... fashionable?)

My grandfather’s expression still pops into my head when I think about a probit analysis. A probit study is based on one very simple premise: Everything has its breaking point.

To illustrate this study, and to relive my childhood, I built some good old-fashioned card houses and tested how...

Giving Thanks for the Regression Menu

Juicy, butter roasted turkey.

Steaming mashed potatoes.

Tangy cranberry relish.

Delicious candied sweet potatoes.

Creamy green bean casserole.

Sweet and airy corn bread.

Silken pumpkin pie.

The traditional Thanksgiving menu has so many mouth-watering dishes on the table, you don’t know where to start.

If you savor statistics as much as food, you might feel similarly as you gaze at all of the delicious analyses on Minitab’s Regression menu:

How can you decide which regression analysis to choose? In this post, I’ll give you some bite-sized samples of each regression dish to help you decide which one to...

Why Do So Many U.S. Voters Go MIA on Election Day? (Part III)

It’s been a grueling election campaign for Senator William Overstate, or Will Overstate, as he is known by his constituents. Senator Overstate has been running his re-election campaign on a single issue: to make Election Day a national holiday.

That sounds good to me!

The senator argues that it's difficult for many people to get to the polls on election day because of work—especially those who work longer hours at lower wage jobs. Therefore, making election day a national holiday would increase voter turnout. Some states have already made election day a state holiday for that reason.

The senator...

Why Do So Many U.S. Voters Go MIA on Election Day? (Part II)

So what stops eligible U.S. voters from showing up at the polls on election day?  I’m not going to be able to tease out all the possible factors associated with variability in voter turnout in one blog post. 

But you can often be forgiven in statistics if you clearly state at the onset that your main objective is a preliminary exploration rather than a final, conclusive analysis. So let’s explore.

Does temperature affect voter turnout?

Weather is sometimes suggested as a possible influence on voter turnout. Can you imagine the impact on the election if Hurricane Sandy had hit just one week later...

Why Do U.S. Voters Go MIA on Election Day? (Part I)

This Tuesday is the big day.

If you think I mean National Saxophone Day, please remember to put your sax down on November 6 and go vote! Otherwise, voter turnout for the election will be nothing to toot your horn over.

As it is, the percentage of  people who turn up at the polls to vote is much lower in the U.S. than in many other democracies around the world.

Or is it?  Surprisingly, a lot depends on how you define the variable you use to measure voter turnout.

The Response: VAP vs VEP

Voter turnout is often calculated as the percentage of persons who voted out of the total number of people...

Happy Fechner Day, Everyone!

Today, October 22, is Fechner Day. Finally! I thought it would never get here.

You might be wondering how you should celebrate.

What to wear? Are stone-washed jeans acceptable? What should you have for dinner? Can you safely serve filet mignon with Whoopie pie?

How should you greet friends and loved ones? "Frolic Freely For a Felicitous Fechner Fest!"? "Happy F-day!"?

Yes, without proper guidance, getting Fechner Day right can be challenging. This year, celebrate with confidence by remembering these 5 simple tips:


Tip 1: Don't confuse ...

The Art of Counting Butterflies: Statistics & Estimation

If you walk along an open field in central Pennsylvania in September, blaze orange is often the first sign of approaching fall you'll see. And it happens before the leaves even begin to turn color.

The annual migration of millions of monarch butterflies in North America is one of the great wonders of nature. Every autumn, these delicate beauties flutter from as far north as Canada to their wintering site in central Mexico—a journey that can cover over 2,800 miles!

Although the peak season for the eastern monarch migration is over in this area, my friend and I did see a straggler heading south...

Teach Yourself to Fish Using Sample Data Sets in Minitab

You know the famous proverb: "Give a man a fish and you feed him for a day. Teach a man to fish and you feed him for a lifetime."

It's especially true when you're casting your line for statistics.

When I first started using Minitab Statistical Software, it was daunting trying to learn all of its analysis capabilities. There are hundreds of commands in the Stat menu alone!

Eventually, I found that working through an example using a sample data set was the easiest way for me to quickly get a handle on an analysis.

Because if you’re a concrete thinker like me, you like your example served first, and...