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...

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...

  “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...

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...

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...

by Matthew Barsalou, guest blogger

Process capability analysis using Minitab Statistical Software’s Capability SixpackTM can be taught using a catapult. A process capability analysis is performed to determine if a process is statistically capable.

In my last blog post, I collected data from a first run of catapult results and found that the run not only had a large amount of variability, it also violated the assumption of normality. Now it's time to do a second run.  

The Second Run and Capability Analysis

A second run was performed using thicker and more robust wire to stretch the rubber band;...

by Matthew Barsalou, guest blogger

We can use a simple catapult to teach process capability analysis using Minitab Statistical Software’s Capability SixpackTM. Here's how.

A process capability analysis is performed to determine if a process is statistically capable. Based on the results of the capability study, we can estimate the amount of defective components the process would produce.

However, a process must be in statistical control and have a normal distribution. A process that is not in statistical control must be brought in control before the capability analysis is performed. In addition,...

Here at the lightsaber factory, we've completed several steps in doing a capability analysis:

• We made sure our data was collected and entered correctly in Minitab
• We identified the distribution of the data
• We made sure all of our assumptions checked out

We’re getting close to our deadline, and it’s finally time to carry out our Capability Analysis and see if we are manufacturing our lightsabers to the correct specifications as set forth by the Jedi Temple.

First, let’s go to Stat > Quality Tools > Capability Analysis > Normal.  (If you want to play along and you don't already have it, get...

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...

by Cory Heid, guest blogger

Almost all of us have tried a Tootsie Pop at some point. I’m willing to bet that most of us also thought, “I wonder how many licks it does take to get to the center of the Tootsie Pop?” If you haven’t wondered about this, here’s the classic commercial that may get you more curious:

Personally, I was not very satisfied with the owl's answer of “3,” so I decided to continue the little boy’s quest to find the number of licks required to reach the center of a Tootsie Pop.

Research

Looking around the ‘net, I found that other studies done by student researchers at various...

Spring is in the air, and Easter is coming up soon! Easter occurs on March 31, 2013, and I’ve heard people exclaim that it’s early this year. I never really remember the date of Easter from one year to the next, but I had vague memories of it being in March not too long ago. Like any good statistician, I started wondering about the distribution of Easter dates. What dates are more common and which are less common? Is Easter in March really that unusual?

Even after reading the official definition of when Easter occurs, I still wasn’t clear about the date range. Easter occurs on the Sunday that...

In college I had a friend who could go anywhere and fit right in. He'd have lunch with a group of professors, then play hacky-sack with the hippies in the park, and later that evening he'd hang out with the local bikers at the toughest bar in the city. Next day he'd play pickup football with the jocks before going to an all-night LAN party with his gamer pals. On an average weekend he might catch an all-ages show with the small group of straight-edge punk rockers on our campus, or else check out a kegger with some townies, then finish the weekend by playing some D&D with his friends from the...

One of the most poorly understood concepts in the use of statistics is the idea of assumptions. You've probably encountered many of these assumptions, such as "data normality is an assumption of the 1-sample t-test."  But if you read that statement and believe normality is a requirement of the 1-sample t-test, then you have missed a subtle and important characteristic of assumptions and need to read on...

An "assumption" is not necessarily a "requirement"!

To understand where this idea of assumptions come from, let's forget about statistics for a minute and imagine we sell bikes online.  We...

In my last post, we talked about using statistical tools to identify the right distribution of our lightsaber manufacturing data. Now that we have our data in Minitab along with a specific distribution picked out, we can find out if we are dealing with an in-control process. If the process is not in control, the capability estimates will be incorrect. Thus, an extremely important (and often overlooked) aspect of Capability Analysis is to make sure our process in first in control. We can do this with a tool Minitab Statistical Software offers called the Capability Sixpack.TM

First, let’s go to S...

It's almost Super Bowl Sunday, and this year’s matchup pits the Baltimore Ravens against the San Francisco 49ers. The 49ers are no huge surprise, as they were favored in both of their playoff games. However the Ravens had to win 3 games, pulling two major upsets along the way, to get to the Super Bowl. It marks the 8th time in the last 10 years that a team that played on Wild Card Weekend advanced the entire way to the Super Bowl. This again shows how much parity there is in the NFL. It’s unpredictable! Any team can win the championship!

Well...not quite. While I agree that the NFL playoffsare...

New to confidence intervals?  Here are some important things to keep in mind!

Confidence Intervals:

• are used to estimate population parameters (commonly the process mean, standard deviation, % of defective units, or even capability indices). 
• provide more meaningful information than any random sample statistic for characterizing the population.

MINI-TIP:
See “Tip 1: Every sample statistic is a little bit wrong.”

When your 95% confidence interval for the mean is (μlow, μhigh), you can be 95% confident that the population (process) mean, μ, is between μlow and μhigh …and 5% confident that μ is not betwe...

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...

In this year's BCS Championship game, Alabama dominated Notre Dame 42-14 in a game that was never really even close. While many people felt Alabama would win the game, most expected a defensive battle. Few predicted it would have been so lopsided (and only a small percentage of those would have actually bet money on a blowout).

But should we really be surprised?  I mean, Alabama clearly outperformaed expectations—but did they do so in a truly unusual manner?

How Can Data Reveal If a Victory Was Unusual?

To investigate how expected or unexpected this game's 28-point margin of victory was, we...

In my previous post, you learned how to prepare your data for capability analysis in Minitab. Now let's see where we need to go in the statistical software to run the correct Capability Analysis.

When it comes to capability analysis, Minitab offers a few different choices. We offer Normal Capability Analysis for when your data follow a normal distribution. If your data follow a different distribution, such as the Weibull distribution, there's Non-normal Capability Analysis. We also offer Binomial Capability and Poisson Capability for when you are looking to produce a process capability report...

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....