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Power and Sample Size

Blog posts and articles about statistical power and sample size, especially in quality improvement projects.

Using a sample to estimate the properties of an entire population is common practice in statistics. For example, the mean from a random sample estimates that parameter for an entire population. In linear regression analysis, we’re used to the idea that the regression coefficients are estimates of the true parameters. However, it’s easy to forget that R-squared (R2) is also an estimate.... Continue Reading
Do you suffer from PAAA (Post-Analysis Assumption Angst)? You’re not alone. Checking the required assumptions for a statistical  analysis is critical. But if you don’t have a Ph.D. in statistics, it can feel more complicated and confusing than the primary analysis itself. How does the cuckoo egg data, a common sample data set often used to teach analysis of variance, satisfy the following formal... Continue Reading
A few weeks ago I looked at the number of goals that were being scored in the World Cup. At the time there were 2.9 goals per game, which was the highest since 1970. Unfortunately for spectators who enjoyed the higher scoring goals, this did not last. By the end, the average had fallen to 2.7 goals per game, the same amount scored in the 1998 World Cup. After such a high-scoring start, the goals... Continue Reading
Remember "The Little Engine That Could," the children's story about self-confidence in the face of huge challenges? In it, a train engine keeps telling itself "I think I can" while carrying a very heavy load up a big mountain. Next thing you know, the little engine has done it...but until that moment, the outcome was uncertain. It's a wonderful story for teaching kids about self-confidence. But... Continue Reading
Minitab graphs are powerful tools for investigating your process further and removing any doubt about the steps you should take to improve it. With that in mind, you’ll want to know every feature about Minitab graphs that can help you share and communicate your results effectively. While many ways to modify your graph are on the Editor menu, some of the best features become available when you... Continue Reading
It's all too easy to make mistakes involving statistics. Powerful statistical software can remove a lot of the difficulty surrounding statistical calculation, reducing the risk of mathematical errors—but  correctly interpreting the results of an analysis can be even more challenging.  No one knows that better than Minitab's technical trainers. All of our trainers are seasoned statisticians with... Continue Reading
We’re in the thick of the Stanley Cup playoffs, which means hockey fans are doing what seems to be every sports fan's favorite hobby...complaining about the refs! While most complaints, such as “We’re not getting any of the close calls!” are subjective and hard to get data for, there's one question that we should be able to answer objectively with a statistical analysis: Are hockey penalties... Continue Reading
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... Continue Reading
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... Continue Reading
Two weeks ago Penn State and Michigan played in a quadruple-overtime thriller that almost went into a 5th overtime. Had Penn State coach Bill O’Brien kicked a field goal in the 4th overtime instead of going for it on 4th and 1, the game would have continued. But the Nittany Lions converted the 4th down (which, by the way, wasn’t a gamble) and went on to score the game winning touchdown in the 4th... Continue Reading
Even the best NHL goalies can get pulled several times each season. Do they really have cold streaks, or is a drop in save percentage on a given day part of normal random variation? My colleague Doug Gorman and I decided to find out using our favorite statistical software package.   Control Charts for Coaching Decisions We used a control chart approach to determine if coaching decisions to pull... Continue Reading
In my home, we’re huge fans of Mythbusters, the show on Discovery Channel. This fun show mixes science and experiments to prove or disprove various myths, urban legends, and popular beliefs. It’s a great show because it brings the scientific method to life. I’ve written about Mythbusters before to show how, without proper statistical analysis, it’s difficult to know when a result is statistically... Continue Reading
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... Continue Reading
When I talk to quality professionals about how they use statistics, one tool they mention again and again is design of experiments, or DOE. I'd never even heard the term before I started getting involved in quality improvement efforts, but now that I've learned how it works, I wonder why I didn't learn about it sooner. If you need to find out how several factors are affecting a process outcome,... Continue Reading
Life is full of choices. Some are simple, such as what shirt to put on in the morning (although if you’re like me, it’s not so much of a “choice” as it is throwing on the first thing you grab out of the closet). And some choices are more complex. In the quality world, you might have to determine which distribution to choose for your capability analysis or which factor levels to use to bake the... Continue Reading
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... Continue Reading
Serving cat food? I sure hope you've set your alpha level high enough. "Bad kitty!" That's a phrase you almost never hear, but even we cats make the occasional mistake. I was reminded of this recently as I watched my human trying to analyze some data. People frequently make mistakes when they test a hypothesis with data analysis. Specifically, they can make either Type I or Type II errors.   When I... Continue Reading
When Alex Smith travels to Seattle, he has to go up against 67,000 screaming Seahawk fans that make Seattle one of the loudest stadiums in football. When Joe Flacco goes into Pittsburgh, he has to overcome 65,000 Steelers fans clad in black and gold and waving Terrible Towels. And when Matt Schaub plays in Jacksonville he has to, well...people do go to football games in Jacksonville, right? Either... Continue Reading
I love talking to people who use data and analysis to improve processes and quality. As I've worked with customers to tell their stories, my definition of "quality" has expanded. In some cases, data has been used not just to improve quality in terms of reducing defects, but even to demonstrate to regulators that a company is already meeting or exceeding regulatory requirements.  A few years ago, I... Continue Reading
Marlowe the Stats Cat here. That guy I share my house with left his laptop unattended again, and I spent the evening searching the web for news about one of my favorite subjects: salmon. Yum. But I wound up getting more than a collection of cool salmon pictures...I also got a better understanding of the role the size of a dataset plays when you're doing a hypothesis test.   You see, my search led... Continue Reading