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T-Test Example

Blog posts and articles about testing hypotheses with the statistical method called the T-Test.

Analysis of variance (ANOVA) can determine whether the means of three or more groups are different. ANOVA uses F-tests to statistically test the equality of means. In this post, I’ll show you how ANOVA and F-tests work using a one-way ANOVA example. But wait a minute...have you ever stopped to wonder why you’d use an analysis of variance to determine whether means are different? I'll also show how... Continue Reading
Among the most underutilized statistical tools in Minitab, and I think in general, are multivariate tools. Minitab offers a number of different multivariate tools, including principal component analysis, factor analysis, clustering, and more. In this post, my goal is to give you a better understanding of the multivariate tool called discriminant analysis, and how it can be used. Discriminant... Continue Reading

7 Deadly Statistical Sins Even the Experts Make

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by Laerte de Araujo Lima, guest blogger The NBA's 2015-16 season will be one for the history books. Not only was it the last season of Kobe Bryan, who scored 60 points in his final game, but the Golden State Warriors set a new wins record, beating the previous record set by 1995-96 Chicago Bulls. The Warriors seem likely to take this season's NBA title, in large part thanks to the performance of... Continue Reading
In statistics, t-tests are a type of hypothesis test that allows you to compare means. They are called t-tests because each t-test boils your sample data down to one number, the t-value. If you understand how t-tests calculate t-values, you’re well on your way to understanding how these tests work. In this series of posts, I'm focusing on concepts rather than equations to show how t-tests work.... Continue Reading
Along with the explosion of interest in visualizing data over the past few years has been an excessive focus on how attractive the graph is at the expense of how useful it is. Don't get me wrong...I believe that a colorful, modern graph comes across better than a black-and-white, pixelated one. Unfortunately, however, all the talk seems to be about the attractiveness and not the value of the... Continue Reading
T-tests are handy hypothesis tests in statistics when you want to compare means. You can compare a sample mean to a hypothesized or target value using a one-sample t-test. You can compare the means of two groups with a two-sample t-test. If you have two groups with paired observations (e.g., before and after measurements), use the paired t-test. How do t-tests work? How do t-values fit in? In this... Continue Reading
People say that I overthink everything. I've given this assertion considerable thought, and I don't believe that it is true. After all, how can any one person possibly overthink every possible thing in just one lifetime? For example, suppose I live 85 years. That's 2,680,560,000 seconds (85 years x 365 days per year x 24 hours per day x 60 min per hour x 60 seconds per minute). I'm asleep about a... Continue Reading
About a year ago, a reader asked if I could try to explain degrees of freedom in statistics. Since then,  I’ve been circling around that request very cautiously, like it’s some kind of wild beast that I’m not sure I can safely wrestle to the ground. Degrees of freedom aren’t easy to explain. They come up in many different contexts in statistics—some advanced and complicated. In mathematics, they're... Continue Reading
I am a bit of an Oscar fanatic. Every year after the ceremony, I religiously go online to find out who won the awards and listen to their acceptance speeches. This year, I was so chuffed to learn that Leonardo Di Caprio won his first Oscar for his performance in The Revenant in the 88thAcademy Awards—after five nominations in  previous ceremonies. As a longtime Di Caprio fan, I still remember... Continue Reading
For the majority of my career with Minitab, I've had the opportunity to speak at conferences and other events somewhat regularly. I thought some of my talks were pretty good, and some were not so good (based on ratings, my audiences didn't always agree with either—but that's a topic for another post). But I would guess that well over 90% of the time, my proposals were accepted to be presented at... Continue Reading
How deeply has statistical content from Minitab blog posts (or other sources) seeped into your brain tissue? Rather than submit a biopsy specimen from your temporal lobe for analysis, take this short quiz to find out. Each question may have more than one correct answer. Good luck! Which of the following are famous figure skating pairs, and which are methods for testing whether your data follow a... Continue Reading
If you're just getting started in the world of quality improvement, or if you find yourself in a position where you suddenly need to evaluate the quality of incoming or outgoing products from your company, you may have encountered the term "acceptance sampling." It's a statistical method for evaluating the quality of a large batch of materials from a small sample of items, which statistical softwar... Continue Reading
P-values are frequently misinterpreted, which causes many problems. I won't rehash those problems here here since my colleague Jim Frost has detailed the issues involved at some length, but the fact remains that the p-value will continue to be one of the most frequently used tools for deciding if a result is statistically significant.  You know the old saw about "Lies, damned lies, and... Continue Reading
This past weekend in the Big Ten showed how being conservative on 4th down decisions can cost you a game. Ohio State punted on 4th and 1 three different times, while Penn State and Illinois both kicked field goals in the 4th quarter when they needed a touchdown to tie or take the lead. All three teams lost. Perhaps taking some advice from the 4th down calculator would have greatly benefited them! If... Continue Reading
Back when I was an undergrad in statistics, I unfortunately spent an entire semester of my life taking a class, diligently crunching numbers with my TI-82, before realizing 1) that I was actually in an Analysis of Variance (ANOVA) class, 2) why I would want to use such a tool in the first place, and 3) that ANOVA doesn’t necessarily tell you a thing about variances. Fortunately, I've had a lot more... Continue Reading
Control charts are a fantastic tool. These charts plot your process data to identify common cause and special cause variation. By identifying the different causes of variation, you can take action on your process without over-controlling it. Assessing the stability of a process can help you determine whether there is a problem and identify the source of the problem. Is the mean too high, too low,... Continue Reading
By Matthew Barsalou, guest blogger A problem must be understood before it can be properly addressed. A thorough understanding of the problem is critical when performing a root cause analysis (RCA) and an RCA is necessary if an organization wants to implement corrective actions that truly address the root cause of the problem. An RCA may also be necessary for process improvement projects; it is... Continue Reading
Since it's the Halloween season, I want to share how a classic horror film helped me get a handle on an extremely useful statistical distribution.  The film is based on John W. Campbell's classic novella "Who Goes There?", but I first became  familiar with it from John Carpenter's 1982 film The Thing.   In the film, researchers in the Antarctic encounter a predatory alien with a truly frightening... Continue Reading
In Part 5 of our series, we began the analysis of the experiment data by reviewing analysis of covariance and blocking variables, two key concepts in the design and interpretation of your results. The 250-yard marker at the Tussey Mountain Driving Range, one of the locations where we conducted our golf experiment. Some of the golfers drove their balls well beyond this 250-yard maker during a few of... Continue Reading
In Part 3 of our series, we decided to test our 4 experimental factors, Club Face Tilt, Ball Characteristics, Club Shaft Flexibility, and Tee Height in a full factorial design because of the many advantages of that data collection plan. In Part 4 we concluded that each golfer should replicate their half fraction of the full factorial 5 times in order to have a high enough power to detect... Continue Reading