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T-Test Example

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

Hypothesis testing is an essential procedure in statistics. A hypothesis test evaluates two mutually exclusive statements about a population to determine which statement is best supported by the sample data. When we say that a finding is statistically significant, it’s thanks to a hypothesis test. How do these tests really work and what does statistical significance actually mean? In this series of... Continue Reading
It’s safe to say that most people who use statistics are more familiar with parametric analyses than nonparametric analyses. Nonparametric tests are also called distribution-free tests because they don’t assume that your data follow a specific distribution. You may have heard that you should use nonparametric tests when your data don’t meet the assumptions of the parametric test, especially the... Continue Reading

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I left off last with a post outlining how the Six Sigma students at Rose-Hulman were working on a project to reduce the amount of recycling thrown in the normal trash cans in all of the academic buildings at the institution. Using the DMAIC methodology for completing improvement projects, they had already defined the problem at hand: how could the amount of recycling that’s thrown in the normal trash... Continue Reading
by Matthew Barsalou, guest blogger.  E. E. Doc Smith, one of the greatest authors ever, wrote many classic books such as The Skylark of Space and his Lensman series. Doc Smith’s imagination knew no limits; his Galactic Patrol had millions of combat fleets under its command and possessed planets turned into movable, armored weapons platforms. Some of the Galactic Patrol’s weapons may be well... Continue Reading
In my recent meetings with people from various companies in the service industries, I realized that one of the problems they face is that they were collecting large amounts of "qualitative" data: types of product, customer profiles, different subsidiaries, several customer requirements, etc. As I discussed in my previous post, one way to look at qualitative data is to use different types of... Continue Reading
If you’re not a statistician, looking through statistical output can sometimes make you feel a bit like Alice in Wonderland. Suddenly, you step into a fantastical world where strange and mysterious phantasms appear out of nowhere.   For example, consider the T and P in your t-test results. “Curiouser and curiouser!” you might exclaim, like Alice, as you gaze at your output. What are these values,... Continue Reading
"Data! Data! Data! I can't make bricks without clay."  — Sherlock Holmes, in Arthur Conan Doyle's The Adventure of the Copper Beeches Whether you're the world's greatest detective trying to crack a case or a person trying to solve a problem at work, you're going to need information. Facts. Data, as Sherlock Holmes says.  But not all data is created equal, especially if you plan to analyze as part of... Continue Reading
A recent study has indicated that female-named hurricanes kill more people than male hurricanes. Of course, the title of that article (and other articles like it) is a bit misleading. The study found a significant interaction between the damage caused by the storm and the perceived masculinity or femininity of the hurricane names. So don’t be confused by stories that suggest all... Continue Reading
by Matthew Barsalou, guest blogger Programs such as the Minitab Statistical Software make hypothesis testing easier; but no program can think for the experimenter. Anybody performing a statistical hypothesis test must understand what p values mean in regards to their statistical results as well as potential limitations of statistical hypothesis testing. A p value of 0.05 is frequently used during... 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
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... 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
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... Continue Reading
If you regularly perform regression analysis, you know that R2 is a statistic used to evaluate the fit of your model. You may even know the standard definition of R2: the percentage of variation in the response that is explained by the model. Fair enough. With Minitab Statistical Software doing all the heavy lifting to calculate your R2 values, that may be all you ever need to know. But if you’re... Continue Reading
Using data analysis and statistics to improve business quality has a long history. But it often seems like most of that history involves huge operations. After all, Six Sigma originated with Motorola, and became adopted by thousands of other businesses after it was adopted by a little-known outfit called General Electric. There are many case studies and examples of how big companies used Six Sigma... Continue Reading
Ever start a fantasy football draft and realize that passing touchdowns are worth 6 points, not 4? Or how about realizing at the last minute that the commissioner of your league decided to have a point per reception (PPR) league. We know that this year running backs are going to be going early in the draft. But if your league is a PPR or gives 6 points for a passing touchdown, should you... Continue Reading
Most of the data that one can collect and analyze follow a normal distribution (the famous bell-shaped curve). In fact, the formulae and calculations used in many analyses simply take it for granted that our data follow this distribution; statisticians call this the "assumption of normality." For example, our data need to meet the normality assumption before we can accept the results of a one- or... Continue Reading
If you've got questions about quality improvement and statistics, I've got a resource for you: the Minitab Network on LinkedIn. I'm privileged to serve as the moderator of this group, which lets people who use Minitab products communicate and network with like-minded people from around the world. LinkedIn is the leading social networking site for professionals, and the Minitab Network on LinkedIn... Continue Reading
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... Continue Reading