T-Test Example

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

Control charts take data about your process and plot it so you can distinguish between common-cause and special-cause variation. Knowing the difference is important because it permits you to address potential problems without over-controlling your process.   Control charts are fantastic for assessing the stability of a process. Is the process mean unstable, too low, or too high? Is observed... Continue Reading
The Six Sigma quality improvement methodology has lasted for decades because it gets results. Companies in every country around the world, and in every industry, have used this logical, step-by-step method to improve the quality of their processes, products, and services. And they've saved billions of dollars along the way. However, Six Sigma involves a good deal of statistics and data analysis,... Continue Reading
One highlight of writing for and editing the Minitab Blog is the opportunity to read your responses and answer your questions. Sometimes, to my chagrin, you point out that we've made a mistake. However, I'm particularly grateful for those comments, because it permits us to correct inadvertent errors.  I feared I had an opportunity to fix just such an error when I saw this comment appear on one of... 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
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
You've collected a bunch of data. It wasn't easy, but you did it. Yep, there it is, right there...just look at all those numbers, right there in neat columns and rows. Congratulations. I hate to ask...but what are you going to do with your data? If you're not sure precisely what to do with the data you've got, graphing it is a great way to get some valuable insight and direction. And a good graph to... Continue Reading
To make objective decisions about the processes that are critical to your organization, you often need to examine categorical data. You may know how to use a t-test or ANOVA when you’re comparing measurement data (like weight, length, revenue, and so on), but do you know how to compare attribute or counts data? It easy to do with statistical software like Minitab.  One person may look at this bar... 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
Statistical inference uses data from a sample of individuals to reach conclusions about the whole population. It’s a very powerful tool. But as the saying goes, “With great power comes great responsibility!” When attempting to make inferences from sample data, you must check your assumptions. Violating any of these assumptions can result in false positives or false negatives, thus invalidating... Continue Reading
True or false: When comparing a parameter for two sets of measurements, you should always use a hypothesis test to determine whether the difference is statistically significant. The answer? (drumroll...) True! ...and False! To understand this paradoxical answer, you need to keep in mind the difference between samples, populations, and descriptive and inferential statistics.  Descriptive Statistics and... Continue Reading
So the data you nurtured, that you worked so hard to format and make useful, failed the normality test. Time to face the truth: despite your best efforts, that data set is never going to measure up to the assumption you may have been trained to fervently look for. Your data's lack of normality seems to make it poorly suited for analysis. Now what? Take it easy. Don't get uptight. Just let your data... Continue Reading
While some posts in our Minitab blog focus on understanding t-tests and t-distributions this post will focus more simply on how to hand-calculate the t-value for a one-sample t-test (and how to replicate the p-value that Minitab gives us).  The formulas used in this post are available within Minitab Statistical Software by choosing the following menu path: Help > Methods and Formulas > Basic... Continue Reading
Earlier this month, PLOS.org published an article titled "Ten Simple Rules for Effective Statistical Practice." The 10 rules are good reading for anyone who draws conclusions and makes decisions based on data, whether you're trying to extend the boundaries of scientific knowledge or make good decisions for your business.  Carnegie Mellon University's Robert E. Kass and several co-authors devised... Continue Reading
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
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
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
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
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
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