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T-Test Example

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

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

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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
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
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've read the first two parts of this tale, you know it started when I published a post that involved transforming data for capability analysis. When an astute reader asked why Minitab didn't seem to transform the data outside of the capability analysis, it revealed an oversight that invalidated the original analysis.  I removed the errant post. But to my surprise, the reader who helped me... Continue Reading
Previously, I’ve written about how to interpret regression coefficients and their individual P values. I’ve also written about how to interpret R-squared to assess the strength of the relationship between your model and the response variable. Recently I've been asked, how does the F-test of the overall significance and its P value fit in with these other statistics? That’s the topic of this post! In... Continue Reading
As a Minitab trainer, one of the most common questions I get from training participants is "what should I do when my data isn’t normal?" A large number of statistical tests are based on the assumption of normality, so not having data that is normally distributed typically instills a lot of fear. Many practitioners suggest that if your data are not normal, you should do a nonparametric version of... Continue Reading
In this series of posts, I show how hypothesis tests and confidence intervals work by focusing on concepts and graphs rather than equations and numbers.   Previously, I used graphs to show what statistical significance really means. In this post, I’ll explain both confidence intervals and confidence levels, and how they’re closely related to P values and significance levels. How to Correctly... Continue Reading
This is a companion post for a series of blog posts about understanding hypothesis tests. In this series, I create a graphical equivalent to a 1-sample t-test and confidence interval to help you understand how it works more intuitively. This post focuses entirely on the steps required to create the graphs. It’s a fairly technical and task-oriented post designed for those who need to create the... Continue Reading
What do significance levels and P values mean in hypothesis tests? What is statistical significance anyway? In this post, I’ll continue to focus on concepts and graphs to help you gain a more intuitive understanding of how hypothesis tests work in statistics. To bring it to life, I’ll add the significance level and P value to the graph in my previous post in order to perform a graphical version of... Continue Reading
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