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

As your customers demand more and organizations fight to stay competitive, the battle to create more value with fewer resources is ever present. How can you leverage Lean tools to thrive in your business?

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