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

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

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