Blog posts and articles about statistical power and sample size, especially in quality improvement projects.

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

When it comes to statistical analyses, collecting a large enough
sample size is essential to obtaining quality results. If your
sample size is too small, confidence intervals may be too wide to
be useful, linear models may lack necessary precision, and
control charts may get so out of control that they become
self-aware and rise up against humankind.
Okay,that last point may have been... Continue Reading

Five-point
Likert scales are commonly associated with surveys and are used in
a wide variety of settings. You’ve run into the Likert scale if
you’ve ever been asked whether you strongly agree, agree, neither
agree or disagree, disagree, or strongly disagree about something.
The worksheet to the right shows what five-point Likert data look
like when you have two groups.
Because Likert item data are... Continue Reading

P values have been around for nearly a century and they’ve been
the subject of criticism since their origins. In recent years, the
debate over P values has risen to a fever pitch. In particular,
there are serious fears that P values are misused to such an extent
that it has actually damaged science.
In March 2016, spurred on by the growing concerns, the American
Statistical Association (ASA) did... 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

There are many reasons why a distribution might not be
normal/Gaussian. A non-normal pattern might be caused by several
distributions being mixed together, or by a drift in time, or by
one or several outliers, or by an asymmetrical behavior, some
out-of-control points, etc.
I recently collected the scores of three different teams (the
Blue team, the Yellow team and the Pink team) after a laser... Continue Reading

Did
you ever wonder why statistical analyses and concepts often have
such weird, cryptic names?
One conspiracy theory points to the workings of a secret
committee called the ICSSNN. The International Committee for
Sadistic Statistical Nomenclature and Numerophobia was formed
solely to befuddle and subjugate the masses. Its mission: To select
the most awkward, obscure, and confusing name possible... Continue Reading

As Halloween
approaches, you are probably taking the necessary steps to protect
yourself from the various ghosts, goblins, and witches that are prowling
around. Monsters of all sorts are out to get you, unless they’re
sufficiently bribed with candy offerings!
I’m here to warn you about a ghoul that all statisticians and
data scientists need to be aware of: phantom degrees of freedom.
These phantoms... Continue Reading

Step
3 in our DOE problem solving methodology is to determine how many
times to replicate the base experiment plan. The discussion in Part 3
ended with the conclusion that our
4 factors could best be studied using all 16 combinations of the
high and low settings for each factor, a full factorial. Each
golfer will perform half of the sixteen possible combinations and
each golfer’s data could stand as... Continue Reading

Step 1 in our DOE problem-solving methodology
is to use process experts, literature, or past experiments to
characterize the process and define the problem. Since I had little
experience with golf myself, this was an important step for me.
This is not an uncommon situation. Experiment designers often
find themselves working on processes that they have little or no
experience with. For example, a... Continue Reading

Repeated measures designs don’t fit our impression of a typical
experiment in several key ways. When we think of an experiment, we
often think of a design that has a clear distinction between the
treatment and control groups. Each subject is in one, and only one,
of these non-overlapping groups. Subjects who are in a treatment
group are exposed to only one type of treatment. This is the... Continue Reading

By Matthew Barsalou, guest
blogger.
Many statistical tests assume the data being tested came from a
normal distribution. Violating the assumption of normality can
result in incorrect conclusions. For example, a Z test may indicate
a new process is more efficient than an older process when this is
not true. This could result in a capital investment for equipment
that actually results in higher... Continue Reading

In
my previous post, I wrote about the hypothesis testing ban in
the Journal of Basic and Applied Social Psychology. I
showed how P values and confidence intervals provide important
information that descriptive statistics alone don’t provide. In
this post, I'll cover the editors’ concerns about hypothesis
testing and how to avoid the problems they describe.
The editors describe hypothesis testing... Continue Reading

All processes have some
variation. Some variation is natural and nothing to be concerned
about. But in other cases, there is unusual variation that may need
attention.
By graphing process
data against an upper and a lower control limit, control charts
help us distinguish natural variation from special cause variation
that we need to be concerned about. If a data point falls outside
the limits on... Continue Reading

Welcome to the Hypothesis Test Casino! The featured game of the
house is roulette. But this is no ordinary game of
roulette. This is p-value roulette!
Here’s how it works: We have two roulette wheels, the Null wheel
and the Alternative wheel. Each wheel has 20 slots (instead of the
usual 37 or 38). You get to bet on one slot.
What happens if the ball lands in the slot you bet on? Well,
that depends... 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

If you wanted to figure out the probability that your favorite
football team will win their next game, how would you do it?
My colleague
Eduardo Santiago and I recently looked at this question, and in
this post we'll share how we approached the solution. Let’s start
by breaking down this problem:
There are only two possible outcomes: your favorite team wins,
or they lose. Ties are a possibility,... Continue Reading

In my experience, one of the
hardest concepts for users to wrap their head around revolves
around the Power and Sample Size menu in Minitab's statistical software, and more specifically, the field that asks
for the "difference" or "difference to detect."
Let’s start with power. In statistics, the definition of power
is the probability that you will correctly reject the null
hypothesis when it is... Continue Reading

Stepwise regression and best subsets regression are both
automatic tools that help you identify useful predictors during the
exploratory stages of model building for linear regression. These
two procedures use different methods and present you with different
output.
An obvious question arises. Does one procedure pick the true
model more often than the other? I’ll tackle that question in this
post.
Fi... Continue Reading

Using a sample to estimate the properties of an entire population
is common practice in statistics. For example, the mean from a
random sample estimates that parameter for an entire population. In linear
regression analysis, we’re used to the idea that the regression coefficients are estimates of the
true parameters. However, it’s easy to forget that R-squared
(R2) is also an estimate.... Continue Reading