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

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

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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

Do you suffer from PAAA (Post-Analysis Assumption Angst)? You’re
not alone.
Checking the required assumptions for a statistical
analysis is critical. But if you don’t have a Ph.D. in statistics,
it can feel more complicated and confusing than the primary
analysis itself.
How
does the
cuckoo egg data, a common sample data set often used to teach
analysis of variance, satisfy the following
formal... Continue Reading

A few weeks
ago I looked at the
number of goals that were being scored in the World Cup. At the
time there were 2.9 goals per game, which was the highest since
1970. Unfortunately for spectators who enjoyed the higher scoring
goals, this did not last.
By the end, the average had fallen to 2.7 goals per game, the
same amount scored in the 1998 World Cup. After such a high-scoring
start, the goals... Continue Reading

Remember
"The Little Engine That Could," the children's story about
self-confidence in the face of huge challenges? In it, a train
engine keeps telling itself "I think I can" while carrying a very
heavy load up a big mountain. Next thing you know, the little
engine has done it...but until that moment, the outcome
was uncertain.
It's a wonderful story for teaching kids about self-confidence.
But... Continue Reading

Minitab graphs are powerful tools for investigating your process
further and removing any doubt about the steps you should take to
improve it. With that in mind, you’ll want to know every feature
about Minitab graphs that can help you share and communicate your
results effectively. While many ways to modify your graph are on
the Editor menu, some of the best features become
available when you... Continue Reading

It's all too easy to make mistakes involving statistics.
Powerful statistical software can remove a lot of the difficulty
surrounding statistical calculation, reducing the risk of
mathematical errors—but correctly interpreting the results of
an analysis can be even more challenging.
No one knows that better than Minitab's technical trainers. All of our trainers
are seasoned statisticians with... Continue Reading

We’re in the
thick of the Stanley Cup playoffs, which means hockey fans are
doing what seems to be every sports fan's favorite
hobby...complaining about the refs! While most complaints, such as
“We’re not getting any of the close calls!” are subjective and hard
to get data for, there's one question that we should be able to
answer objectively with a statistical analysis: Are hockey
penalties... Continue Reading

One-way
ANOVA can detect differences between the means of three or more
groups. It’s such a classic statistical analysis that it’s hard to
imagine it changing much.
However, a revolution has been under way for a while now.
Fisher's classic one-way ANOVA, which is taught in Stats 101
courses everywhere, may well be obsolete thanks to Welch’s
ANOVA.
In this post, I not only want to introduce you to... Continue Reading

My
previous post examined how an equivalence test
can shift the burden of proof when you perform hypothesis test of
the means. This allows you to more rigorously test whether the
process mean is equivalent to a target or to another mean.
Here’s another key difference: To perform the analysis, an
equivalence test requires that you first define, upfront, the size
of a practically important difference... Continue Reading

I’ve
written a number of blog posts about regression analysis and I've
collected them here to create a regression tutorial. I’ll
supplement my own posts with some from my colleagues.
This tutorial covers many aspects of regression analysis
including: choosing the type of regression analysis to use,
specifying the model, interpreting the results, determining how
well the model fits, making... Continue Reading

Two
weeks ago Penn State and Michigan played in a quadruple-overtime
thriller that almost went into a 5th overtime. Had Penn
State coach Bill O’Brien kicked a field goal in the 4th
overtime instead of going for it on 4th and 1, the game
would have continued. But the Nittany Lions converted the
4th down (which, by the way,
wasn’t a gamble) and went on to score the game winning
touchdown in the 4th... Continue Reading

Even
the best NHL goalies can get pulled several times each season. Do
they really have cold streaks, or is a drop in save percentage on a
given day part of normal random variation?
My colleague Doug Gorman and I decided to find out using our
favorite statistical software
package.
Control Charts for Coaching Decisions
We used a control chart approach to determine if coaching
decisions to pull... Continue Reading

In
my home, we’re huge fans of Mythbusters, the show on Discovery Channel. This fun
show mixes science and experiments to prove or disprove various
myths, urban legends, and popular beliefs. It’s a great show
because it brings the scientific method to life. I’ve written about
Mythbusters
before to show how, without proper statistical analysis, it’s
difficult to know when a result is statistically... Continue Reading

Over on the Indium Corporation's blog, Dr. Ron Lasky has been
sharing some interesting ideas about using the Weibull distribution
in electronics manufacturing. For instance, check out this discussion of how dramatically an early
first-failure can affect an analysis of a part or component (in
this case, an alloy used to solder components to a circuit
board).
This got me thinking again about all the... Continue Reading

When I talk to quality professionals about how they use
statistics, one tool they mention again and again is design of
experiments, or DOE. I'd never even heard the term before I started
getting involved in quality improvement efforts, but now that I've
learned how it works, I wonder why I didn't learn about it sooner.
If you need to find out how several factors are affecting a process
outcome,... Continue Reading