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
by Laerte de Araujo Lima, guest blogger
The NBA's 2015-16 season will be one for the history books. Not
only was it the last season of Kobe Bryan,
who scored 60 points in his final game, but the Golden State
a new wins record, beating the previous record set by 1995-96
Warriors seem likely to take this season's NBA title, in large part
thanks to the performance of... 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
How do t-tests work? How do t-values fit in? In this... 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
Probability. It's really the heart and soul of most statistical
analyses. Anytime you get a
p-value, you're dealing with a probability. The probability is
telling you how likely it was (or will be) for an event to occur.
It has numerous applications across a wide variety of areas. But
today I want to focus on the probability of a specific event.
A basketball tournament.
I’ll be using the Sagarin...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
Awards—after five nominations in previous ceremonies. As a
longtime Di Caprio fan, I still remember... Continue Reading
What is an interaction? It’s when the effect of one factor
depends on the level of another factor. Interactions are important
when you’re performing ANOVA, DOE, or a regression analysis.
Without them, your model may be missing an important term that
helps explain variability in the response!
For example, let’s consider 3-point shooting in the NBA. We
previously saw that the number of 3-point... Continue Reading
In my last post, I looked at
viewership data for the five seasons of HBO’s hit series Game of
created a time series plot in Minitab that showed how
viewership rose season by season, and how it varied episode by
episode within each season.
My next step is to fit a statistical model to the data, which
I hope will allow me to predict the viewing numbers for future
I am going to... Continue Reading
If you want to convince someone that at least a basic
understanding of statistics is an essential life skill, bring up
the case of Lucia de Berk. Hers is a story that's too awful to be
true—except that it is completely true.
flawed analysis irrevocably altered de Berk's life and kept her
behind bars for five years, and the fact that this analysis
targeted and harmed just one person makes it more... Continue Reading
In the world of linear models, a hierarchical model contains all
lower-order terms that comprise the higher-order terms that also
appear in the model. For example, a model that includes the
interaction term A*B*C is hierarchical if it includes these terms:
A, B, C, A*B, A*C, and B*C.
Fitting the correct regression model can be as
much of an art as it is a science. Consequently, there's not always
a... 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!
of the following are famous figure skating pairs, and which are
methods for testing whether your data follow a... Continue Reading
If you perform linear regression analysis, you might need to
compare different regression lines to see if their constants and
slope coefficients are different. Imagine there is an established
relationship between X and Y. Now, suppose you want to determine
whether that relationship has changed. Perhaps there is a new
context, process, or some other qualitative change, and you want to
determine... 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
P-values are frequently misinterpreted, which causes many
problems. I won't rehash those
problems here here since my colleague Jim Frost has
detailed the issues involved at some length, but the fact remains
that the p-value will continue to be one of the most frequently
used tools for deciding if a result is statistically
You know the old saw about "Lies, damned lies, and... 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
Fortunately, I've had a lot more... Continue Reading
I have two young children, and I
work full-time, so my adult TV time is about as rare as finding a
Kardashian-free tabloid. So I can’t commit to just any TV
show. It better be a good one. I was therefore extremely
excited when Netflix analyzed viewer
data to find out at what point
watchers get hooked on the first season of various
they identified the episode at which 70% of...Continue Reading
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
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