Previously,
I’ve written about when to choose nonlinear regression and
how to model curvature with both linear and
nonlinear regression. Since then, I’ve received several
comments expressing confusion about what differentiates nonlinear
equations from linear equations. This confusion is understandable
because both types can model curves.
So, if it’s not the ability to model a curve, what isthe... Continue Reading

As someone who has collected and analyzed real data for a
living, the idea of using simulated data for a Monte Carlo
simulation sounds a bit odd. How can you improve a real product
with simulated data? In this post, I’ll help you understand the
methods behind Monte Carlo simulation and walk you through a
simulation example using Companion by Minitab.
Companion by Minitab is a software platform that... Continue Reading

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Dear Readers,
As
2016 comes to a close, it’s time to reflect on the passage of time
and changes. As I’m sure you’ve guessed, I love statistics and
analyzing data! I also love talking and writing about it. In fact,
I’ve been writing statistical blog posts for over five years, and
it’s been an absolute blast. John Tukey, the renowned statistician,
once said, “The best thing about being a statistician... Continue Reading

Once
again, with the arrival of autumn, it's time for a flu shot.
I get a flu shot every year even though I know they’re not
perfect. I figure they’re a relatively easy and inexpensive way to
reduce the chance of having a miserable week.
I’ve heard on various news media that their effectiveness is
about 60%. But what does 60% effectiveness mean, exactly? How much
does this actually reduce the... Continue Reading

Regardless of who you support in the upcoming U.S. election, we
can all agree that it’s been a very bumpy ride! It’s been a
particularly chaotic election cycle. Wouldn’t it be nice if we
could peek into the future and see potential election results right
now? That’s what we'll do in this post!
In 2012, I used binary logistic regression to predict that President Obama would be reelected for
a second... Continue Reading

Data mining can be helpful in the exploratory phase of an
analysis. If you're in the early stages and you're just figuring
out which predictors are potentially correlated with your response
variable, data mining can help you identify candidates. However,
there are problems associated with using data mining to select
variables.
In my previous post, we used data mining to settle on
the following... Continue Reading

Data
mining uses algorithms to explore correlations in data sets. An
automated procedure sorts through large numbers of variables and
includes them in the model based on statistical significance alone.
No thought is given to whether the variables and the signs and
magnitudes of their coefficients make theoretical sense.
We tend to think of data mining in the context of big data, with
its huge... Continue Reading

You’ve
performed multiple linear regression and have settled on a model
which contains several predictor variables that are statistically
significant. At this point, it’s common to ask, “Which variable is
most important?”
This question is more complicated than it first appears. For one
thing, how you define “most important” often depends on your
subject area and goals. For another, how you collect... 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

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’ve written about R-squared before and I’ve concluded that it’s
not as intuitive as it seems at first glance. It can be a
misleading statistic because a high R-squared is not always good and a low
R-squared is not always bad. I’ve even said that R-squared is overrated and that the standard error of the estimate (S) can be
more useful.
Even though I haven’t always been enthusiastic about... Continue Reading

In statistics, there are things you need to do so you can trust
your results. For example, you should check the sample size, the
assumptions of the analysis, and so on. In regression analysis, I
always urge people to check their residual plots.
In this blog post, I present one more thing you should do so you
can trust your regression results in certain
circumstances—standardize the continuous... 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

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

I’ve
written a fair bit about P values: how to correctly interpret P values, a graphical representation of how they work,
guidelines for using P values, and why the
P value ban in one journal is a mistake. Along
the way, I’ve received many questions about P values, but the
questions from one reader stand out.
This reader asked, why is it so easy to interpret P
values incorrectly? Why is the common... 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

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