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

With
Speaker John Boehner resigning, Kevin McCarthy quitting before the
vote for him to be Speaker, and a possible government shutdown in
the works, the Freedom Caucus has certainly been in the news
frequently! Depending on your political bent, the Freedom Caucus
has caused quite a disruption for either good or bad.
Who are these politicians? The Freedom Caucus is a group of
approximately 40... Continue Reading

An exciting new study sheds light on the relationship between P
values and the replication of experimental results. This study
highlights issues that I've emphasized repeatedly—it is crucial to
interpret P values correctly, and significant
results must be replicated to be trustworthy.
The study also supports my disagreement with the decision
by the Journal of Basic and Applied Social Psychology to
b... 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

In regression
analysis, overfitting a model is a real problem. An overfit model
can cause the regression coefficients, p-values, and R-squared to be misleading. In this post,
I explain what an overfit model is and how to detect and avoid this
problem.
An overfit model is one that is too complicated for your data
set. When this happens, the regression model becomes tailored to
fit the quirks and... 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

Scientists who use the Hubble Space Telescope to explore the
galaxy receive a stream of digitized images in the form binary
code. In this state, the information is essentially worthless-
these 1s and 0s must first be converted into pictures before the
scientists can learn anything from them.
The same is true of statistical distributions and parameters that are used to describe sample data. They... 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

Banned! In February 2015, editor David Trafimow and associate
editor Michael Marks of the Journal of Basic and Applied Social
Psychology declared that the null hypothesis statistical
testing procedure is invalid. They promptly banned P values,
confidence intervals, and hypothesis testing from the journal.
The journal now requires descriptive statistics and effect
sizes. They also encourage large... Continue Reading