Adventures in Statistics

What Is the Difference between Linear and Nonlinear Equations in Regression Analysis?

Jim Frost 6 July, 2017

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

Understanding Monte Carlo Simulation with an Example

Jim Frost 25 April, 2017

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

The Joy of Playing in Endless Backyards with Statistics

Jim Frost 30 November, 2016

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

How Effective Are Flu Shots?

Jim Frost 9 November, 2016

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

Simulating the U.S. Presidential Election of 2016

Jim Frost 3 November, 2016

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

Problems Using Data Mining to Build Regression Models, Part Two

Jim Frost 19 October, 2016

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

Problems Using Data Mining to Build Regression Models

Jim Frost 21 September, 2016

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

How to Identify the Most Important Predictor Variables in Regression Models

Jim Frost 7 September, 2016

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

Understanding Analysis of Variance (ANOVA) and the F-test

Jim Frost 18 May, 2016

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

Understanding t-Tests: 1-sample, 2-sample, and Paired t-Tests

Jim Frost 4 May, 2016

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

Understanding t-Tests: t-values and t-distributions

Jim Frost 20 April, 2016

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

Best Way to Analyze Likert Item Data: Two Sample T-Test versus Mann-Whitney

Jim Frost 6 April, 2016

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

The American Statistical Association's Statement on the Use of P Values

Jim Frost 23 March, 2016

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

Five Reasons Why Your R-squared Can Be Too High

Jim Frost 24 February, 2016

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

When Is It Crucial to Standardize the Variables in a Regression Model?

Jim Frost 10 February, 2016

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

When Should You Fit a Non-Hierarchical Regression Model?

Jim Frost 27 January, 2016

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 to Compare Regression Slopes

Jim Frost 13 January, 2016

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

Why Are P Value Misunderstandings So Common?

Jim Frost 10 December, 2015

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 - Not Just for Statistical Process Control (SPC) Anymore!

Jim Frost 12 November, 2015

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

Beware of Phantom Degrees of Freedom that Haunt Your Regression Models!

Jim Frost 29 October, 2015

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

Jim Frost