Tell me if you can relate to this:
You love your field of study, you enjoy asking the big questions and discovering answers. But, when it comes to data analysis and statistics you get a little bogged down. You might even feel a bit lost sometimes.
And that is hard to admit.
Because after all, you are supposed to be the expert. Right?
Learning Statistics is Hard but We Make it a Lot Easier
The thing is, statistics is a field unto itself. But as a researcher, you need to be adept with statistics even though you may only have very basic training in this field. In essence, you learned statistics — a new language — out of context. You had no real immersion experience to practice this language. You had few opportunities to apply the strange new terms and concepts as you learned them.
At the Analysis Factor, we understand the pain of learning and doing statistics. We have been in the trenches with hundreds of researchers like you across many fields of study. Everyone is struggling to grow their statistical, data analysis, and software skills.
In Statistically Speaking we support and guide you as you learn — every step of the way. We know where to start, where to go next, and next, and next.
We know that your field and research question(s) determine the type of data and complexity of statistical analyses you will choose. And we know that everyone shows up in a different place, and needs different things to help them get where they need to go.
So we have created a treasure trove of resources on hundreds of topics — from data cleaning and research design to logistic regression and structural equation modeling.
And to keep it all about you, we have created a customizable learning platform, one where you make a plan for your own unique journey. We have crafted a series of comprehensive Maps, curated guides on essential topics at each Stage of mastery, offering you a structured pathway through the maze of statistical knowledge.
You create the plan you need, and choose the maps you need to do your research.
Maps
At The Analysis Factor, we classify the statistical content and skills into 4 Stages to help you decide where to begin your learning journey. In Statistically Speaking, the Maps are categorized into these Stages.
Here are just a few examples:
Stage 1: Fundamentals

Preparing Data: Understanding the fundamental steps in data preparation, from cleaning and transforming to structuring datasets for analysis.

Bivariate Statistics: Grasping the basics of relationships between two variables, laying the groundwork for more complex analyses.
Stage 2: Linear Models

Graphing: Learning visualization techniques to represent data and derive meaningful insights.

Introduction to Regression: Unraveling the fundamentals of regression analysis, a cornerstone of statistical modeling.

Interpreting Results: Developing the skill to interpret statistical results and draw valid conclusions from analyses.
Stage 3: Extensions of Linear Models

Count Models: Exploring specialized models for count data analysis, understanding their application and nuances.

Logistic Regression: Diving into binary outcome analysis, understanding probabilities, and logistic models.

Factor Analysis: Delving into multivariate analysis, understanding latent variables and their relationships.
Stage 4: Advanced Models

GLMM: Embracing the complexity of generalized linear mixed models, integrating fixed and random effects.

SEM: Venturing into structural equation modeling, exploring complex relationships among variables.

Survival Analysis: Understanding timetoevent data, its application in various fields, and survival modeling techniques.
By mapping out the key content and skills you want to learn at each Stage, you’ll gain a clearer understanding of the vast statistical landscape and feel empowered to take on the learning journey ahead.
So, what are you waiting for? Members, head on over to explore the Maps in Statistically Speaking.
And if you are not yet a member, you can signup for our waitlist to join Statistically Speaking. We would love to meet you, learn about your research, and help you get started on your statistical learning adventure.
One of the important issues with missing data is the missing data mechanism. You may have heard of these: Missing Completely at Random (MCAR), Missing at Random (MAR), and Missing Not at Random (MNAR).
The mechanism is important because it affects how much the missing data bias your results. This has a big impact on what is a reasonable approach to dealing with the missing data. So you have to take it into account in choosing an approach.
The concepts of these mechanisms can be a bit abstract.
And to top it off, two of these mechanisms have really confusing names: Missing Completely at Random and Missing at Random.
Missing Completely at Random (MCAR)
Missing Completely at Random is pretty straightforward. What it means is what is (more…)
The field of statistics has a terminology problem.
It affects students’ ability to learn statistics. It affects researchers’ ability to communicate with statisticians; with collaborators in different fields; and of course, with the general public.
It’s easy to think the real issue is that statistical concepts are difficult. That is true. It’s not the whole truth, though. (more…)
Much like General Linear Model and Generalized Linear Model in #7, there are many examples in statistics of terms with (ridiculously) similar names, but nuanced meanings.
Today I talk about the difference between multivariate and multiple, as they relate to regression.
Multiple Regression
A regression analysis with one dependent variable and eight independent variables is NOT a multivariate regression model. It’s a multiple regression model.
And believe it or not, it’s considered a univariate model.
This is uniquely important to remember if you’re an SPSS user. Choose Univariate GLM (General Linear Model) for this model, not multivariate.
I know this sounds crazy and misleading because why would a model that contains nine variables (eight Xs and one Y) be considered a univariate model?
It’s because of the fundamental idea in regression that Xs and Ys aren’t the same. We’re using the Xs to understand the mean and variance of Y. This is why the residuals in a linear regression are differences between predicted and actual values of Y. Not X.
(And of course, there is an exception, called Type II or Major Axis linear regression, where X and Y are not distinct. But in most regression models, Y has a different role than X).
It’s the number of Ys that tell you whether it’s a univariate or multivariate model. That said, other than SPSS, I haven’t seen anyone use the term univariate to refer to this model in practice. Instead, the assumed default is that indeed, regression models have one Y, so let’s focus on how many Xs the model has. This leads us to…
Simple Regression: A regression model with one Y (dependent variable) and one X (independent variable).
Multiple Regression: A regression model with one Y (dependent variable) and more than one X (independent variables).
References below.
Multivariate Regression
Multivariate analysis ALWAYS describes a situation with multiple dependent variables.
So a multivariate regression model is one with multiple Y variables. It may have one or more than one X variables. It is equivalent to a MANOVA: Multivariate Analysis of Variance.
Other examples of Multivariate Analysis include:
 Principal Component Analysis
 Factor Analysis
 Canonical Correlation Analysis
 Linear Discriminant Analysis
 Cluster Analysis
But wait. Multivariate analyses like cluster analysis and factor analysis have no dependent variable, per se. Why is it about dependent variables?
Well, it’s not really about dependency. It’s about which variables’ mean and variance is being analyzed. In a multivariate regression, we have multiple dependent variables, whose joint mean is being predicted by the one or more Xs. It’s the variance and covariance in the set of Ys that we’re modeling (and estimating in the VarianceCovariance matrix).
Note: this is actually a situation where the subtle differences in what we call that Y variable can help. Calling it the outcome or response variable, rather than dependent, is more applicable to something like factor analysis.
So when to choose multivariate GLM? When you’re jointly modeling the variation in multiple response variables.
References
In response to many requests in the comments, I suggest the following references. I give the caveat, though, that neither reference compares the two terms directly. They simply define each one. So rather than just list references, I’m going to explain them a little.
 Neter, Kutner, Nachtsheim, Wasserman’s Applied Linear Regression Models, 3rd ed. There are, incidentally, newer editions with slight changes in authorship. But I’m citing the one on my shelf.
Chapter 1, Linear Regression with One Independent Variable, includes:
“Regression model 1.1 … is “simple” in that there is only one predictor variable.”
Chapter 6 is titled Multiple Regression – I, and section 6.1 is “Multiple Regression Models: Need for Several Predictor Variables.” Interestingly enough, there is no direct quotable definition of the term “multiple regression.” Even so, it’s pretty clear. Go read the chapter to see.
There is no mention of the term “Multivariate Regression” in this book.
2. Johnson & Wichern’s Applied Multivariate Statistical Analysis, 3rd ed.
Chapter 7, Multivariate Linear Regression Models, section 7.1 Introduction. Here it says:
“In this chapter we first discuss the multiple regression model for the prediction of a single response. This model is then generalized to handle the prediction of several dependent variables.” (Emphasis theirs).
They finally get to Multivariate Multiple Regression in Section 7.7. Here they “consider the problem of modeling the relationship between m responses, Y_{1}, Y_{2}, …,Y_{m}, and a single set of predictor variables.”
Misuses of the Terms
I’d be shocked, however, if there aren’t some books or articles out there where the terms are not used or defined the way I’ve described them here, according to these references. It’s very easy to confuse these terms, even for those of us who should know better.
And honestly, it’s not that hard to just describe the model instead of naming it. “Regression model with four predictors and one outcome” doesn’t take a lot more words and is much less confusing.
If you’re ever confused about the type of model someone is describing to you, just ask.
Read More Explanations of Confusing Statistical Terms.
First Published 4/29/09;
Updated 2/23/21 to give more detail.