Back when I was doing psychology research, I knew ANOVA pretty well. I’d taken a number of courses on it and could run it backward and forward. I kept hearing about ANCOVA, but in every ANOVA class that was the last topic on the syllabus, and we always ran out of time.
The other thing that drove me crazy was those stats professors kept saying “ANOVA is just a special case of Regression.” I could not for the life of me figure out why or how.
It was only when I switched over to statistics that I finally took a regression class and figured out what ANOVA was all about. And only when I started consulting, and seeing hundreds of different ANOVA and regression models, that I finally made the connection.
But if you don’t have the driving curiosity about ANOVA and regression, why should you, as a researcher in Psychology, Education, or Agriculture, who is trained in ANOVA, want to learn regression? There are 3 main reasons.
1. There a many, many continuous independent variables and covariates that need to be included in models. Without the tools to analyze them as continuous, you are left forcing them into ANOVA using an arbitrary technique like median splits. At best, you’re losing power. At worst, you’re not publishing your article because you’re missing real effects.
2. Having a solid understanding of the General Linear Model in its various forms equips you to really understand your variables and their relationships. It allows you to try a model different ways–not for data fishing, but for discovering the true nature of the relationships. Having the capacity to add an interaction term or a squared term allows you to listen to your data and makes you a better researcher.
3. The multiple linear regression model is the basis for many other statistical techniques–logistic regression, multilevel and mixed models, Poisson regression, Survival Analysis, and so on. Each of these is a step (or small leap) beyond multiple regression. If you’re still struggling with what it means to center variables or interpret interactions, learning one of these other techniques becomes arduous, if not painful.
Having guided thousands of researchers through their statistical analysis over the past 10 years, I am convinced that having a strong, intuitive understanding of the general linear model in its variety of forms is the key to being an effective and confident statistical analyst. You are then free to learn and explore other methodologies as needed.
The beauty of the Univariate GLM procedure in SPSS is that it is so flexible. You can use it to analyze regressions, ANOVAs, ANCOVAs with all sorts of interactions, dummy coding, etc.
The down side of this flexibility is it is often confusing what to put where and what it all means.
So here’s a quick breakdown.
The dependent variable I hope is pretty straightforward. Put in your continuous dependent variable.
Fixed Factors are categorical independent variables. It does not matter if the variable is (more…)
Statistical models, such as general linear models (linear regression, ANOVA, MANOVA), linear mixed models, and generalized linear models (logistic, Poisson, regression, etc.) all have the same general form.
On the left side of the equation is one or more response variables, Y. On the right hand side is one or more predictor variables, X, and their coefficients, B. The variables on the right hand side can have many forms and are called by many names.
There are subtle distinctions in the meanings of these names. Unfortunately, though, there are two practices that make them more confusing than they need to be.
First, they are often used interchangeably. So someone may use “predictor variable” and “independent variable” interchangably and another person may not. So the listener may be reading into the subtle distinctions that the speaker may not be implying.
Second, the same terms are used differently in different fields or research situations. So if you are an epidemiologist who does research on mostly observed variables, you probably have been trained with slightly different meanings to some of these terms than if you’re a psychologist who does experimental research.
Even worse, statistical software packages use different names for similar concepts, even among their own procedures. This quest for accuracy often renders confusion. (It’s hard enough without switching the words!).
Here are some common terms that all refer to a variable in a model that is proposed to affect or predict another variable.
I’ll give you the different definitions and implications, but it’s very likely that I’m missing some. If you see a term that means something different than you understand it, please add it to the comments. And please tell us which field you primarily work in.
Predictor Variable, Predictor
This is the most generic of the terms. There are no implications for being manipulated, observed, categorical, or numerical. It does not imply causality.
A predictor variable is simply used for explaining or predicting the value of the response variable. Used predominantly in regression.
Independent Variable
I’ve seen Independent Variable (IV) used different ways.
1. It implies causality: the independent variable affects the dependent variable. This usage is predominant in ANOVA models where the Independent Variable is manipulated by the experimenter. If it is manipulated, it’s generally categorical and subjects are randomly assigned to conditions.
2. It does not imply causality, but it is a key predictor variable for answering the research question. In other words, it is in the model because the researcher is interested in understanding its relationship with the dependent variable. In other words, it’s not a control variable.
3. It does not imply causality or the importance of the variable to the research question. But it is uncorrelated (independent) of all other predictors.
Honestly, I only recently saw someone define the term Independent Variable this way. Predictor Variables cannot be independent variables if they are at all correlated. It surprised me, but it’s good to know that some people mean this when they use the term.
Explanatory Variable
A predictor variable in a model where the main point is not to predict the response variable, but to explain a relationship between X and Y.
Control Variable
A predictor variable that could be related to or affecting the dependent variable, but not really of interest to the research question.
Covariate
Generally a continuous predictor variable. Used in both ANCOVA (analysis of covariance) and regression. Some people use this to refer to all predictor variables in regression, but it really means continuous predictors. Adding a covariate to ANOVA (analysis of variance) turns it into ANCOVA (analysis of covariance).
Sometimes covariate implies that the variable is a control variable (as opposed to an independent variable), but not always.
And sometimes people use covariate to mean control variable, either numerical or categorical.
This one is so confusing it got it’s own Confusing Statistical Terms article.
Confounding Variable, Confounder
These terms are used differently in different fields. In experimental design, it’s used to mean a variable whose effect cannot be distinguished from the effect of an independent variable.
In observational fields, it’s used to mean one of two situations. The first is a variable that is so correlated with an independent variable that it’s difficult to separate out their effects on the response variable. The second is a variable that causes the independent variable’s effect on the response.
The distinction in those interpretations are slight but important.
Exposure Variable
This is a term for independent variable in some fields, particularly epidemiology. It’s the key predictor variable.
Risk Factor
Another epidemiology term for a predictor variable. Unlike the term “Factor” listed below, it does not imply a categorical variable.
Factor
A categorical predictor variable. It may or may not indicate a cause/effect relationship with the response variable (this depends on the study design, not the analysis).
Independent variables in ANOVA are almost always called factors. In regression, they are often referred to as indicator variables, categorical predictors, or dummy variables. They are all the same thing in this context.
Also, please note that Factor has completely other meanings in statistics, so it too got its own Confusing Statistical Terms article.
Feature
Used in Machine Learning and Predictive models, this is simply a predictor variable.
Grouping Variable
Same as a factor.
Fixed factor
A categorical predictor variable in which the specific values of the categories are intentional and important, often chosen by the experimenter. Examples include experimental treatments or demographic categories, such as sex and race.
If you’re not doing a mixed model (and you should know if you are), all your factors are fixed factors. For a more thorough explanation of fixed and random factors, see Specifying Fixed and Random Factors in Mixed or Multi-Level Models
Random factor
A categorical predictor variable in which the specific values of the categories were randomly assigned. Generally used in mixed modeling. Examples include subjects or random blocks.
For a more thorough explanation of fixed and random factors, see Specifying Fixed and Random Factors in Mixed or Multi-Level Models
Blocking variable
This term is generally used in experimental design, but I’ve also seen it in randomized controlled trials.
A blocking variable is a variable that indicates an experimental block: a cluster or experimental unit that restricts complete randomization and that often results in similar response values among members of the block.
Blocking variables can be either fixed or random factors. They are never continuous.
Dummy variable
A categorical variable that has been dummy coded. Dummy coding (also called indicator coding) is usually used in regression models, but not ANOVA. A dummy variable can have only two values: 0 and 1. When a categorical variable has more than two values, it is recoded into multiple dummy variables.
Indicator variable
Same as dummy variable.
The Take Away Message
Whenever you’re using technical terms in a report, an article, or a conversation, it’s always a good idea to define your terms. This is especially important in statistics, which is used in many, many fields, each of whom adds their own subtleties to the terminology.
Confusing Statistical Terms #1: The Many Names of Independent Variables
