If your graduate statistical training was anything like mine, you learned ANOVA in one class and Linear Regression in another. My professors would often say things like “ANOVA is just a special case of Regression,” but give vague answers when pressed.
It was not until I started consulting that I realized how closely related ANOVA and regression are. They’re not only related, they’re the same thing. Not a quarter and a nickel–different sides of the same coin.
So here is a very simple example that shows why. When someone showed me this, a light bulb went on, even though I already knew both ANOVA and multiple linear (more…)
A Linear Regression Model with an interaction between two predictors (X1 and X2) has the form:
Y = B0 + B1X1 + B2X2 + B3X1*X2.
It doesn’t really matter if X1 and X2 are categorical or continuous, but let’s assume they are continuous for simplicity.
One important concept is that B1 and B2 are not main effects, the way they would be if (more…)
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.
There are many dependent variables that no matter how many transformations you try, you cannot get to be normally distributed. The most common culprits are count variables–the variable that measures the count or rate of some event in a sample. Some examples I’ve seen from a variety of disciplines are:
Number of eggs in a clutch that hatch
Number of domestic violence incidents in a month
Number of times juveniles needed to be restrained during tenure at a correctional facility
Number of infected plants per transect
A common quality of these variables is that 0 is the mode–the most common value. 1 is the next most common, 2 the next, and so on. In variables with low expected counts (number of cars in a household, number of degrees earned), (more…)
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…)
Nearly all granting agencies require an estimate of an adequate sample size to detect the effects hypothesized in the study. But all studies are well served by estimates of sample size, as it can save a great deal on resources.
Why? Undersized studies can’t find real results, and oversized studies find even insubstantial ones. Both undersized and oversized studies waste time, energy, and money; the former by using resources without finding results, and the latter by using more resources than necessary. Both expose an unnecessary number of participants to experimental risks.
The trick is (more…)
