Regression models

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When learning about linear models —that is, regression, ANOVA, and similar techniques—we are taught to calculate an R². The R² has the following useful properties:

• The range is limited to [0,1], so we can easily judge how relatively large it is.
• It is standardized, meaning its value does not depend on the scale of the variables involved in the analysis.
• The interpretation is pretty clear: It is the proportion of variability in the outcome that can be explained by the independent variables in the model.

The calculation of the R² is also intuitive, once you understand the concepts of variance and prediction. (more…)

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Whether or not you run experiments, there are elements of experimental design that affect how you need to analyze many types of studies.

The most fundamental of these are replication, randomization, and blocking. These key design elements come up in studies under all sorts of names: trials, replicates, multi-level nesting, repeated measures. Any data set that requires mixed or multilevel models has some of these design elements. (more…)

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The following statement might surprise you, but it’s true.

To run a linear model, you don’t need an outcome variable Y that’s normally distributed. Instead, you need a dependent variable that is:

• Continuous
• Unbounded
• Measured on an interval or ratio scale

The normality assumption is about the errors in the model, which have the same distribution as Y|X. It’s absolutely possible to have a skewed distribution of Y and a normal distribution of errors because of the effect of X. (more…)

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by Christos Giannoulis

Many data sets contain well over a thousand variables. Such complexity, the speed of contemporary desktop computers, and the ease of use of statistical analysis packages can encourage ill-directed analysis.

It is easy to generate a vast array of poor ‘results’ by throwing everything into your software and waiting to see what turns up. (more…)

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What is a Confounder?

Confounder (also called confounding variable) is one of those statistical terms that confuses a lot of people. Not because it represents a confusing concept, but because of how it’s used.

(Well, it’s a bit of a confusing concept, but that’s not the worst part).

It has slightly different meanings to different types of researchers. The definition is essentially the same, but the research context can have specific implications for how that definition plays out.

If the person you’re talking to has a different understanding of what it means, you’re going to have a confusing conversation.

Let’s take a look at some examples to unpack this.

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