5.1 What are sampling distributions?

When we talk about sampling distributions, we are talking about the probability that a variable we can measure (e.g. temperature) takes on some value. In most cases, there is a higher probability that the variable will take on certain values than others. That probability may be governed by any number of processes and thus may assume a number of different shapes with respect to the likelihood of any given value of our variable. The differences in the shapes that we assume, and the mathematical parameters that we use to describe those shapes are called “probability distributions”. And, when they are estimated from data, they are sampling distributions.

There was a time when biologists were largely restricted to using models that relied heavily on the assumption that the things we measured, and their errors, followed “normal” distributions, which you have probably heard of or seen in a scientific paper. This was because of how computationally intensive other methods were. This often led to the use of strictly parametric tools like ANOVA and t-tests, or the use of strictly non-parametric tools like frequency analyses and rank-order methods. While these are still useful techniques in our toolboxes, that time has passed, and now we have access to a wide range of tools that allow us to extend simple parametric and non-parametric tools to relax or change distributional assumptions. We will discuss these throughout the book, but we need to look at the underlying distributions that govern our decisions about which of these tools to use. So, this week we’ll look at a few probability distributions that correspond to sampling distributions we frequently encounter in biology. To wrap-up, we will use this new information to talk about how we calculate descriptive statistics such as means and standard deviations from samples.