This is a table of contents of sorts for five posts on the visualization, fitting, and comparison of frequency distributions. The goal of these posts is to expose ecologists to the ideas and language related to good statistical practices for addressing frequency distribution data. The focus is on simple distributions and likelihood methods.

Summary Likelihood, likelihood, likelihood (and maybe some other complicated approaches), but definitely not r^2 values from fitting regressions to binned data. A bit more nitty gritty detail In addition to causing issues with parameter estimation, binning based methods are also inappropriate when trying to determine which distribution provides the best fit to empirical data.

Summary Don’t bin you’re data and fit a regression. Don’t use the CDF and fit a regression. Use maximum likelihood or other statistically grounded approaches that can typically be looked up on Wikipedia. A bit more detail OK, so you’ve visualized your data and after playing around a bit you have an idea of what the basic functional form of the model is. Now you want to estimate the parameters.

Beyond simple histograms there are two basic methods for visualizing frequency distributions. Kernel density estimation is basically a generalization of the idea behind histograms. The basic idea is to put an miniature distribution (e.g., a normal distribution) at the position of each individual data point and then add up those distributions to get an estimate of the frequency distribution.

Well, I guess that grant season was a bit of an optimistic time to try to do a 4 part series on frequency distributions, but I’ve got a few minutes before heading off to an all day child birth class so I thought I’d see if I could squeeze in part 2. OK, so you have some data and you’d like to get a rough visual idea of its frequency distribution. What do you do know? There are 3 basic approaches that I’ve seen used: Histograms.

Dealing with frequency distribution data is something that we as ecologists haven’t typically done in a very sophisticated way. This isn’t really our fault. Proper methods aren’t typically taught in undergraduate statistics courses or in the graduate level classes targeted at biologists.

Nathan over at Flowing Data just posted an interesting piece on the emergence of a new class of scientists whose work focuses on the manipulation, analysis and presentation of data.

Data is the sword of the 21st century, those who wield it well, the Samurai.