I have wood density data for a number of tree species given a tree's state of decay. I am presented with mean density and standard errors (SE). I am NOT provided with sample sizes.
For example, a decay class 1 fir tree has a mean density of 0.305 with a standard error of 0.024.
I am using R. I would like to generate a density value for a given decay class 1 fir tree similarly to using rnorm(n, mean, standard deviation) when pulling from a normal distribution.
In this case, is it appropriate to substitute the SE for SD, such as density<-rnorm(1, mean=0.305, sd=0.024)?
Best Answer
No! They're not really interchangeable like that. Standard deviation is a measure of central tendency or or dispersion: i.e., how close your values are to one another. A high standard deviation indicates that the values are pretty spread out, while a low standard deviation indicates that they're all fairly close to one another (and the mean). The standard error (which is the shortened form of standard error of the mean), however, represents the (im)precision in your estimate of the mean.
If you draw from a distribution with the same mean and standard deviation, you will effectively simulate a dataset similar to the original (assuming they're both normally distributed, etc). However, if you draw from a distribution with the same mean and standard error, you'll be drawing other plausible estimates for the mean of that distribution.
If you knew the sample size, you can easily recover the standard deviation from the standard error, since $$\textrm{SE} = \frac{s}{\sqrt{n}}$$ but it sounds like you don't have that information available. Can you estimate the sample size from the text (e.g., "we collected 1-2 dozen samples of each type") or the nature of the experiment? The square-root buys you some flexibility here--if you're off by a factor of 10 (e.g., you think they used 100 samples, but they only used 10), you'll only be off by about three-fold. If this is from an academic paper or something, you might try emailing them. People are often surprisingly helpful about things like this, especially if the paper is fairly recent.