# How to standardize count data for different sampling site sizes

I want to do a linear regression for my data but I’m not sure what I need to do with my raw data before running a linear regression. I have counts for species in several forests of differing sizes. I want to compare these counts to percentages of a certain land type within a fixed region around the forest. My worry is that large forests will have large species counts and won’t reflect the land type which is the whole purpose. How can I standardize the count data (is it even standardizing I should be doing?)

• Welcome to CV. Your question isn't completely clear. What is your dependent variable? What are your independent variables? – Peter Flom Dec 7 '18 at 12:39
• @Peter Flom Sorry about that. My independent variable is percentage of developed land within a fixed distance around a forest. The dependent variable is the number of trees of a certain species (count). I have multiple forests of different sizes, some small with low counts and some large. I’m assuming I can’t just plot percentage and counts on a graph as they are. – NeedtoPass Dec 7 '18 at 15:30

You should include an offset term. With count data I'm assuming you're doing some kind of poisson or negative binomial regression.

So, for example, using the formula for a negative binomial regression with a log link:

$$\ln(\mu_i)=\beta^tx_i$$

$$\mu=e^{\beta_1x_1+\beta_2x_2+\epsilon}$$

adding an offset for size of forests makes it

$$\ln(\frac{\mu_i}{size_i})=\beta^tx_i$$

$$\mu=e^{\beta_1x_1+\beta_2x_2+ \epsilon}+size$$

Size gets added in 'raw' it doesn't have a beta. The interpretation is now the expected number of species per unit of size of forest is whatever.

• my notation's very bad, but i hope it still conveys the message – Huy Pham Dec 7 '18 at 15:43
• I understand what you mean and that looks like the right way to go about it. The only problem is I don't have the size of each forest delineated in my dataset. I will try replacing size with number of sampling sites within in each forest and see if that works. Thank you! – NeedtoPass Dec 7 '18 at 16:47