# Thread: Growth Rate with Zeros?

1. ## Growth Rate with Zeros?

I have a data set dealing with the citation rates of journal publications. In each year, a published article is cited by other articles. I would like to calculate the citation rate on a per year basis.

For example, if a paper was cited 10 times in Year 1 and 11 times in Year 2, then I calculate the rate as ln(11/10).

However, I am not sure how to address cases when an article was not cited in a given year. This occurs in two ways:

Case 1: Year 1 = 0 citations and Year 2 = 11 citations. The rate would be ln(11/0) which is undefined?

Case 2: Year 1 = 10 and Year 2 = 0. The rate would be ln(0/10) = -infinity?

Is there any way to "deal" with these cases such that I don't get these "problems". Is there a valid work-around, such as adding 1 to all cases to avoid zeros?

Thank you.

2. Originally Posted by Ochotona

For example, if a paper was cited 10 times in Year 1 and 11 times in Year 2, then I calculate the rate as ln(11/10).
Why use the logarithm? I would say the the growth rate is simply $\frac{11}{10}$

Originally Posted by Ochotona

Case 1: Year 1 = 0 citations and Year 2 = 11 citations. The rate would be ln(11/0) which is undefined?
My previous advice won't help with the zero divisor so I suggest you either only report growth rates on citations with a non zero baseline or you change the statistic you are reporting on to 'citation increase' which is simply the difference from the previous year.