# Comparing relative change for different base value

I need to compare change in employment size for a sample of companies. I could use percentage change, however, the problem with it is that when the base is small, a small absolute change result in a large percentage change.

For instance, company A and B employment is 10 and 10,000 respectively. assuming both company increase their employment by 5. the percentage increase is 50% for A and 0.05% for B.

I recall reading somewhere that there are some measures that take into account the different initial value when measuring changes (e.g., multiplying relative change by a function of absolute change). However, I can't recall where I read it or the name of the indicator.

Anyone is aware of such indicator or is able to propose a solution?

TIA

• What is this for? Regression analysis? – TheSaint321 Jun 4 '18 at 1:01
• For flagging out extreme changes that might be data entry error – Seamus Lam Jun 5 '18 at 2:02
• Is there some reason not to compare % difference with average employment churn for that company? If company X generally increases/decreases their employment by 500 per month on average but this month they increased/decreased it by 9000 then it would flag that? You could calculate the standard deviation from average employment for each company? – TheSaint321 Jun 5 '18 at 3:05
• thanks for the suggestion. I should have been clearer in my question or comment. The data come in annually, and some companies may only have one other data point for comparison. As such, we cant use standard deviation as a measure – Seamus Lam Jun 5 '18 at 8:22

## 1 Answer

https://en.wikipedia.org/wiki/Relative_change_and_difference

Törnqvist, Leo; Vartia, Pentti; Vartia, Yrjö (1985), "How Should Relative Changes Be Measured?", The American Statistician, 39 (1): 43–46, doi:10.2307/2683905