# Ratio measure vs. difference measure?

I am comparing food inflation estimates from different sources for the same year and country. Food inflation can be negative or positive, e.g. year 2010: 5% in Source A and 7.5% in Source B; year 2011 1% in Source A and -2% in Source B.

I want to flag cases where inflation for the same country and year differ considerably between the two sources. I thought that I could flag cases where the absolute difference in inflation percentage points between the two sources is >2.

So, if source A has 5% and source B 1%, then this case would be flagged since |5%-1%|=4% is greater than 2%.

The choice that the absolute difference be greater than 2 percentage points of inflation is arbitrary. However, what am I missing by using a difference measure to assess differences between sources? Should I use a ratio measure instead, e.g. 5%/1%?

• To see whether it matters to you, why not consider some specific cases? For instance, if the inflation in Source A were 1% and that in Source B were 0.1%, would you view that ratio of 1/0.1 = 10 to be a difference equivalent to, say, inflation in Source A of 20% and in Source B of 2%? Or how about the pairs (-1%,1%) and (-50%,50%), both with ratios of -1? – whuber Sep 12 '18 at 18:58
• I guess you know this really, but you mean |difference| > 2. |2| is always just 2 . For example, -3 is not greater than 2 while |-3| certainly is. More positively, there is a long and manifold literature on change measures, particularly in economics. See e.g. jstor.org/stable/pdf/4615624.pdf – Nick Cox Sep 12 '18 at 19:17
• @NickCox. Good catch, I edited the question. Also, it would be great to get any insights from the paper you link for my question. I don't have the required math and/or index number expertise to fully comprehend it. – StatsScared Sep 12 '18 at 19:35