# Why is measuring percent change (or Year over year change) of percents bad?

So I'm calculating female representation of our workforce and trying to track changes over time. So say in Jan 2018 I had 40% of the workforce are females and in Jan 2019 I had 45%. The percent change is 12.5%. I'm getting push back on this because "calculating percent change of percents is bad". However, if I was to calculate percent change on the actual number of females let's say 100 in Jan 2018, and 200 in Jan 2019, it would seem like our female representation should have doubled, but in reality the business grew. So by taking the percent change of percents, I feel like I'm accounting for any major fluctuations in headcount movement.

What am I missing here?

• Your calculation seems perfectly reasonable to me. As for the shibboleth, "calculating percent change of percents is bad" I don't understand it. May 22 '19 at 14:26
• @saulspatz This is about communicating well, not calculating correctly. These are two quite different things. May 22 '19 at 14:34
• @HansEngler I don't think I said he shouldn't communicate well. He should say, "The percentage grew from $40$ to $45$ a $12.5\%$ increase." The question, if you take the trouble to read it, is about calculation. May 22 '19 at 14:42
• @HansEngler You started it. May 22 '19 at 14:45

Hello and welcome to math.stackexchange.

First off, a narrative accompanying a numerical report (as in your post) is always good. Our XYZ grew from 40% to 45% because blablabla is better than Our XYZ grew from 40% to 45%. But a percentage change of a percentage can be downright misleading. Our XYZ percentage grew by 100% is misleading when in fact Our XYZ grew from 1 (in 50) to 2.

There are other ways to be misleading about percentages: 95% fat free is the same as contains 5% fat, but it sounds better and therefore is misleading.

In some cases it may be OK to report a percentage change of a rate, but then it should be accompanied by information about the actual rates: The frequency of work accidents fell from 3 per 100,000 person hours to 2 per 100,000 person hours, which is a 33% decline in the accident rate.

• I agree. In my chart, (which is in tableau) I have Year-over-Year percent change, the percent of female, and the total number of heads to provide all that context. I always pushed back to ask why it was "bad" and people just say it's misleading and inaccurate. But it's good to hear i'm not going insane. May 22 '19 at 16:35

Don't calculate the percentage change of the percentage, or the percentage change of the absolute, calculate the absolute change of the percentage.

So, if last year you had 40%, and this year you have 45%, the important number is 45% - 40% = 5%.

• Why is that? A change from $5\%$ to $10\%$ seems much more significant to me than a change from $50\% to$55\%\$ May 22 '19 at 14:28
• I suppose it's really a matter of personal taste, but if you're getting pushback on percents of percents then try this method. May 22 '19 at 14:55