# Wording for comparing two percentages

I am trying to figure out how to make a correct statement with two values:

X = 59.8% Y = 26.7%

Is this correct?

X has 44.6% more apples than Y

If I wanted to use the word "margin" what does that imply?

Can I say

X has more apples than Y by a margin of 44.6%

Also, is there a cheat sheet for a non-stats person that you can point to? I tried googling but I'm not getting the words right. Thanks!

• Both statements are mathematically incorrect and evidently ambiguous. Either one could be interpreted as meaning $X=(100 + 44.6)/100\times Y.$ Why don't you simply state the truth, such as "$X-Y$ is $33.1\%$"? – whuber Apr 24 '18 at 14:58
• How did you calculate your X and Y in the first place ? Do they represent the proportion of apples in two baskets ? – AshOfFire Apr 24 '18 at 14:59
• There was one basket of apples shared between 5 people. I am supposed to compare the apples for person X and Y above. But it has to be in sentence format, not calculation. Like as though it was a feature story in the news. Apologies as I am not a stats person! – tiffylou Apr 24 '18 at 15:04

## 3 Answers

In your specific case, as mentioned by whuber, both statements are incorrect.

First let me explain how they are incorrect using your example with simple figures.

• The basket contained 100 apples to be shared between 5 people
• X took 60% of the basket (= 60 apples)
• Y took 27% of the basket (= 27 apples)
• The remainder (13 apples) was split between the remaining folks

In this case, the first sentence

X has Z% more apples than Y

Means that X has Z more apples than Y (33) relatively to the number of apples possessed by Y (27). What you are looking for is a representation of the exceeding number of apples in terms of percentage.

Hence, Z should be calculated this way. $$Z = 100*\frac{(X-Y)}{Y} = 100*\frac{33}{27} \sim 122\%$$

Because $33 = 27*122\%$

Now for the second sentence

X has more apples than Y by a margin of Z%

Margin is inappropriate in this sentence. Leaving aside that it is quite a "business-oriented" term (e.g. gross margin), margin represents an idea of proportion, so once again, with a division operated somewhere. While it could represent the calculation in the first sentence, I would strongly recommend you to avoid using this term.

So what is the appropriate wording ?

I frankly don't know how did you get the 44.6%. $X - Y = 33.1\%$, so at most, you can say.

The difference between the share of X and Y represents 33.1% of the total share/basket.

• Playing around with the numbers, I found 26.7/59.8 = .446488, so presumably this is where the OP got 44.6% – Acccumulation Apr 24 '18 at 15:49

(1) X is 33.1 percentage points larger than Y.

(2) If you take this difference and divide it by X, you get 33.1/26.7 = 1.2397, so X is 124% more than Y.

(3) If you divide X by Y, you get 2.2397, so X is 224% of Y.

(4) Note that the number I got in (3) is 100% more than (2). This is because X is equal to Y plus the difference between X and Y. Since Y is equal to 100% of Y, we add 100% when going from "X is [percentage] larger than Y" to "X is [percentage] of Y.

(5) A lot of people in this sort of situation will say "X is 224% more than Y", but that is incorrect.

(6) If you divide Y by X, you get 44.6%. You seem to think that the correct statement of this is "X is 44.6% more than Y". But the actual correct statement is "Y is 44.6% of X".

(7) If X were 40%, then dividing Y by X would get 66.75%. It doesn't make sense that making X smaller increases the percentage by which X is larger than Y.

I have this problem all the time with clients/colleagues! The real answer is whatever works to make sure that it is understood. Possibly the easiest solution to that is to show your working.

I would go with "33.1 percentage points larger."
but I might say, for greater clarity:
"33.1 percentage points (that is 59.8%-26.7%) larger."

I do have one client who simply refuses to think that way. So for him, I would say
"124% larger - that is (59.8%/26.7%)."
or "larger by a factor of 124% - that is (59.8%/26.7%)." (this is close to the OP's idea of a margin)
This sounds clumsy, but is the equivalent of "twice as big" in the simple case of 40% vs 20%, say.