<p>Two comments. First: the "frequentist" format appears to be easier to understand than the normed percentages, at least if information needs to be chained as in Bayesian reasoning. On the other hand, probably normed percentages are easier to understand if two fractions are to be compared. 
Second, I'd say that you should only use percentages if your sample is large enough. For example, "4 out of 5 respondents" amounts to 80% but the latter figure would probably suggests higher confidence than is warranted, given that it is really only a single respondent away from 3 out of 5 (60%)…</p>

CC BY-SA 3.0
2014-08-15T09:21:25.877Z
2014-08-15T09:21:25.877Z
jlc
<p>People perceive numbers, percentages and values in different ways depending on what it is and how it is presented.</p>

<p>I'm looking for research on when to communicate with an actual percentage and when it is perceived better to say <em>n out of x</em>.</p>

<p>For example in commercials we hear,</p>

<blockquote>
  <p>9 out of 10 dentists recommend</p>
</blockquote>

<p>We do not hear</p>

<blockquote>
  <p>90% of dentists recommend</p>
</blockquote>

<p>I'm currently working on some marketing materials and a study has found <code>4 out of 5</code> in one instance and <code>12 out of 19</code> in the other. I believe <code>4 out of 5</code> works better than <code>80%</code> but <code>Over 65%</code> sounds better than <code>12 out of 19</code>.</p>

<p>Does anyone have information about the way humans perceive percentages and how to determine the most favorable format?</p>

CC BY-SA 3.0
2014-08-12T22:26:15.623Z
I think it is important to clarify what objective is being achieved by the 'speaker' in this situation. It seems like you are asking about which format makes the proportion seem larger. If that's right, then you should probably clarify the question.
Josh
CC BY-SA 3.0
2014-08-13T01:55:53.633Z
@Josh What difference would it make? Its kinda like you're saying you can't explain how people perceive relative speed / motion without knowing if the objective is to feel fast or feel slow. If you understand how people perceive motion you should be able to make something appear fast or slow. I'm looking for a similar understanding regarding how people perceive percentages.
Ryan
CC BY-SA 3.0
2014-08-13T02:15:20.767Z
Let me rephrase. In your question it says: 'I'm looking for research on when to communicate with an actual percentage and when it is perceived better to say n out of x.' What does better mean in this case -- i.e. how could we operationalize 'better' in an experiment?
Josh
CC BY-SA 3.0
2014-08-13T03:18:27.950Z
@Josh based on your comment I believe my first comment still holds true. I'm not sure what relevance it has on the question which is the last sentence in my original post. If you want to get hung up on my use of the word better than I can edit it out. "I'm looking for research on how people perceive actual percentages vs n out of x." Now, if I'm missing something and you believe there is a fundamental difference in the answer if the word better is left in vs removed please comment. Otherwise I'm still not sure what difference any of this makes on the question.
Ryan
CC BY-SA 3.0
2014-08-13T16:12:22.500Z
I think @Josh's question is appropriate. When you say "most favorable format", do you mean (i) most likely to be remembered; (ii) sounds like a big number; (iii) sounds like a small number; (iv) reads better, etc. The "best" way of presenting information depends on your goal.
Eoin
CC BY-SA 3.0
2014-08-13T16:14:53.660Z
PS: If you want to make your proportion sound like a lot, [ratio bias](http://journal.sjdm.org/8210/jdm8210.html) is your friend here.
Eoin
CC BY-SA 3.0
2014-08-13T16:29:55.220Z
@Eoin if you leave ratio bias as an answer I'll certainly upvote it. Thanks for that information
Ryan
CC BY-SA 3.0
2014-08-13T19:14:44.437Z
I will tomorrow, but you still haven't answered our question, I'm afraid.
Eoin
<perception><communication>
When should a percentage be written as a percentage and when should it be written x out of n?
Ryan
# When should a percentage be written as a percentage and when should it be written x out of n?

(Asked by: username_0 on 2014-08-11)

People perceive numbers, percentages and values in different ways depending on what it is and how it is presented.

I'm looking for research on when to communicate with an actual percentage and when it is perceived better to say *n out of x*.

For example in commercials we hear,

> 9 out of 10 dentists recommend

We do not hear

> 90% of dentists recommend

I'm currently working on some marketing materials and a study has found `4 out of 5` in one instance and `12 out of 19` in the other. I believe `4 out of 5` works better than `80%` but `Over 65%` sounds better than `12 out of 19`.

Does anyone have information about the way humans perceive percentages and how to determine the most favorable format?

**Tags:** perception, communication

> **Comments:**
> **username_1**: I think it is important to clarify what objective is being achieved by the 'speaker' in this situation. It seems like you are asking about which format makes the proportion seem larger. If that's right, then you should probably clarify the question.  
> **username_0**: @username_1 What difference would it make? Its kinda like you're saying you can't explain how people perceive relative speed / motion without knowing if the objective is to feel fast or feel slow. If you understand how people perceive motion you should be able to make something appear fast or slow. I'm looking for a similar understanding regarding how people perceive percentages.  
> **username_1**: Let me rephrase. In your question it says: 'I'm looking for research on when to communicate with an actual percentage and when it is perceived better to say n out of x.' What does better mean in this case -- i.e. how could we operationalize 'better' in an experiment?  
> **username_0**: @username_1 based on your comment I believe my first comment still holds true. I'm not sure what relevance it has on the question which is the last sentence in my original post. If you want to get hung up on my use of the word better than I can edit it out. "I'm looking for research on how people perceive actual percentages vs n out of x." Now, if I'm missing something and you believe there is a fundamental difference in the answer if the word better is left in vs removed please comment. Otherwise I'm still not sure what difference any of this makes on the question.  
> **username_2**: I think @username_1's question is appropriate. When you say "most favorable format", do you mean (i) most likely to be remembered; (ii) sounds like a big number; (iii) sounds like a small number; (iv) reads better, etc. The "best" way of presenting information depends on your goal.  
> **username_2**: PS: If you want to make your proportion sound like a lot, [ratio bias](http://journal.sjdm.org/8210/jdm8210.html) is your friend here.  
> **username_0**: @username_2 if you leave ratio bias as an answer I'll certainly upvote it. Thanks for that information  
> **username_2**: I will tomorrow, but you still haven't answered our question, I'm afraid.  

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## 1 answers

### Answer by username_3 on 2014-08-15. Score: 1

Two comments. First: the "frequentist" format appears to be easier to understand than the normed percentages, at least if information needs to be chained as in Bayesian reasoning. On the other hand, probably normed percentages are easier to understand if two fractions are to be compared.
Second, I'd say that you should only use percentages if your sample is large enough. For example, "4 out of 5 respondents" amounts to 80% but the latter figure would probably suggests higher confidence than is warranted, given that it is really only a single respondent away from 3 out of 5 (60%)…


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