# When should a percentage be written as a percentage and when should it be written x out of n?

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?

• 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
Aug 12, 2014 at 22:26
• @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
Aug 13, 2014 at 1:55
• 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
Aug 13, 2014 at 2:15
• @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
Aug 13, 2014 at 3:18
• 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
Aug 13, 2014 at 16:12