# minimum total N (value for denominator) when calculating a percentage

I am presenting a lot of percentages in a report. I understand that when the denominator is a small number (say 2 people) percentages should be avoided altogether - e.g. presenting 1 out of 2 people as 50%. At one point a Statistics Professor told me that one should not show percentages when the total N is less than 50.

I'm interested in thoughts about the minimum number (and any sources, if there are any). I understand it's somewhat arbitrary. However, I need to specify something.

For what purpose are you giving this list of percentages? What do you want your readers to get from it?

I know of no rule for this. For some purposes 50 might be a reasonable, but quite arbitrary, number. How many percentages will you show altogether? And how many with denominators below 50? 100? 200? My personal rule might be more like 200.

You would probably like to have a large majority of the entries in your table to appear in the same format. But you don't want to mislead.

To many people "81%" might give an impression "low 80%s" and they might feel deceived to find out that's actually just 13 out of 16---which, under random sampling, could imply a 95% Confidence Interval of $$(.58, .94).$$

By contrast, if "81%" is from 260 out of 320, then my similarly "implied" CI would be $$(.77, .85).$$ I grant that the average reader of your chart is not going to do the math to get a CI, but you might want to consider what impression your percentages are giving.

Note: For illustration, I'm using Jeffreys CIs for binomial proportions, computed in R as follows:

qbeta(c(.025,.975), 13.5, 16-13+.5)
[1] 0.5792148 0.9441870

qbeta(c(.025,.975), 260.5, 320-260.5)
[1] 0.7697719 0.8547530

• TY! The percentages are success rates of applications for different groups. For example, (made up data) those with Bachelor's degrees had a 20% success rate, Masters had 30%, PhD had 50% success rate. So the purpose of calculating is to compare the success rates of different categories, but with a high enough total N that it is reasonable to make this comparison and reasonable to calculate a success rate for the specific group to begin with. With 200 or 100 quite a lot of the data would not be shown, but if it is unreliable to show the data with an N of 50 then I would rather do 100 or 200. Aug 2 at 20:41
• For a statistical audience you might use two styles of entries: For 260 in 320 maybe "$81.1\% \pm 4\%$" and for 13 in 16, "81% (13 / 16)" or just "13 in 16." with a footnote that the cut-off between styles is 100 or 200 or whatever and that "$\pm$" indicates 95% CI. Aug 7 at 0:02
• Thank you Bruce! This is very helpful. Aug 8 at 19:00