Proportion Uncertainty

The amount of uncertainty in a proportion is not intuitive.  Use this tool to help understand how much uncertainty exists in a calculated proportion.  In other words, how sure are you that the proportion is that number and not higher or lower?  The amount of uncertainty is affected by both sample size and the value of the proportion, i.e. its position within the distribution.  For example, values towards the extremes (closer to 0% or 100%) have less uncertainty than those in the middle close to 50%.

1. Set the alpha value to the percentage of time that you are willing to accept that the calculated value randomly occurred (the value is wrong).   Alpha is commonly set to 0.05 (5%). However this is simply convention and not appropriate for all situations.

2. Set the sample size to equal the denominator for your proportion.  For example, if you had 100 calves and 30 were sick, you would calculate a morbidity of 30/100 or 30%.  The sample size in this case is 100.  

3. Set the count value to equal the numerator in your proportion. For the example above the count value is 30.

4. Look at the X axis and find the value for your count, and draw a straight line up from your count value (the red line) .  Find the uncertainty where the red line intersects the black dots (dots appear as a line if your sample size is large).   For this example, the uncertainty is 9%.  This means in a pen of 100 calves where 30 are sick, we are 95% (1-alpha) certain that the true morbidity is between 21% and 39%.