Cosmic Ray Detector - Data Center
Calculating Statistical Uncertainties
For counting experiments, the expected statistical uncertainty can be calculated from what is known as the Poisson Distribution. For practical purposes it is usually okay to estimate the statistical uncertainty of a count as the square root of the count. To calculate the statistical uncertainty in a count rate, you'll need to divide the square root of the count by the time interval.
However, when the square root of the number of counts is small, in particular zero, this estimate is not valid. The uncertainty in a zero count is, in fact, one -- but only in the positive direction (you can't have a negative count). The uncertainty in a count of one is slightly more than one in the positive direction and slightly less than one in the negative direction. But in many pictures you will see that the error bar is only approximated: for a zero count we use plus or minus one, for all other numbers we use the square root.
