The Art of Statistics: Learning from Data

by David Spiegelhalter

The standard deviation of this Poisson distribution is the square root of m, written √m, which is also the standard error of our estimate. This would allow us to create a confidence interval, if only we knew m. But we don’t (that’s the whole point of the exercise). Consider the 2014–2015 period, when there were 497 homicides, which is our estimate for the underlying rate m that year. We can use this estimate for m to estimate the standard error √m as √497 = 22.3. This gives a margin of error of ± 1.96 × 22.3 = ± 43.7. So we can finally get to our approximate 95% interval for m as 497 ± 43.7 = 453.3 to 540.7. Since 95% confidence intervals are often assumed to be plus or minus 1.96 standard errors, this means that we can be 95% confident that during this period the true underlying homicide rate lies between 453 and 541 per year.

Sd is 1.96 times square root of mean (for 95% confidence interval)