Confidence intervals - of one value

[Peter Pedant]

 

If you have a data set, one can calculate the confidence interval for the set.

but you can also do it for a single data point. If the datum is n say, then the CI is something like 3n

Does anyone know a reference for this ? I am not very good at statistics

[Brugel]

The answer to the question depends on whether or not you know the standard deviation of the population from which the sample was taken.

A confidence interval is two numbers. One is given by working out x - ks/sqr(n) and the other by x + ks/sqr(n) ( sqr means square root). x is the mean of the data set, n is the size of the data set and k is a constant (for example, if you want a 95% confidence interval then k is 1.96). 

Now s is either the standard deviation of the data set or the standard deviation of the population. If it is the former- in other words, if you actually have to work out s using the data set- then you cannot get a confidence interval using only one point. This is because the formula only works if n is relatively large (say, at least 30).

You can, however, use the formula if you actually know s for the population. However, it is extremely unlikely that you would ever be in a situation where the population standard deviation were known but the population mean were not. So even though you could get a confidence interval here, it would be a somewhat contrived situation (although one that might come up in a text book).

[Peter Pedant]

Thank you Bruegel - I was wondering if there were any statistical artistes out there