Quizzes & Puzzles1 min ago
Confidence intervals - of one value
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
Answers
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For more on marking an answer as the "Best Answer", please visit our FAQ.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).
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