# How useful is a confidence interval formed using the sample variance

A 95% confidence interval under Neyman-Pearson is defined as the interval upon which if we took many samples of size n from the population, 95% of the intervals formed around the sample means would contain the population mean.

In the circumstance where you have knowledge of the population variance, this interval will have the same range for each sample, assuming each sample is of size n.

However, in the circumstance where you don't have knowledge of the population variance, each sample of size n will use its sample standard deviation and therefore the interval range will vary across the samples as a result.

With this in mind, I am struggling to see the material benefit, as a part of a piece of analysis, to provide a confidence interval when the population variance isn't known. It feels as though I am presenting a metric which a) requires the reader to consider an almost-abstract number of samples, b) has a range which is going to vary across those samples.

Are there any benefits to presenting a confidence interval formed using the sample variance?

Edit - to clarify - I am mainly focusing on presenting to non-statistical audiences, such as decision makers within an organisation.

• In practice, you never know population variance. So when you are asking if there are any benefits to presenting CIs constructed using sample variance -- benefits as compared to what? Commented Feb 27, 2015 at 18:10
• It is a good point - perhaps I am asking the marginal benefit of providing a confidence interval built on the sample variance alongside other metrics/analysis, as opposed to only providing the other metrics/analysis. Does it genuinely enhance the ability of an individual to make decisions? I do appreciate this may move into the territory of opinion however. Commented Feb 27, 2015 at 18:18
• But what other "metrics/analysis" are you referring to? It's important. Perhaps you do have some metrics that convey similar information to CI. But perhaps you don't. One metric is the sample mean itself. What else? Commented Feb 27, 2015 at 18:31
• I think you mean Neyman-Pearson? Commented Feb 27, 2015 at 20:11
• @StatsStudent I agree, at the very least, certainly Neyman that should be credited with work on confidence intervals ... I've edited NickB's question to correct "Neyton" to "Neyman". Commented Feb 28, 2015 at 1:00