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My (basic) understanding of a 95% confidence interval is that it is the interval within which the sample mean would fall 95 times should you take 100 random samples from the population.

My query is this, I often see confidence intervals being used in situations that I would call descriptive, rather than inferential. Is this a proper and correct way of using them?

For instance, if I measure every single washer in my factory, and plot the mean with the 95% confidence interval, what am I saying? If I retake the 'sample' 100 times, I'll get the same mean 100 times. But I'd argue it's useful to have a confidence interval because it serves a descriptive function in terms of sample size and spread of the data.

Let's say I measure all the washers in my factory every month and want to use confidence intervals to see if there is a significant difference between the mean diameter between this month and the previous month. Is this concept flawed because I am looking at populations rather than samples? If I am 100% certain of the mean each month then do questions of significance cease to matter?

I'm aware this may be a stupid question, links to suitable reading material accepted gratefully!

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    $\begingroup$ Not stupid. There is some fuzziness in many definitions of sample and population. The idea that the population is definite, concrete and a finite set seems natural for many problems (all the elephants now in some area of land), while the idea that the population is what might have happened seems natural for many problems (all the coin tosses you might make with a coin). You get to decide what the population is best thought to be, depending on your problem. $\endgroup$ – Nick Cox May 28 '13 at 14:59
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    $\begingroup$ You run into trouble at the very first line, because it does not correctly characterize a confidence interval. Please check out this related thread before continuing. $\endgroup$ – whuber May 28 '13 at 15:00
  • $\begingroup$ Related - stats.stackexchange.com/questions/2628/… $\endgroup$ – Peter Ellis May 29 '13 at 5:29
  • $\begingroup$ Thank you all! Whuber, I can see the definition I've given isn't quite right, the following is what I was trying to say (from Hinkley & Cox via Wikipedia): "Were this procedure to be repeated on multiple samples, the calculated confidence interval (which would differ for each sample) would encompass the true population parameter 90% of the time." $\endgroup$ – Tumbledown May 30 '13 at 12:26
  • $\begingroup$ I think this line from stats.stackexchange.com/a/2630/13526 addresses my point: "...if you're really positive you have the whole population, there's even no need to go into statistics. Then you know exactly how big the difference is, and there is no reason whatsoever to test it any more. A classical mistake is using statistical significance as "relevant" significance. If you sampled the population, the difference is what it is." $\endgroup$ – Tumbledown May 30 '13 at 12:29

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