We often take data at where I work. We’re engineers, and unfortunately we do not have a good grasp of statistical concepts. I vaguely remember taking a stats course as an undergrad in 1988…
When we perform multiple measurements on something we will calculate the standard deviation (s[sub]n-1[/sub]), multiply it by 2, and then proclaim, “We believe 95% of the population lies between ±2s of the average.”
We’ve been doing this for years. But over the past few weeks I have been doing some reading on confidence intervals and estimating population parameters. I am now thinking our simple “±2s” technique is wrong. Or at the very least a misapplication.
I want to improve the way we analyze our data. So here is where I am at:
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We take data at work. As an example, someone will measure ten resistance values for ten 500 ohm resistors. We usually don’t know anything about the population. Often our sample size is small (e.g. N = 10).
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I believe what we are trying to do is estimate the mean of the population and estimate the standard deviation of the population. Would you agree that this is the goal of taking measurements?
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Based on what I’ve read, it looks like we should be using the Student’s t-distribution to estimate the mean of the population. (Given a confidence value – example 95% – the Student’s t-distribution will calculate a confidence interval for the actual mean value.) Would you agree with this?
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When reading about Student’s t-distribution and confidence intervals, all of the articles I’ve read talk about estimating the mean of the population, not the standard deviation of the population. Yesterday I did some more google searching and discovered the Chi-Squared distribution can be used to estimate the standard deviation of the population from sampled data. Is this what we should be using?
Am I on the right track here?