# Accuracy and confidence intervals onf measurements

1. May 8, 2012

### king_kong

Dear all,

I have a specification from a tool, which says, 80% of the reported measurements are within plus or minus 10% of the actual, at 95% confidence level.

I am trying to make sense out of this statement.

Assuming a normal distribution, please can someone tell me how to interpret these data?

I was interpreting that 95% of the measurements will be within the shaded area represented by a normal curve. The right hand side limit will be = actual+10% of actual, the left side limit will be actual-10% of actual. Where does 80% come from?

Thanks.

2. May 8, 2012

### Stephen Tashi

I think you are making a common misinterpretation of the meaning of "confidence interval". Its technical meaning doesn't give as much "confidence" as people tend to assume.

A confidence interval that is stated with specific numerical endpoints (like "56 plus or minus 14.32 ) doesn't guarantee anything about the probability of where future measurements will fall and if it is associated with estimating the parameter of a probability distribution (like the mean of the distribution), it doesn't guaranteee anything about the probability that the mean is in that interval. To get that type of guarantee, you need a "prediction interval" or a "credible interval". The current article on "Confidence Interval" in the Wikipedia mentions this.

Even if a confidence interval said something about the probability of future measurements, the actual frequency of an event doesn't have to match its probability. Probability and actual frequency are different things.

3. May 8, 2012

### king_kong

Hi Stephen,

So am I right in assuming that in the above case I mentioned, 80% represents the area under the normal curve, with plus 10% as the limit on the right and minus 10% as the limit on the left?

Thanks.

4. May 8, 2012

### Stephen Tashi

I can't tell what the report meant without knowing what it said. You haven't given a coherent summary of what it says; you only summarized one phrase from it. I don't even know what is being measured and whether a numerical confidence interval was given.

Not all statistical quantities follow a normal distribution.

5. May 9, 2012

### viraltux

Yeah, it is a bit confusing, what I interpret though is the following:

1. "80% of the reported measurements are within plus or minus 10% of the actual"
Given a measurement μ, the range (μ-0.1μ , μ+0.1μ) contains 80% of all possible measurements

2. "at 95% confidence level."
You don't know the actual statistics of your distribution, you can only estimate the parameters of a distribution, which means you do calculations within a confidence level. So I interpret that what they mean is that the range they give you has that confidence level.

Last edited: May 9, 2012