Accuracy and confidence intervals onf measurements

[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?

I am totally confused. Please help.

Thanks.

 

[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.

 

[king_kong]

Hi Stephen,

Thanks for your reply.
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.

 

[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.

 

[viraltux]

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?

I am totally confused. Please help.

Thanks.

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.