Re: Probability vs. Confidence Levels
- From: "randovaro" <randovaro@xxxxxxxxx>
- Date: 20 Feb 2007 15:10:14 -0800
On Feb 21, 2:24 am, suare...@xxxxxxxxxxx wrote:
I'm looking at the work that a coworker is working on and I want to
see if someone can help me to understand where he went wrong or where
I want wrong in understanding.
Situation: He wants to determine what the confidence level is for
detecting faults inserted into a circuit card. He uses the
probability formula, but ties it to a confidence level.
For example: The current process calculates the percent detection as
being equal to the percentage of sampled faults that were
detected( e.g. - if 18 of 20 faults inserted were detected the percent
detection would be 18/20=.90 or 90%)
In reality, a program that detects 18 of 20 sampled faults has only a
32.3% probability (confidence level) of 90% fault detection. He used
the probability formula to get this number)
From what I understand, which isn't much, probability involves random
variables and confidence refers to a constant even if it is an unknown
constant.
What I think he should of said was, The probability of at least one
non-detect(success) is 67.7% given the true probability is 10%. This
in no way has anything at all to do with confidence levels.
I'm I understanding this correctly or can the above be stated as a
confidence level?
Any help would be greatly appreciated.
Sampled proportions can be expressed in terms of a confidence
interval. The online Engineering Statistics Handbook has this chapter
that may be of some use, suggesting a variation to the standard p_hat
+/- z_crit*S.E. approach:
http://www.itl.nist.gov/div898/handbook/prc/section2/prc241.htm
Applying their upper & lower limit formulae to your example
(p_hat=0.90, n=20) I get a 95% confidence interval of {0.97213,
0.69897}. This seems to be a better result than using the standard
approach that gives a 95% confidence interval of {1.03148, 0.76852}
(i.e. an upper limit that is impossible in your situation).
.
- References:
- Probability vs. Confidence Levels
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