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Science Forum Index » Statistics - Education Forum » Probability vs. Confidence Levels
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| Guest |
 Posted: Tue Feb 20, 2007 12:24 pm |
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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)
Quote: 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. |
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| randovaro |
| Posted: Tue Feb 20, 2007 7:10 pm |
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Guest
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On Feb 21, 2:24 am, suare...@hotmail.com wrote:
Quote: 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). |
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| David Winsemius |
| Posted: Wed Feb 21, 2007 11:18 pm |
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Guest
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suarez_k@hotmail.com wrote in news:1171988696.738901.216950
@k78g2000cwa.googlegroups.com:
Quote: 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.
I get the sense that ideas regarding confidence levels and ideas
regarding the statistical power of tests are being confused. The
confidence level is the probability that an interval (for example 1.96
sample std deviations around a sample mean) includes the unknown
population parameter (say the population mean) of interest. That may be
the "constant" you are referring to below.
Quote: 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)
The power of a test (equal to one minus the probability of incorrectly
accepting the null hypothesis when it isn't true) is the probability that
the null hypothesis will be rejected when the population parameter is
different than hypothesized. Say you want to know mu= true proportion of
errors. Power increases with larger samples and with greater difference
between the H0 value of mu (say 0.9) and the true value of mu. You are
not going to have very much power to detect a difference of 0.1 with a
sample size of 20.
Quote: 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.
Not intending to confuse you, but the confidence intervals are random
intervals when they are built from sample estimates.
Quote: 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 wish I understood what you were trying to say in those sentences.
Quote: I'm I understanding this correctly or can the above be stated as a
confidence level?
Any help would be greatly appreciated.
I am not sure. Sometimes it takes a bit of back_and_forth before ideas
get clarified.
--
David Winsemius |
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