Statistical accuracy
Due to the sampling technique used, accurate results are obtained when the number of samples is significant, such as 10,000 samples. Therefore, not only should the standard deviation of a measurement be considered when analyzing report data, but the number of samples counts should also be considered.
The sample counts produced are shown at the top of the report.
The measures reported by CMF MONITOR are a percentage (P) of the total number of samples taken (N) for which the measured conditions were true.
Statistical measures (with errors that are normally distributed) are usually expressed as a percentage (P) plus or minus a confidence interval (E) with a confidence level of (C).
- The confidence interval is an estimate of the maximum error from the true value of P.
- The confidence level is the probability that the difference between P and the true value is less than (E).
To calculate the statistical error, see Figure 1 and locate the following data:
- number of samples taken by the Extractor (the N-axis)
- desired confidence level (one of the plotted diagonal lines)
The intersection point yields the uncorrected value for the confidence interval (E).
Figure 1. Confidence levels for P=50%
The true confidence interval is the product of the correction factor multiplied by the value of (E) determined above.
For example, if a measure reported by the Analyzer is 10%, the desired confidence level is 95%; if the Extractor took 5000 samples, the uncorrected confidence interval is plus or minus 1.5%. Since the correction factor for a 10% measure is 0.64, then the corrected confidence interval is 0.64 x 1.5% = 0.96%.
In other words, the analyst can expect only 1 chance in 20 (95% confidence level) that the actual value (reported as 10%) was less than 9.04% or greater than 10.96%.
Figure 2. Correction factors for confidence intervals
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