Interpreting Results 
Definitions 


Index
This page contains the following sections:
You can go to a section by selecting the link. 
Accuracy and Precision
ERNDIM, reference AB02, defines accuracy as:
and precision as:
ERNDIM, reference AB02, illustrates the difference between accuracy and precision:
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Confidence Interval (CI)
Wolfram Mathworld, reference AB30, defines a confidence interval in general terms:
A confidence interval is an interval in which a measurement or trial falls corresponding to a given probability. 
On this site, I define confidence intervals in terms of the percentage of results of tests, on identical samples, that would be expected to fall within that interval.
The 95% confidence interval is used by pathologists to define significance of differences in results. A result that is outside the 95% confidence interval is considered to be significantly different.
This diagram shows the 95% confidence interval for a normally distributed set of results:
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Error
The term error has two possible meanings when I use it on this site; the intended meaning must be taken from the context in which it is used:
Analytical
I use the word error in a strict analytical sense if it is used in the expression significant error or very significant error.
Error is the difference between a measured value and the true value, or between a measured value and the mean, or between two measured values.
All measurements contain errors; what is important is whether or not the error is within normal limits, described as the significance of the error.
General
When I use the word error by itself, then I mean a mistake, blunder or a result that is outside the normal error limits.
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Error, ab
I use the term ab error to mean the difference between two reported results from a split sample, either from one lab or from two different labs.
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Error, xu
I use the term xu error to mean the difference between a reported result from one lab, and the mean reported value for that sample.
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Error, significant
In chemical pathology, an error is considered to be significant if the result falls outside the 95% confidence interval:
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Error, very significant
On this site, I define an error as very significant if the result falls outside the 99.0% confidence interval:
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Probability, pab
I use the term pab to mean the probability that the difference between two results will be greater than the number of standard deviations (# SD) difference measured. Refer to Method for details of derivation of pab.
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Probability, pxu
I use the term pxu to mean the probability that the difference between any result and the mean will be greater than the number of standard deviations (# SD) difference measured. Refer to Method for details of derivation of pxu.
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Standard Deviation (SD)
Wolfram Mathworld, reference AB30, defines the standard deviation in mathematical terms:
The standard deviation of a probability distribution is defined as the square root of the variance 
The standard deviation is a measure of the spread of a set results from identical samples; the smaller the SD, the less spread are the results, and the smaller is the imprecision.
The imprecision of a result is quoted as the size of one standard deviation: 1SD = N units. By mathematical means, it is possible to relate the quoted size of 1SD and the width of the confidence interval. It is therefore possible to determine the significance of any error, or difference, between a result and the mean (xu error) , or between any two results (ab error). Refer to Method for details of derivation of the significance, in terms of probability of occurrence of the error..
The following table shows the relationship between commonly used confidence intervals, probability of occurrence of the error and number of standard deviations of error:
 
CI 
p 
CI 
p 
CI 
p 
 
95% 
<0.05 
99.0% 
<0.01 
99.9% 
<0.001 
x  u 
1.96 
2.58 
3.29 
a  b 
2.77 
3.64 
4.65 
There is a probability calculator available in Sheet A21 in the Excel file, Series 1, which may be downloaded under Evidence.
This diagram shows the 95% confidence interval, in terms of number of standard deviations, for the xu error:
This diagram shows the 95% confidence interval, in terms of number of standard deviations, for the ab error:
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