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In analytical chemistry, the detection limit, lower limit of detection, also termed LOD for limit of detection or analytical sensitivity (not to be confused with statistical sensitivity), is the lowest quantity of a substance that can be distinguished from the absence of that substance (a blank value) with a stated confidence level (generally 99%).
However, at 95% confidence, Q = 0.455 < 0.466 = Q table 0.167 is not considered an outlier. McBane [ 1 ] notes: Dixon provided related tests intended to search for more than one outlier, but they are much less frequently used than the r 10 or Q version that is intended to eliminate a single outlier.
The major weakness of MPN methods is the need for large numbers of replicates at the appropriate dilution to narrow the confidence intervals. However, it is a very important method for counts when the appropriate order of magnitude is unknown a priori and sampling is necessarily destructive.
For example, the 68% confidence limits for a one-dimensional variable belonging to a normal distribution are approximately ± one standard deviation σ from the central value x, which means that the region x ± σ will cover the true value in roughly 68% of cases. If the uncertainties are correlated then covariance must be taken into account ...
Because of the complex inter-relationship between analytical method, sample concentration, limits of detection and method precision, the management of Analytical Quality Control is undertaken using a statistical approach to determine whether the results obtained lie within an acceptable statistical envelope.
Classically, a confidence distribution is defined by inverting the upper limits of a series of lower-sided confidence intervals. [15] [16] [page needed] In particular, For every α in (0, 1), let (−∞, ξ n (α)] be a 100α% lower-side confidence interval for θ, where ξ n (α) = ξ n (X n,α) is continuous and increasing in α for each sample X n.
A 95% confidence level does not mean that 95% of the sample data lie within the confidence interval. A 95% confidence level does not mean that there is a 95% probability of the parameter estimate from a repeat of the experiment falling within the confidence interval computed from a given experiment. [25]
This is justified by considering the central limit theorem in the log domain (sometimes called Gibrat's law). The log-normal distribution is the maximum entropy probability distribution for a random variate X —for which the mean and variance of ln( X ) are specified.