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From figure 2.1-4B it is also obvious that a standart deviation calculated from three

values (df=2) (unfortunately not an exception in validation literature) is rather

meaningless as ơ can be expected up to 4.4 fold of the calculated standard

deviation! However, if several sets of data can be combined (pooled), the overall

degress of freedom and thus the reliability are increased. In succh a case, only the

overall standard deviation should be reported. A prerequisite for such pooling of data

is that all data sets must have similiar ơ  (if means are looked at, they must also

have the same true mean; for verification, see the discussion on precision level in

section 2.1.2). interestingly, a confidence interval is mentioned in the ICH guideline

(althought it is not clearly stated whether with respect to the standard deviation on

the mean) 1b

However, the author is not aware of any publiation on pharmaceutical validation

which reports it. Following the standard approach with six or more determinations for

a standard deviation, the confidence interval will not provide much additional

information, but the benefit could be to cause people to hesisate before reporting

standard deviations from three determinations only.

Significance tests

Confidence intervals are also the basis of statistical tests. In the case of significance

tests, the test hypothesis (H0) assumes, for example, no difference (zero) between

two mean results. This is fulfilled (or strictly, the hypothesis can not be rejected),

when the two confidence intervals overlap. However, as the confidence intervals

become tighter with increasing number of determinations, (theoretically) any

difference- however small- can be shown to be significant. For example, assuming a

standard deviation of 0,5 . a difference of 0.5 is significant with nine determinstions,

but even a difference of 0.1 will become significant when there are 200 values. Of

course, this is (usually) not of (practical) interest ( see accuracy, section 2.3.1)

Rebust parameters

The above-described parameters are based on the assumption of normal

distribution. If this prerequisite is not fulfilled, or disturbed, for example by a singledeviating result (outlier), the application of rebust parameters that are not based on

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specific assumptions. The analogue to the arithmetic mean is the median. The

middle value in an ordered sequence of results. A comparison between mean and

median may provide information about a possible disturbance in the data. However,

it is often a very complex matter to estimate confidence intervals or variabilities for

rebust parameters.

 Another alternative to estimate description parameters of any distribution is the

(thousand fold) repeated calculation from an experimental set of data (re-sampling)

to achieve a simulated distribution, the so-called bootstrap, or the estimination of

variability from the noise of a single measurement using a probabbility theory named

the ‘function of mutual information’. However, these techniques are beyond the

scope of this book, and the reader is referred to spesialised literature.

Precision levels

Regarding an analytical procedure, each of the steps will contribute to the overall

variability. Therefore, the overall uncertainty can be estimated by summing up each

of contributing variabilities, the so-called bottom-up approach. However, this

approach is quite complex because each and every step has not only to be taken

into account, but also its variability must be known or determined.

 Alternatively, the othee approach (top-down) usually applied in pharmaceutical

analysis combines groups of contributions obtained experimentally the precision

levels. Such a holistic approach is easier to apply, bacause each of the individual

contributinng.