The errors that are solely attributed to sampling, specifically in the instance of heterogeneous solids, usually give rise to the most important source of uncertainty in carrying out analysis of pharma-ceutical substances.

**SAMPLING STATISTICS**

The errors that are solely attributed to sampling,
specifically in the instance of heterogeneous solids, usually give rise to the
most important source of uncertainty in carrying out analysis of
pharma-ceutical substances.

Thus, the overall standard deviation, *s*_{T}, *i.e.*, the total error is given by the following expression :

......................(i)

where, S_{S} = Standard deviation of the sampling procedure (*i.e.*, the sampling error), and S_{A}
= Standard deviation of the analytical procedures (*i.e.*, the analytical error).

The Eq. (*i*) may
also be expressed as :

where V_{S} = Variance due to sampling, and

V_{A} = Variance due to analytical method(s).

The individual determination of V_{S} and V_{A}
may be accomplished by using the method described under variance.

** Example : **If the sampling error is ±
2.8% and the analytical errors by two different analysts come out

From Eqs. (*a*)
and (*b*) it is quite evident that the
actual contribution of the analytical error *viz*.,
± 0.9% and ± 0.1%, to the total error (S _{T}) is more or less
insignificant.

**Note :** Youden* (1967) suggested that
once the analytical error is reduced to 1/3rd of the sampling error, further
reduction of the former is not required anymore.

In order to have a meaningful ‘sampling plan’ the
following points should be taken into consideration**, namely :

·
Number of samples to be taken :

·
Size of the sample, and

·
Should separate samples be analysed or should a sample
made up of two or more increments (*i.e.*,
composite sample) be prepared.

A container-load of
Paracetamol (10 MT) arrives at a raw-material stores** **and the composition of the bulk material is unknown, it will be a
sensible and logical practice to carry out first and foremost a preliminary
investigation by collecting a large number of samples and assaying the analyte
of interest.

Thus, the confidence limits are given by the following
expression :

............................(c)

where, µ = Estimate of the true mean,

* _{ }*x’ = Mean of the analytical
results,

*t *= Parameter depending upon the
number of degrees of freedom (ν) and the confidence level* *required,

S_{S} = Standard deviation of individual sample,
and

*n *= Number of samples taken.

** Example : **The estimate in variability of
Paracetamol in a consignment of 10 MT, based on 20

The 0.5% value, in reality, represents the difference
between the sample mean *x* and the
actual value µ. If this value is designated by E, then Eq. (*c*) may be expressed as :

From the tables [Percentage Points of the *t*-Distribution] the value of *t* for (*n* – 1 ), 19 degrees of freedom at 95% confidence level is 2.09.

From this test it has been
established that at least 34 samples are required if the specifi-cations
provided in the above cited example are to be fulfilled adequately.

Another major problem
associated with the sampling process is that of the sample size.

In fact, the sample size withdrawn from a heterogeneous
material is solely guided by two factors, namely :

(*a*) Variation
in particle size, and

(*b*) Precision
required in the results of the analysis.

The sampling variance, V, is inversely proportional to
the actual number of sampling increments (*n*)
and may be expressed as :

where, *k* = Constant entirely dependent on the
size of the increment and variation within the bulk material.

The following points with regard to sampling may be
observed carefully :

·
A major source of error in sampling may be incorporated
from the actual process of taking increments from the bulk material,

·
The accuracy of the sample is determined by its total
size (based on Random Sampling Theory), and

·
The number of increments taken shall directly influence
the sampling accuracy provided the bulk material comprises of varying particle
sizes.

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Pharmaceutical Drug Analysis: Errors In Pharmaceutical Analysis and Statistical Validation : Sampling Statistics |

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