Transcript Standard deviation

Professor Abdul Muttaleb Jaber
Faculty of Pharmacy
Office: Room # 512 (Faculty of
Pharmacy)
Tel:
E-mail: [email protected]
Office hours: M & W 10-12 am
Chapter 1
Control of the quality of analytical methods
Uncertainty in measurements
Significant figures and calculations
Control of errors in analysis
Fundamental statistical terms
Validation of analytical procedures
Standard operating procedure (SOP)
Reporting of results
Some terms used in the control of
analytical procedures
Basic calculations in pharmaceutical
analysis
Electronic
Analytical
Balance
Uncertainty in Measurement
Exact: numbers with defined values
– Examples: counting numbers, conversion
factors based on definitions
Inexact: numbers obtained by any
method other than counting
– Examples: measured values in the
laboratory
Copyright McGraw-Hill 2009
4
A measurement always has
some degree of uncertainty.
Uncertainty has to be indicated in any
measurement.
Any measurement has certain digits and
one uncertain digit.
A digit that must be estimated is
called uncertain.
Uncertainty in Measurements
Significant Figures
– Used to express the uncertainty of
inexact numbers obtained by
measurement
– The last digit in a measured value is an
uncertain digit - estimated
The number of certain digits + the
uncertain digit is called number of
significant figures.
Rules for Counting Significant Figures
1.
2.
3.
Nonzero integers
Zeros
 leading zeros
 captive zeros
 trailing zeros
Exact numbers
Rules for Counting Significant Figures
Nonzero integers always count as significant
figures.
3456 has
4 sig figs.
Zeros
Leading zeros do not count as significant figures.
(Zeros before the nonzero digit)
0.0486 has
3 sig figs.
0.0003 has
one significant figure
Captive (sandwiched) zeros always count as
significant figures.
16.07 has
4 sig figs.
Zeros
Trailing zeros are significant only
if the number contains a decimal point.
9.300 has
4 sig figs.
Exact numbers have an infinite
number of significant figures.
1 inch = 2.54 cm, exactly
• Zeros at the end of a number before a
decimal place are ambiguous
10,300 g has: 3 or 4 or 5??
Practice
Determine the number of significant figures in
each of the following.
345.5 cm
4 significant figures
0.0058 g
2 significant figures
1205 m
4 significant figures
250 mL
2 significant figures
250.00 mL
5 significant figures
Significant Figures in Calculations
A calculated answer cannot be more precise than the
measuring tool.
A calculated answer must match the least precise
measurement.
Significant figures are needed for final answers from
1) adding or subtracting
2) multiplying or dividing
Rules for Significant Figures in Mathematical Operation
Multiplication and Division: # sig figs in the
result equals the number in the least precise
measurement used in the calculation.
6.38  2.0 =
12.76  13 (2 sig figs)
Rules for Significant Figures in Mathematical Operation
Addition and Subtraction: # sig figs in the result
equals the number of decimal places in the least
precise
measurement.
Answer cannot have more digits to the right of the
decimal than any of original numbers
6.8 + 11.934 =
22.4896 
22.5 (3 sig figs)
Scientific Notation
•Addition and Subtraction
(6.6 x
10-8)
(3.42 x
+ (4.0 x
-5
10 )
10-9)
– (2.5 x
=
-6
10 )
7.0 x 10-8
= 3.17 x 10-5
Multiple computations
2.54 X 0.0028
0.0105 X 0.060
1) 11.3
2) 11
=
3) 0.041
Continuous calculator operation =
2.54 x 0.0028
 0.0105 
0.060 = 11
 Here, the mathematical operation requires
that we apply the addition/ subtraction rule
first, then apply the multiplication/division
rule.
= 12
Exact numbers
– Do not limit answer because exact
numbers have an infinite number of
significant figures
– Example:
A tablet of a drug has a mass of 2.5 g. If
we have three such tablets, the total
mass is
3 x 2.5 g = 7.5 g
– In this case, 3 is an exact number and
does not limit the number of significant
figures in the result.
To get the correct number of
significant digits you need to round
numbers
Rounding rules
– If the number is less than 5 round
“down”.
– If the number is 5 or greater round
“up”.
Fundamental statistical terms
• Central value = Arithmetic mean = average
 Xi
• Arithmetic Mean = Mean or average;
X 
N
• Median: Modern numerical value
• 20.6
20.1
20.7
20.0
20.4
• Accuracy: Nearness of the experimental value to the
true value
•
– Absolute Error = Xi - 
or X - 
(+ve or –ve)
– Relative mean error = Absolute error/
– Percent relative error = Relative error X 100
•
Accuracy and precision
– Two ways to judge the quality of a
set of measured numbers
– Accuracy: how close a
measurement is to the true or
accepted value
– Precision: how closely
measurements of the same thing
are to one another
Precision and Accuracy
Relationship between accuracy and
precision
Inaccurate &
imprecise
Inaccurate but
precise
25
Accurate but
imprecise
Accurate and Precise
• Central value = Arithmetic mean = average
• Arithmetic Mean = Mean or average; X  Xi
N
• Median: Modern numerical value
• 20.6
20.1
20.7
20.0
• Ways to express the accuracy of data
•
– Absolute Error = Xi - 
or - 
(+ve or –ve)
– Relative mean error = Absolute error/
– Percent relative error = Relative error X 100
20.4
Ways to express the precision of data
• Average Deviation: d 
• Standard deviation: s =
Σ Xi  X
n
 (Xi - X)
2
n -1
• Relative average deviation =
d
X
• Relative standard deviation =
• RSD may be called: Coefficient of variation
s
X
Percent relative standard deviation = %RSD
s
=
X 100
X
Range = Absolute difference between the
largest and the smallest values
Range = w = Xhighest - Xlowest
Significance of standard deviation
• The standard deviation, s,
measures how closely the
data are clustered about the
mean.
• The significance of s is that
the smaller the standard
deviation, the more closely
the data are clustered about
the mean.
• A set of light bulbs having a
small standard deviation in
lifetime must be more
uniformly manufactured than
a set with a large standard
deviation
Example
Calculate the average and the standard deviation for the following
four measurements: 821, 783, 834, and 855 hours. The average is
To avoid round-off errors, we generally retain one more significant
figure for the average and the standard deviation than was present in
the original data. The standard deviation
is
X
The average and the standard deviation should both end at the
same decimal place. For X = 823.2, the value s = 30.3 is
reasonable, but s = 30.34 is not.
Types of Errors
Determinate Errors or Systematic Errors:
– They can be determined and eliminated
– Those originate from a fixed cause.
– They may be either high or low every time the
analysis is run
• Sources: Methods, Equipment and materials,
Personal judgment, Mistakes
• Random (indeterminate errors)
– They originate from indeterminate processes.
– They produce a value that sometimes is high and
sometimes is low.
– Ex: Flipping a coin!!
Characteristics of indeterminate errors
 They cannot be controlled
 They can be evaluated statistically to
supply information about the reliability of
the data
 They vary in a nonreproducible way and
never the same except by chance
• In mathematical description of Gaussian
distribution, the scatter or precision is
represented by a standard deviation if indefinitely
large data set,  ( the term s is used for a small
data set, for a finite number of measurements)
•  varies according to data but 68.3% of the curve
area always lies within 1  of the mean
• 95.4% of the curve area always lies within 2  of
the mean
• 99.7% of the curve area always lies within 3  of
the mean
• A large  means a broad error curve, a small value
means a small narrow curve.
• Number of degrees of freedom always equals to
the number of measurements –1; (n-1).
Linearity (Fitting the Least Square Line)
• Statistics provides a mathematical relationship
that enables calculating the slope and intercept of
the best straight line
• The equation for a straight line is
y = a + bx
a = intercept; b = slope
• It is assumed that the values of x are almost free
of error
• The failure of the data points to fall exactly on the
liens assumed to be caused entirely by the
intermediate errors in the instrument readings, y
• The sum of the squares of the deviations, Q, of
the actual instrument readings from the correct
values are minimized (made minimum) by
adjusting the values of the slope, b and the
intercept, a
• If a linear relationship between x and y does exist,
this puts the line through the best estimates of
the true mean values.
• a =y
 bX
;
X and y
are the means of x’s
and y’s
[( X  X )( y  y )

• b=
(X  X )
i
i
2
i
• Once the best slope and intercept have been
determined, a line with those values can be put on
the graph along with the original data points to
complete the plot
Example
• Many instrumental methods of analysis utilize calibration plots
of measured signal versus concentration. Below are shown the
data collected for such a plot. Assume that a linear relationship
exists and that the concentration is the independent variable,
known with a high degree of certainty.
Concentration
(ppm)
Signal
1.00
0.116
2.00
0.281
5.00
0.567
7.00
0.880
10.00
1.074
Calculate, using the least-squares method, the slope and intercept
of the "best-fit" line. along with the confidence interval of each at
the 95 % level.
• Let the independent variable of concentration equal x and the
dependent variable of signal equal y. Then
Data necessary for equations are:
• From the equations given above for a and b
• a=
y  bX
 [( X  X )( y  y )
• b=
(X  X )
i
i
2
i
5.817
 0.1092 = 0.092
• Slope = b =
53.26
• Intercept = a = 0.584 – (0.1092)(5.20) = 0.016
Terms used in the control of analytical
procedures
ICH: The International Conference on Harmonisation
of Technical Requirements for Registration of
Pharmaceuticals for Human Use
ICH brings together the regulatory authorities and
pharmaceutical industry of Europe, Japan and the US to
discuss scientific and technical aspects of drug
registration.
Validation of analytical methods
Definition of method validation
Method validation: What is it?
Method validation is the evaluation of a method to
ensure that its performance is suitable for the analysis
being carried out.
ISO Definition
• Confirmation by examination and provision of
objective evidence that the particular requirements
for a specified intended use are fulfilled”
• [ISO 8402:1994]
41
Validation of analytical methods
 Introduction:
 Why analytical monitoring?
 Definition of method validation
 Why method development and method validation?
 How method validation is done?
 Requirements for a Validation of analytical procedures
 Validation protocol for analytical method
 Analytical Procedure
 Tests Required for Validation of the Analytical Procedure
 Specificity and selectivity
 Accuracy
 Precision
 Repeatability
 Reproducibility
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













Sensitivity
Linearity and range
Limit of detection
Limit of quantitation
System Stability
Ruggedness
Robustness
System Suitability
Extent of validation
Protocols
Classification of analytical tests
Chemical laboratory validation requirements
Revalidation
Standard Reference Materials (SRMs) (or Primary
Standards)
 Accreditation of laboratory methods
43
Why method development and method validation?
• Validation of an analytical method will ensure that
the results of an analysis are reliable, consistent and
perhaps more importantly that there is a degree of
confidence in the results.
• As either a customer of an analytical laboratory or as
a performing laboratory, it must be demonstrated
that the parameter you determine is the right one
and that the results have demonstrated “fitness for
purpose”.
– Method validation provides the necessary proof
that a method is “fit for purpose”.
44
Comments on method development
and method validation?
• Official analytical methods described in and
recognized publications for a particular active
constituent or formulation are regarded as validated
and do not require revalidation. (Regulatory methods)
• However, the suitability of these methods must be
verified under actual conditions of use i.e., the
specificity and precision of the method should be
demonstrated for the published method when applied
to the relevant sample matrix and laboratory
conditions.
45
Tests Required for Validation of the
Analytical Procedure
Data submitted should, as appropriate, address the
following parameters:
• Specificity of the procedure
• Accuracy and precision of the procedure
• Linearity of response for the analyte (and internal
standard, if appropriate)
• Limit of detection
• Limit of quantitation
• Sensitivity
• Ruggedness/Robustness
46
The USP Eight Steps of Method Validation
47
1. Specificity and selectivity
• It is the ability to assess clearly the analyte in the presence of
components which may be expected to be present.
• Typically, these might include impurities, degradants, matrix,
etc.
• The specificity of the analytical method must be demonstrated
by providing data to show that:
– Known degradation products and synthetic impurities do
not interfere with the determination of the active
constituent in bulk actives
– Known degradation products, synthetic impurities and
sample matrix present in the commercial product do not
interfere with the determination of the active constituent
•
48
2. Accuracy and Precision
•
Accuracy
•
Precision
(could be expressed by : standard deviation,
variance, or coefficient of variation)
–
Repeatability (intra-assay precision):
same operating conditions under short
interval of time) same person using
single instrument)
– Intermediate precision
– Reproducibility
49
Accuracy
• The closeness of agreement between the value
which is accepted either as a conventional true
value or an accepted reference value, and the
value found.
• When measuring accuracy, it is important to spike
the sample matrix with varying amounts of active
ingredient(s).
• If a matrix cannot be obtained, then a sample
should be spiked at varying levels.
• In both cases, acceptable recovery must be
demonstrated.
50
• Accuracy is often described as “trueness”
– Trueness: The closeness of agreement between
the arithmetic mean of a large number of test
results and the true or accepted reference value.
[BS ISO 5725-1:1994]
51
• For some methods the true value cannot be
determined exactly and it may be possible to
use an accepted reference value to
determine this value.
• For example if suitable reference materials
are available or if the reference value can be
determined by comparison with another
method.
52
Measurements of Accuracy
• Accuracy may be measured in different ways
and the method should be appropriate to the
matrix.
• The accuracy of an analytical method may be
determined by any of the following ways:
53
a. Analyzing a sample of known concentration
and comparing the measured value to the
‘true’ value . However, a well characterized
sample (e.g., reference standard, a Certified
Reference Material (CRM) must be used.
54
55
b. Spiked –Product matrix recovery method (Most widely
used)
• A known amount of pure active constituent is
added to the blank [sample that contains all other
ingredients except the active(s)] matrix.
• Spiked samples are generally prepared at 3 levels in the
range 50 - 150 % of the target concentration.
• The matrix is constructed to mimic representative samples
in all respects where possible. For impurities, spiked
samples are prepared over a range that covers the
impurity content, for example 0.1 - 2.5 % w/w.
• The resulting mixture is assayed, and the results obtained
are compared with the expected result.
56
c. Standard addition method
• This method is used if a blank sample
cannot be prepared without the analyte
being present.
• A sample is assayed, a known amount of
pure active constituent is added, and the
sample is again assayed.
• The difference between the results of the
two assays is compared with the expected
answer.
57
58
• The accuracy of a method may vary across
the range of possible assay values and
therefore must be determined at several
different levels.
• The accuracy should cover at least 3
concentrations (80, 100 and 120% or others)
in the expected range.
• Accuracy may also be determined by
comparing test results with those obtained
using another validated test method.
59
Acceptance criteria:
• The expected recovery depends on the sample
matrix, the sample processing procedure and
on the analyte concentration.
• The mean % recovery should be within the
following ranges:
60
%Active/impurity
content
> 10
>1
0.1 - 1
< 0.1
61
Acceptable mean
recover
(%)
98 - 102
90 - 110
80 - 120
75 - 125
Precision
• It is the closeness of agreement
(degree of scatter) between a series of
measurements obtained from multiple
sampling of the homogeneous sample
under the prescribed conditions.
• Precision may be considered at three
levels: repeatability, intermediate
precision and reproducibility.
62
a. Repeatability
• It expresses the precision under the same operating
conditions over a short interval of time. Repeatability is
also termed intra-assay precision
• Factors such as the operator, equipment, calibration and
environmental considerations, remain constant and have
little or no contribution to the final results
• Repeatability consists intra-laboratory assay:
repeated analysis (a minimum of 5 replicate
determinations must be made and the mean, % Relative
Standard Deviation ,RSD, and number of determinations
reported) of an independently prepared sample on the
same day by the same operator in the same laboratory.
63
b. Intermediate Precision
• It expresses variations within-laboratories :
different days, different analysts, different
equipment, etc.
• Repeated analysis (a minimum of 5 replicate
determinations must be made and the mean, %
RSD and number of determinations reported)
of an independently prepared sample by
different operators on different days in the
same laboratory.
64
c. Reproducibility
• It expresses the precision between laboratories (collaborative
studies usually applied to standardization of methodology).
• It is a measure of a method’s ability to perform a routine
analysis and deliver the same results using a particular
method irrespective of laboratory, equipment and operator
changes.
• Confirmation of reproducibility is important if the method is
to be used in different laboratories for routine analysis.
• Reproducibility is expressed in terms of relative standard
deviation. The unmodified Horwitz equation is used as a
criterion of acceptability for measured reproducibility.
65
• The modified Horwitz equation which
suggests
RSD < 2 (1 - 0.5 log C) x 0.67
Where C is the concentration of the
analyte expressed as a decimal fraction (i.e.
0.1, 1x10-6 etc.)
• Collaborative methods do not require
validation of reproducibility since by their
nature they are validated in this way
(providing that the analysis falls within the
validated range of that method).
66
General considerations for precision
• Precision should be investigated using
homogeneous, authentic (full scale-true) samples.
However, if it is not possible to obtain a full-scale
sample it may be investigated using a pilot-scale or
bench-top scale sample or sample solution.
• The precision of an analytical procedure is usually
expressed as the variance, standard deviation or
coefficient of variation of a series of measurements.
• A minimum of 5 replicate sample determinations
should be made together with a simple statistical
assessment of the results, including the percent
relative standard deviation.
67
68
Mebendazole is used as anthelmintic
69
70
%Component measured in
sample
Precision
RSD
%
 10.0
2
1.0 to 10.0
5
0.1 up to 1.0
 10
< 0.1
 20
71
• The following figure illustrates how
precision may change as a function of
analyte level. The %RSD values for
ethanol quantitation by GC increased
significantly as the concentration
decreased from 1000 ppm to 10 ppm.
Higher variability is expected as the
analyte levels approach the detection
limit for the method. The developer
must judge at what concentration the
imprecision becomes too great for the
intended use of the method.
72
Figure 2. %RSD versus concentration for a GC
headspace analysis of ethanol.
73
3. Sensitivity, linearity, limit of detection,
limit of quantification
•Sensitivity
•Linearity and range
•Limit of detection
•Limit of quantitation
74
Sensitivity
It is the gradient of the response curve,
i.e. the change in instrument response
that corresponds to a change in analyte
concentration within the linear range
75
Linearity
• A linearity study verifies that the sample
solutions are in a concentration range where
analyte response is linearly proportional to
concentration.
• For assay methods, this study is generally
performed by preparing standard solutions
at five concentration levels, from 50 to 150%
of the target analyte concentration.
• Five levels are required to allow detection of
curvature in the plotted data.
76
•Standards should be prepared and analyzed
a minimum of three times.
•For impurity (low concentrations) methods,
linearity is determined by preparing standard
solutions at five concentration levels over a
range such as 0.05-2.5 wt%.
•When linear regression analyses are performed,
it is important not to force the origin as (0,0) in
the calculation. This practice may significantly
skew the actual best-fit slope through the
physical range of use.
77
• The linearity of the method over an
appropriate range must be determined and
reported. The range selected must cover the
nominal concentration of the analyte in the
product ± 25%.
• Duplicate determinations must be made at 3
(nominal concentration ± 25%) or more
concentrations.
• Reports submitted must include, the slope
of the line, intercept and correlation
coefficient data.
78
0.040
0.035
0.030
0.025
0.020
0.015
0.010
0.01
79
Calculated analyte in mg/mL
Linearity
Table of values (x,y)
Linearity
of an analyte in a material
0.015
Reference material mg/ml
0.02
0.025
0.03
0.035
0.04
x
y
#
Reference
material mg/ml
Calculated
mg/ml
1
0.0100
0.0101
2
0.0150
0.0145
3
0.0200
0.0210
4
0.0250
0.0260
5
0.0300
0.0294
6
0.0400
0.0410
Linearity Statistics
•Intercept
-0.0002
•Limit of Linearity and Range 0.005 – 0.040 mg/mL
•Slope
1.0237
•Correlation coefficient
0.9978
•Relative standard deviation
80
3.4%
• Acceptability of linearity data is often
judged by examining the correlation
coefficient and y-intercept of the linear
regression line for the response versus
concentration plot.
• A correlation coefficient of > 0.999 is
generally considered as evidence of
acceptable fit of the data to the regression
line.
• The y-intercept should be less than a few
percent of the response obtained for the
analyte at the target level.
81
82
Calibration and Standards
• In almost all chemical analysis, chemical concentrations
are found by indirect measurements, which are based on
direct measurements together with calibration
• Calibration is to ascertain the relationship between the
content of the sample and the response of the assay
method and is essential for quantitative analysis.
• Chemical standards are pure substances, mixtures,
solutions, gases, or materials such as alloys or biological
substances that are used to calibrate and validate all or
part of the methodology of a chemical analysis.
• Experimental optimization of an assay normally
requires the use of chemical standards
83
Range
• It is the interval between the upper and
lower concentration of analyte in the
sample (including these concentrations)
for which it has been demonstrated that
the analytical procedure has a suitable
level of precision, accuracy and
linearity.
84
Determination of the range
• In practice, the range is determined using
data from the linearity and accuracy
studies.
• Assuming that acceptable linearity and
accuracy (recovery) results were obtained
85
Acceptance criteria for the Range
• An example of range criteria for an assay
method is that the acceptable range will be
defined as the concentration interval over
which linearity and accuracy are obtained
per previously discussed criteria and that
yields a precision of 3% RSD.
• For an impurity method, the acceptable
range will be defined as the concentration
interval over which linearity and accuracy
are obtained per the above criteria, and
that, in addition, yields a precision of 10%
RSD.
86
Limit of Detection
• It is the lowest amount of analyte in a sample
which can be detected but not necessarily
quantitated as an exact value.
• Limit of detection is the point at which a
measured value is larger than the uncertainty
associated with it.
• In chromatography,e.g., limit of detection is an
amount that produces a peak with a height at
least 3 times that of the baseline noise level.
• For validation it is usually sufficient to indicate
the level at which detection becomes
problematic.
87
LOQ, LOD and S/N-R
• Limit of Quantitation
• Limit of Detection
• Signal to Noise Ratio
Peak B
LOQ
• Noise level plays an
important role in the LOD
and LOQ!
Peak A
LOD
Baseline
88
noise
• The LOD may be determined by
injecting the lowest calibration standard
10 (could be 20) times and calculating
the standard deviation. Three times the
standard deviation will be the LOD.
89
Limit of quantitation (LOQ)
• The limit of quantitation is a parameter of
quantitative assays for low levels of compounds in
sample matrices and is used particularly for the
determination of impurities and/or degradation
products or low levels of active constituent in a
product.
• The limit of quantitation is the lowest amount of
the analyte in the sample that can be quantitatively
determined with defined precision under the stated
experimental conditions.
90
• The LOQ may be determined by preparing
standard solutions at estimated LOQ
concentration (based on preliminary
studies).
• The solution should be injected and analyzed
n (normally 6-10) times.
• The average response and the relative
standard deviation (RSD) of the n results
should be calculated and the RSD should be
less than 20%.
• If the RSD exceeds 20%, a new standard
solution of higher concentration should be
prepared and the above procedure repeated.
91
• The EURACHEM approach is to inject 6
samples of decreasing concentrations of
analyte.
• The calculated RSD is plotted against
concentration and the amount that
corresponds to a predetermined RSD is
defined as the limit of quantitation
92
93
4. System Stability
• Many solutes readily decompose prior to
analytical investigations, for example during
the preparation of the sample solutions, during
extraction, clean-up, phase transfer, and
during storage of prepared vials (in
refrigerators or in an automatic sampler).
• Under these circumstances, method
development should investigate the stability of
the analytes.
94
Determination of the stability of the samples
being analyzed in a sample solution
• It is a measure of the bias in assay results generated
during a pre-selected time interval, for example every
hour up to 46 h, using a single solution.
• System stability should be determined by replicate
analysis of the sample solution.
• System stability is considered to be appropriate if the
relative standard deviation calculated on the assay
results obtained in different time intervals does not
exceed more than 20 % of the corresponding value of
the system precision.
• If the value is higher on plotting the assay results as a
function of time, the maximum duration of the
usability of the sample solution can be calculated.
95
96
Example of system stability
• The effect of long-term storage and freeze-thaw
cycles can be investigated by analyzing a spiked
sample immediately upon preparation and on
subsequent days of the anticipated storage period.
• A minimum of two cycles at two concentrations
should be studied in duplicate.
• If the integrity of the drug is affected by freezing
and thawing, spiked samples should be stored in
individual containers and appropriate caution
should be employed for study samples.
97
5. Ruggedness and robustness of the method
•
•
•
Ruggedness
Robustness
Variability caused by:
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Day-to-day variations
Analyst-to-analyst
Laboratory-to-laboratory
Instrument-to-instrument
Chromatographic column-to-column
Reagent kit-to-kit
Instability of analytical reagents
Robustness
• The robustness of an analytical procedure is a
measure of its capacity to remain unaffected by
small, but deliberate, variations in method
parameters and provides an indication of its
reliability during normal usage.
• Ideally, robustness should be explored during
the development of the assay method.
• For the most efficient way to do this is through
the use of a designed experiment.
• Such experimental designs might include a
Plackett-Burman matrix approach to investigate
first order effects, or a 2k factorial design that
will provide information regarding the first
(main) and higher order (interaction) effects.
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• In carrying out such a design, one must first identify
variables in the method that may be expected to
influence the result.
• For instance, consider an HPLC assay which uses an
ion-pairing reagent. One might investigate: sample
sonication or mixing time; mobile phase organic
solvent constituency; mobile phase pH; column
temperature; injection volume; flow rate; modifier
concentration; concentration of ion-pairing reagent;
etc.
• It is through this sort of a development study that
variables with the greatest effects on results may be
determined in a minimal number of experiments.
•The actual method validation will ensure that the final,
chosen ranges are robust
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