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The relationship between Analysis and the Analytical Blank
The relationship between Analysis and Sampling Uncertainty, How we got there:
Some Additional Notes and some repeat notes that are in the PDF file "SAMPLING NOTES FOR CLASS"
These are primarily a copy of 30 of the 50 pages and some additional references and examples only and are not necessary if you have read the PDF file.
"Poor sample collection procedures yield samples that are not representative
of the population of interest, are of little use, seriously compromise the purpose
of sampling, and contribute to the uncertainty of the analytical results."
"Furthermore, sampling and analytical errors occur independently of each
other, so sampling-related errors cannot be accounted for by laboratory blanks or
control samples."
Ref. "Environmental sampling: A Summary"
by L. H. Keith.
ES&T, Vol.24, no. 5 1990.
Other observations from your review of
Principles of Environmental
Sampling, by L. H. Keith, ACS Professional Reference Book, ACS , Washington
DC, 1988.
Other observations from experience, observation and common sense.
Artifacts or contamination
(contamination)
Analyte loss
(species stability)
Sample collection
(appropriateness)
Preservation
(stability of species)
Handling
(alteration of species)
Storage
(stability, alteration)
Transport to laboratory
(stability, alteration)
Modification & Bias in analysis
(recovery, DL, etc.)
Homogeneity
(correct sample)
Appropriate sub sample
(bias at laboratory)
etc.
"Data Quality Objectives (DQOs) are statements that provide critical
definitions of the confidence that must be inherent in the conclusions drawn from
the data produced by the whole project. These objectives determine the degree of
total variability (uncertainty of error) that can be tolerated in the data. These
limits of variability must be incorporated in the sampling and analysis plan and
be achievable by using detailed sampling and analysis protocols"
Note:
- These are different from accuracy and precision which are
instrumental and individual measurement components.
How are these different and/or additional errors sources unique and where do
originate?
- as defined by Keith.
Exploratory sampling goals - (surveillance) provide preliminary information
about the site or material being analyzed.
Monitoring sampling goals - (assessment) undertaken for regulatory enforcement
or non regulatory purposes; initiated to provide information on the variation in
the specific period, and specific area.
Do these different goals require different sampling protocols?
If so then
-
How do these different goals require different sampling protocols?
"Sampling protocols are written descriptions of the detailed procedures
to be followed in the collection, packaging, preservation, transportation,
storage, and documentation of the samples... Most Protocols should have a
statistical design to prove that the samples represent the matrix to be
evaluated." -Keith
- pg. 612 Keith paper & Keith sampling book
Examples:
Site dependent ...
DQO dependent ...
Common sense dept. ...
(sometimes it is uncommon)
Selecting the specific analysis method ...
Sampling method is dependent on the analysis method
Specific
selection of the analysis method will be addressed separately.
Types of sampling approaches:
Figure 1. Keith, examples of each type
(Modified)
Random
Makes no assumptions about distribution or movement of analytes
Usually cost more because it requires more sample and relies less specific knowledge
Why? No assumptions are made it is a blind study
Systematic
Makes no assumptions about distribution or movement of analytes
Judgmental
Implements assumptions about movement and distribution with time, distance (fate and transport)
Combinations
Frequently Judgment combined with systematic or random is used to take advantages from each
Figure 2. (Keith)
The general relationship of Judgmental (J), Systematic (S), and Random (R) sampling approaches to relative numbers of samples needed and relative amounts of bias introduced.
Water
Surface
Rain
Ground
Human pumped
Human chemical
modification
Wind
Natural
Human barriers and perturbation
grass in the desert
Cities and thermal updrafts
Human Intervention
Waste-water pipes
Drainage ditches
Roadways
Railways
Irrigation
Ponding
Physical transformation
Physical collection and
concentration
Human species transformation
{These topics developed in ESM 551 Intro. to Env. Sci. (course prerequisite)}
Reference
Principles of Environmental Sampling, by Lawrence H.
Keith,
ACS professional Reference Book. 1988.
Defining the Accuracy, Precision, and Confidence Limits of Sample Data,
by John K. Taylor
chapter 6, pages 101-107. (assigned)
"Sample data contain a degree of uncertainty, and this uncertainty must
be considered whenever the data are used."
Limit of quantitation is about 3 times the limit of detection (LOD).
The total variance of measurement data (s2total) can be
expressed in the terms of
s2total = s2measurement +
s2sample
where:
s2measurement - is the sampling variances
due to measurement
s2sample - is the sampling variances
due to sample
Both the measurement and sampling uncertainties must be considered
Youden has shown that, once the measurement uncertainty has been reduced to
one third or less of the sampling uncertainty "further improvement in the
measurement uncertainty is fruitless."
(s2 m < s2 s/3),
Reference
W. J. Youden, J, Assoc. Off. Anal. Chem., 1981, 50, 1007.
| Situation | Significance | |
|---|---|---|
| A | Measurement variance | No |
| Sample variance | No | |
| B | Measurement variance | Yes |
| Sample variance | No | |
| C | Measurement variance | No |
| Sample variance | Yes | |
| D | Measurement variance | Yes |
| Sample variance | Yes |
A - confined to single-specimen analysis or where semiquantitive data are
required
B - homogeneous materials
C - single measurements of sample are sufficient
D - most frequent case both the sample have variance and the measurement
method has variance.
Measurement Variance (uncertainty) -
can be controlled and
evaluated.
Sample variance (uncertainty) -
may contain systematic and random
components of error form population representation and sampling protocol.
s2sampling = s21 +
s22 + s23 ...
s2n additive
s2sample = s2sampling +
s2 population additive
A sampling protocol for a soil sample is a 1.5% s, due to homogeneity in the
soil particle (this calculation demonstrated later in this section), a mean and
measurement error of 34.8 ± 0.5, a blank mean and measurement error of 9
± 3 (due to the fact that it is closer to the detection limit) and a field
sampling protocol estimate at approximately 5% s. What is the mean and total
uncertainty or error of this sample.
Mean with blank subtracted 34.8 - 9 = 25.8 ±?
s2total = s21 +
s22 + s23 ...
s2n additive
s2total = (0.015x25.8)2 + 0.52 +
32 + (0.05x25.8)2
s2total = 0.15 + 0.25 + 9 + 1.7 = 11.1
stotal = 
+ 
= 3.3
stotal = 3.3
so
the mean and standard deviation of the measurement with the uncertainty
standard deviation for the total measurement and sampling yield a result of:
25.8 ± 3.3
Where did most of the uncertainty come from?
From what? Is this typical?
Why? What did you learn?
"The sampling operation should be based on protocols especially developed
for the specific analytical problem."
- Taylor pg. 105.
Quality control includes
application of good laboratory practices
sample specific standard operations procedures
Taylor
~ strict adherence to the established protocols is imperative
He concludes that Judgment and statistically based sampling are necessary to
evaluate a site
Judgment sampling - requires technical expertise - but different experts can
draw different conclusions from the same data
Statistical based sampling - requires statistics to provide probabilistical
conclusions independent of personal judgment.
He uses a statistical approach to ask and then answer these questions
References:
Principles of Environmental Sampling Ed. by
Lawrence H. Keith, ACS professional Reference Book. 1988.
in Planning and
Sample Design, Overview of the Sampling Process, by Michael J. Brcelona,
chapter 1, pages 1-23.
"Sampling of Contaminated Soil: Sampling Error in Relation to Sample Size and Segregation" by Frank P. L. Lame', and Peter R. Deflze, ES&T, Vol. 27, No. 10, pp. 2035-2044, 1993.
Fundamentals of Analytical Chemistry, Skoog, West, Holler, Saunders College Publishing, 6th ed. NY, NY, pg. 750-760, 1992.
"Environmental sampling: A Summary by L. H. Keith. ES&T, Vol.24, no. 5 1990.
"Defining the Accuracy, Precision, and Confidence Limits of Sample
Data," by John K. Taylor, ACS professional Reference Book. 1988. chapter 6,
pages 101-107.
"An environmental scientist's view of the sampling process is often quite
different from that of a statistician."
The scientist may be interested in representative samples of water from
a particular salinity or sediment pores etc.
The statistician ... may envision samples as a subset of the universe
of all reducing surface water samples.
"Samples suitable for analysis must be representative parts of the
object."
Examples, Definitional in nature and relationships
Figure 1. pg. 6 and
Figure 2 pg. 7.
Green page 8 proposes a method consisting of 8 parts.
ACS Committee on Environmental Improvement recommends 3 minimum requirements
for an acceptable sampling program:
"There are far too many potential types and purposes of investigations in
environmental chemistry to present a generally applicable strategy of formula for
preparing sampling protocols." pg. 10
Figure 3. Relationship of program purpose and protocols to the scientific
method.
| Main Point Program Purpose |
Sub-elements |
|---|---|
| Analytes of interest | Primary and secondary chemical constituents and criteria for representativeness |
| Locations | Design, construction, and performance evaluation |
| Sample collection | Mechanism, materials, and methodology |
| Sample handling | Preservation, filtration, and field control samples |
| Field determinations | Unstable species and additional sampling variables |
| Sample storage and transport | Preservation of sample integrity |
"From this point, the specifics of what the samples are to be analyzed
for and the questions "how many", "where", "when",
and "how" are addressed in order."
Some are:
There are basically two types of controls:
Check control - solution and calibration standards for instrument
performance and limit of detection
Standard Reference Materials (SRMs) (called "Laboratory controls" by
Keith) Citified for analyte concentration in the same or similar matrix for
establishing accuracy.
Also verifies calibration.
Spike and background control
Controls and Blanks
Specific Environmental Sample Types
Sample Controls
Control Site
Local Control Site
Area Control Site
National
Controls
Matrix Controls (filed spikes)
Background Site Controls
homogeneous at the molecular level, etc.
heterogeneous spacially and
temporally
multiphase solid liquid
plumes
stratified thermally,
density
flow rate
depth
type (rain, snow, fog, due)
devolved gases under go hydrolysis
(NOx, SO3)
depth
recharge rate,
soil composition
topography
(slope)
fate of analyte
Contamination and blank
Sorption of analytes
Organics
Metals
Sample Preservation
Stability, pH, pElight, chemical reactions, T, time, microbes,
adsorption, micells, mineral layers,
side reactions Cl2 and
Organics, solubility, etc.
Indoor
Ambient (outdoor)
Soil/atmosphere
Solutions
Suspensions (not a homogeneous solution)
Aerosols (not a homogeneous
solution)
Interactions
Sorbed
Filter interactions
Thermal desorption (volatile)
Photochemical reactions
General Sampling Considerations
Sample size goes down with sample homogeneity
Sample seze goes up with heterogeneity
Sample preservation may not stabolize the sample
Loss of volatile (analyte may be lost)
Contamination (analyte may be contaminated)
Bio-degradation (unique reaction with biosphere cont.)
Primary and secondary analytes may be different
Many others
Water (liquids) and air (gasses) are homogeneous at the molecular level. Solid sample are not and can be even more difficult.
"Sampling" Definitions
Sampling - This is the term for the process by which a representative fraction is obtained from a bulk (or gross sample) material for analysis.
Sample -
Note - IUPAC has 18 separate definitions for the word sample.
analyzed sample, subsample, working sample etc.
Bulk samples are usually "inhomogeneous" such as tissues, soils, natural waters, ores etc.
Gross sample - (also called bulk sample, lot sample) One or more increments of material taken from a larger quantity (lot) of material for assay
The Gross Sample must correspond to the whole in composition, particle-size distribution.
Homogeneity - The degree to which a property or substance is uniformly distributed throughout a material.
Homogeneity depends on the size of the units under consideration.
Sample size - the quantity chosen for the analysis
Samples are inhomogeneous at different levels and in different amounts
Sample - A portion of a population or lot. It may consist of an individual or groups of individuals.
Sub- sample - a portion taken from a sample. A laboratory sample may be a sub-sample of a gross sample; similarly, a test portion may be a sub-sample of a laboratory sample.
Reference
"Quality Assurance of Chemical Measurements", by John K. Taylor, Lewis, Chelsea, MI, 1987.
Analysis of the sample
Skoog -
"the reliability of the analysis cannot exceed that of the sampling step, and painstaking analysis of a poor sample is wasted effort."
"Often, sampling is the most difficult step in the entire analytical process and the step that limits the accuracy of the procedure."
Skoog - pg 750, 6th ed.
Three steps involved in sampling bulk materials:
1. identification of the population from which the sample is to be obtained,
2. collection of a gross sample that is truly representative of the population being sampled,
3. reduction of the gross sample to a few hundred grams or a homogeneous laboratory sample that is suitable for the analysis to be performed.
4. sub- sample a portion taken from a gross sample.
5. laboratory sample may be an additonal sub- sample of a gross sample; a test portion actually taken for analysis.
Note: The process used to accomplish the sampling depends on the Homogeneity of the sample
Homogeneity and Heterogeneity
The size of the Gross Sample is determined by its composition, homogeneity and particle size distribution
Homogeneity - is the degree of uniform distribution of the analyte and mixing defined at some level
Factors to consider:
1. The uncertainty that can be tolerated between the composition of the gross sample and that of the whole.
2. The degree of heterogeneity of the whole,
3. The level of particle size at which heterogeneity begins
4. Distribution of the analyte between the particles
5. The size sample that can be analyzed
6. Ways of increaseing the effective homogeneity
(example: decomposing a large sample and taking a small sample of the solution {solutions by definition are homogeneous}
Sampling Solid Material
Lets use a soil or ore sample for the example
Relationships have been developed to evaluate the uncertainty and the number of particles in the gross sample and those that are to be taken.
Examples form:
*Reference Fundamentals of Analytical Chemistry, Skoog, West, Holler, Saunders College Publishing, 6th ed. NY, NY, pg. 750-760, 1992.
and
"Sampling for Tests of Hypothesis When Data Are Correlated in Space and Time," by Leon E. Borgman and William F. Quimby, chapter 2, ACS professional Reference Book. 1988, pages 25-42.
and
"Sampling of Contaminated Soil: Sampling Error in Relation to Sample Size and Segregation" by Frank P. L. Lame', and Peter R. Deflze, ES&T, Vol. 27, No. 10, pp. 2035-2044, 1993.
This is one of the most difficult type of sampling because of:
1. discrete particles,
2. relative lack of homogeneity
3. different particle composition (concentration)
4. particle density differences
5. particle size (bimodal distribution)
A mathematical relationship in homogeneity
Question -
How many particles must be sampled to obtain a 1% error in standard deviation, SD or (s) ([[sigma]], if population is known) or a 0.1% error in SD due to sampling
Givern the relationship:
n =
Where:
n=the number of particles that must be taken to obtain the specified [[sigma]]
P = the fraction containing the analyte
[[sigma]] = the relative standard deviation
If [[sigma]] is 1% (or [[sigma]] = 0.01) & P is 60% (0.60) then
n = = 6,666 particles
If [[sigma]] is 0.1% ([[sigma]] = 0.001) & P is 60% (0.60) then
n = = 666,666 particles
Since the complexity can get out of hand very quickly and leave us with non-viable solution a group of assumptions are usually used.
Assumptions
Only 2 particle sizes P1 and P2 in our example
(in real sample there could be more)
We will assume that there are two descrete particls and that Pb is what is bing evaluated and the main source of Pb is Galena a Pb containing mineral in this case.
p or
The equations now becomes
n = p( 1 - p ) ( d1 d2 / d2 )2 x ( (P1 - P2 ) / (sigma) P )2
n = the number of particles to be taken in a gross sample
p = fraction of galina (or Pb analyte containing material)
P1 = fraction of particle 1
P2 = fraction of particle 2
P = average percent of the element
d1 = density of particle 1
d2 = density of particle 2
d = average density of the entire sample
Degree of heterogeneity P1 - P2 has a lot to do with the size of the sample necessary to get a representative sample
Sampling solids continued
Example 30-1 (Skoog)
Assume that the average particle in a truck load of soil (from a Superfund site) that had some soil and lead ore mixed in it is judged to be approximately spherical with radius of about 5 mm. Roughly 4% of the particles appear to be galena (P1) (galena is ~ 70% Pb), which has a density of 7.6 g/cm3; the remaining particles have a density of about 3.5 g/cm3 (silicon dioxide based stony or rock particles) and contain little or no Pb (soil, sand, minerals). How many pounds of soil (ore) would the gross sample contain if the sampling uncertainty is to be kept below 0.5% relative error?
We first need the average density (d) and %Pb.
d= (0.04 x 7.6) + (0.96 x 3.5) = 3.7 g/cm3 (average density)
P = (0.4 x 7.6 x 0.70) g Pb cm3 / (3.7 g sample/cm 3)x 100% = 5.8% Pb (average % Pb)
using an equation derived for 2 particles (Skoog, pg. 753, 6th ed.)
n = p( 1 - p ) ( d1 d2 / d2 )2 x ( (P1 - P2 ) / (sigma) P )2
n = 0.04( 1 - 0.04 ) ( 7.6 x 3.5 / (3.7)2)2 x ((70 - 0) / (0.005 x 5.8))2 = 8.45 x 105
0.0384 x 3.77 x 5.826x106 = 8.45 x 105
particles required
Now calculating the weight of the sample that 8.45 x 105 particles represents.
8.45x 105 particles x (4/3)[[pi]] (0.5)3 cm3/particle x 3.7 g/cm3 x(1 / 454 g/lb)
= 3.61 x 103 lb. or ~ 1.8 ton
for a 0.5% relative standard deviation for sampling this matrix
NOW
Rework the problem for a 5 or 10% error due to sampling and what do you get?
For 5% error
n = p( 1 - p ) ( d1 d2 / d2 )2 x ( (P1 - P2 ) / (sigma) P )2
n = 0.04( 1 - 0.04 ) ( 7.6 x 3.5 / (3.7)2)2 x ((70 - 0) / (0.05 x 5.8))2 = 8.43 x 103 particles required
0.0384 x 3.77 x 5.826 x 104= 8.43 x 103
NOW
For 10% error
n = p( 1 - p ) ( d1 d2 / d2 )2 x ( (P1 - P2 ) / (sigma) P )2
n = 0.04( 1 - 0.04 ) ( 7.6 x 3.5 / (3.7)2)2 x ( (70 - 0) / (0.10 x 5.8))2 = 2.11x 103 particles required
0.0384 x 3.77 x 1.456 x 104= 2.11 x 103
REMEMBER - ALL PARTICLES ARE 5mm IN DIAMETER
Calculate actual weight of the sample needed
Now calculating the weight of the sample that respective number of particles required represents.
For 0.5% standard deviation (Original problem)
8.45 x 105 particles x (4/3)[[pi]] (0.5)3 cm3/particle x 3.7 g/cm3 x(1 / 454 g/lb)
= 3.61 x 103 lb.
or ~ 1.8 ton
For New 10% standard deviation
2.11 x 103 particles x (4/3)[[pi]] (0.5)3 cm3/particle x 3.7 g/cm3 x(1 / 454 g/lb)= 9.01 lb
REMEMBER - ALL PARTICLES ARE 5mm IN DIAMETER
Preparation of a Laboratory Sample (Example)
Reduction of a non homogeneous solid to a gross sample may weigh several hundred pounds of more, and reduction of the gross sample to a homogeneous laboratory sample requires grinding and homogenizing.
The number of particles will be the same as computed previously but they will be smaller.
What size gives the same number of particles?
REMEMBER - ALL PARTICLES ARE WERE 5mm IN DIAMETER
Continuing with the same example the laboratory sample to obtain a laboratory sample of approximately 1 lb. that has the same distribution as the 3.61 x 103 lb. or ~ 1.8 ton will require the average wt. of a particle =
av. wt. of particle
= 1 lb x 454 g/lb. x 1/ (8.45 x 105 particles) = 5.37 x 10-4 g/particle
The average weight of a particle is related by;
av. wt. of particle = [4/3[pi]] [r(cm)]3 x 3.7 g/cm3
Solving for r the radius of the particle
r = ( 5.37 x 10-4 g x3/4[pi] x cm3 / 3.7 g)1/3 = 3.3 x 10-2 cm or 0.3 mm
So the sample must be ground and mixed and subdivide into 0.3 mm particles and a replicate samples of 1 lb.
8.45 x 105 particles x 5.37 x 10-4 = 454 g or 1 lb.
SO, GOING FROM 5mm particle to 0.3 mm particle goes from 1.8 ton ton 1 lb. in sample size with the same 0.5% RSD.
Preparation of Homogeneous Samples
Good Examples are Standard Reference Materials (SRMs)
Why - The nature of these standards requires them to be homogeneous, representative in discrete sizes, reproducible and stable
How were the three Standard Reference Materials (SRMs) that we are using as examples of Homogeneous materials prepared.
Soil and River Sediment SRMs
Evaluate SRMs
Standard Reference Material 2704: Buffalo River Sediment
National Institute of Standards and Technology; June 1988
Standard Reference Material 2709: San Joaquin Soil, Baseline Trace Element Concentrations, National Institute of Standards and Technology; August 1993
Ground and sieved and only a certain particle size distribution and fraction was bottled after "V" blender mixing.
River Sediment
Dried, Ground, Sieved, Bottled in Glass, Sealed from the environment
Standards for total elemental analysis and for environmental leaching
How was the material packaged for stability?
How were the SRM example materials dried? Why?
What is the relative sample size required for each of the SRMs? Why?
Specialized sample types have unique considerations
Environmental samples have specific transport mechanisms such as:
water,
precipitation,
chemical binding,
biological uptake of one specific specie over another, etc.
Alterations such as partitioning and species shifts also can occur on:
shipping,
manipulation,
laboratory sub-sampling,
and analysis
Mineral and soils like ceramics have specific micro-fine grains and crystals of specific composition and gel or glassy interfaces.
These are examples of spacial inhomogeneity
Other inhomogeneous sample types
Food has various components associated with specific molecules such as fat soluble vitamins and pesticides and water soluble ions, etc.
Tissues are biologically active and can be altered by interaction with many common materials and environmental components such as oxygen and bacteria.
Geological systems as previously discussed.
Each of these require studying the sample and the analysis and planning the sampling intelligently. This is part of analytical problem solving of environmental evaluation.
Preparation of the Laboratory Sample
and Alteration of the "sample" during processing
Because preparation of the laboratory sample from the gross sample frequently requires grinding and matrix specific alterations can be identified with this process.
It is difficult to maintain some aspects of many samples as they were originally encountered.
Examples sample preparation problems and concerns:
In a geological rock sample iron(II) specie decreases by 40% and is converted to iron(III) by air oxidation upon grinding.
Grinding of gypsum (CaSO4 * 2H2O) decreases the water from 21% to 5% when the compound was ground and exposed to air.
Screening (sieving or sizing) using a sieve can separate particular particles by hardness or because they are finely or coarsely present or because of density. (remember the soil and galena sample example)
Sample contamination from grinding equipment is also very prevalent because of the abrasive nature of the process.
Water in the Sample as part of the Sample
Water content can change the composition of a sample by 10 - 20%
Many materials are hygroscopic and pick up water upon contact with moist air.
Some materials change their associated water content with atmospheric humidity.
Since samples are generally analyzed on a weight basis water can "bias" the answer.
Samples must be at a uniform moisture content prior to analysis if comparison to standards or other samples of similar materials is to be made.
Forms of water
Essential Water
Water of crystallization
Hydrates
Nonessential Water
Absorbed water
Sorbed water (colloidal, starch, protein)
Occluded water (in cavities within the substance)
Some chemical forms react with atmospheric water depending on the humidity and temperature
Example of Temperature and
Humidity Effects on Water Content
Anhydrous barium chloride reacts with moisture to give two stable hydrates, depending upon temperature and relative humidity.
BaCl2 + H2O <=> BaCl2 * H2O
or
BaCl2 * H2O + H2O <=> BaCl2 * 2H2O
At room temperature and relative humidity 25% to 90%, BaCl2 * 2H2O is the stable species.
At relative humidity of < 25% or less BaCl2 * 2H2O looses a water molecule and converts to BaCl2 * H2O.
At relative humidity of < 8% or less BaCl2 * H2O looses a water molecule and converts to BaCl2.
Drying the Laboratory Sample
Drying can change the sample
Loss of other volatile species Examples Hg, Se, Ga, Te, and organics with vapor pressures Alcohols, ketones etc.
Decrepitation of crystalline materials
Many compounds loose hydrated and adsorbed water at 100 - 120 °C drying conditions.
By oven, or Vacuum oven, or microwave drying (only affects free water or by, drying (over) KClO4 or other drying agents
An alternative to drying the sample
Take several samples and determine the water content of some and correct the others for the water.
How to determine water content:
1. Determine the water content by drying at 100 - 120 °C until constant weight is achieve.
2. An alternative is to use microwave drying and only the non-associated water (adsorbed and sorbed) will be lost.
A way of speciating the water by association and specific bonding
An example of the concepts of sampling, modeling analysis and data evaluation using water analysis. The quality assurance baseline study of the Chesapeake Bay.
1. "Environmental samples must be representative of the portion of the environment being investigated."
Matrix Type Consideration
There are many primary types of wastes
With in each of these primary matrix types there are subcategories:
Examples - Water
1. "Procedures for sampling and analysis influence each other, and so plans for sampling and analysis are codependent."
The analytical analysis method influences the:
a. number of samples needed and taken
b. the amount of sample needed
c. preservation techniques
7 Steps to the Data Quality Objective Process
"Developing DQOs is a structured way to plan data collection and analysis efforts."
1. State the problem to be resolved
2. Identify the decision(s) that must be made
3. Identify all the inputs needed to make the decision(s)
4. Define the study boundaries (e.g., in space, time and analytes)
5. Develop a decision rule for each decision
6. Specify limits on decision errors
7. Optimize the design for collecting data
Calculating the Number of Environmental Samples Needed
Assumptions are necessary to make these estimates
Case 1.
Assumptions
a. The goal of the analysis effort is to determine the average concentration
of the pollutant in the sampling sites.
b. The concentration of the pollutant is distributed over the entire study
area.
Under these conditions the number of samples can be estimated to be:
n=(z(sigma)p/E)2 ,
Where:
n = is the number of samples calculated to be needed
z = is the value of the standard normal variant (1.96 with a 95% C.L)
(sigma)p = is the standard deviation for the sample population
E = is the tolerable error in the estimate of the mean for the characteristic
of interest (an arbitrary value of the amount of error one is willing to accept
in the data)
This is applied in an iterative process in the following manner:
First Pass Equation: n = [Z(1-(alpha)/2)(SD/E)]2
Second pass equation: n = [t(1-(alpha)/2)(SD/E)]2
Where:
Z = is the standard normal deviate from Z distribution using a for a two tailed
distribution
SD = is the standard deviation for a sample set
E = is the amount of error tolerable in the estimate of the average in absolute
terms (e.g., 4µg/L)
t = is the t statistic
Relative:
The equation to determine the number of samples when variation or relative standard deviation are used (CV or RSD). Where RSD or CV are based on the analytical method imprecision.
First Pass Equation: n = {Z(1-(alpha)/2)[RSD/E(r)]}2
Second pass equation: n = {t(1-(alpha)/2)[RSD/E(r)]}2
Where:
Z = is the standard normal deviate from Z distribution using (alpha) for a
two tailed distribution
RSD = is the relative standard deviation based on the analytical method uncertainty
of the data
SD = is the standard deviation for a sample set
E = is the amount of error tolerable in the estimate of the average in absolute
terms (e.g., 4µg/L)
t = is the t statistic
E(r) = is the amount of error tolerable in the estimate of the average in
relative terms (e.g., 5%); a is type I error (rate of false positives, e.g.,
5%), but b (type II error; false negatives) may also be substituted in the
equation
These equation with appropriate
(alpha),
RSD and
t statistics
are implemented in the
DQO-PRO model program module called "Enviro-Calc"
Download these models from the web site.
They are government software model programs to assist your estimate of the number of environmental samples appropriate for your studies.
The site may be many sites in reality
The example of a site that is contaminated that has a stream flowing through the site into a lake provides multiple sites for example:
The number of samples are determined, the method of analysis must be decided.
Analytical method accuracy and precision differ over an order of magnitude.
The calculation of n (the number of samples needed) is related to RSD which is determined by the analytical method.
When an analytical method has multiple analyte capability the larger RSD should be used to estimate.
Thus the method of analysis to be used partially determines the number of samples to be taken.
An example of an Enviro-Calc is provided where:
Other Sampling Protocols Discussed
HotSpot-Calc
A model for calculating hot spots in the environment.
HotSpot-Calc model assists with this effort.
This model uses similar logic and hypothesis testing to evaluate contaminated hotspot presence or absence at a site.
Quality Assurance and Quality Control
Quality Assurance (QA) - is a system of activities that assures the producer or user of a product or service the defined standards of quality with a stated level of confidence are met.
Quality Control (QC) - is a system of activities that controls the quality of a product or service so that it meets the needs of users.
QC samples access the measurement system and establish the amount of bias or imprecision in the data.
DQO-PRO is a collection of models that assist in the sampling and quality assurance process. This program may be downloaded from the class web site.
Additonal References:
"Defining the Accuracy, Precision, and Confidence Limits of Sample Data," by John K. Taylor, ACS professional Reference Book. 1988. chapter 6, pages 101-107.
"Defining Control Sites and Blank Sample Needs", by Stuart C. Balck, ACS professional Reference Book. 1988. chapter 7, pages 109-116
Other assigned paper
"Sampling of Contaminated Soil: Sampling Error in Relation to Sample Size and Segregation" by Frank P. L. Lame', and Peter R. Deflze, ES&T, Vol. 27, No. 10, pp. 2035-2044, 1993.
Other Reference Material Related Or Alternative Readings
"An Elemental Ratioing Technique for Assessing Concentration Data from a Complex Water System", H.M. Kingston and R.R. Greenberg, Environment International; 1984
Reference Materials: Their Role in Measurement Accuracy, W.P. Reed and S.D. Rasberry
Standard Reference Material 2709: San Joaquin Soil, Baseline Trace Element Concentrations, National Institute of Standards and Technology; August 1993
Standard Reference Material 2704: Buffalo River Sediment
National Institute of Standards and Technology; June 1988
For Reference, Fundamentals of Analytical Chemistry, Skoog, West, Holler, Saunders College Publishing, 6th ed. NY, NY, pg. 750-760, 1992.
A Fun Experiment to demonstrate sampling to a class: (for your use, not required)
Sampling, an in Class Experiment (m&ms et. al.)
(An experiment you can really sink your teeth into!)
Situation you have a soil sample arrive at the laboratory. You must analyze it for any PCB, Pb, Fe (II and III) and Doxin. You must take a "grab sample" (sub-sample)
Key
Color Representation
Green PCB
Light Brown Pb
Dark Brown Fe (chocolate =Fe+2, peanut butter =Fe+3)
Red Chlorinated Doxin
Orange & Yellow Soil Matrix
Before sampling are any special preparations necessary?
Should sampler be allow to select the sample visually prior to analysis?
Instructions:
Student Group A
Take a One small "grab sample" (palm full ~ 5-10)
Take a Second small "grab sample"
Keep the two samples separate
Subdivide one sample by color prior to counting (separate)
Student Group B {10 x greater sample size}
Take a Large "grab sample" (cupped hands full ~ 75-100)
Count each color
Take a second and a thrird Large "grab sample"
Subdivide one sample by color prior to counting (separate)
Count each color
Calculate the mean and standard deviation
Calculate the 95% confidence limit (C. L.)
Take a fourth sample and determine if it falls in the
expected C. L.
Groups A and B
Determine the concentration of each part in Parts Per Hundred (pph)
Based on the grab samples
Using visible photometry (a non-destructive detection method)
{ Calculation is - # that color particle/total# of particles x 100 = pph}
Student Group C
Determine the true sample by evaluating the remaining sample and obtaining the true population including the entire sample as originally received by the laboratory. Use data from both Groups A and B to complete your evaluation.
Group A only
Determine the pph of Fe+2 = chocolate and Fe+3 = peanut butter
Group D Record and compile the results of group A, B, and C.
Table set up
Table for Visible spectroscopy test of "grab samples"
Actual # of Actual
Color "Contaminant" "Molecules" Conc. (pph)
Green PCB
Light Brown Pb
Dark Brown Fe
Red Chlorinated Doxin
Orange&Yellow Soil Matrix -
For Other detection method (Group A)
chocolate =Fe+2,
peanut butter =Fe+3
Group Sample
Table for Visible spectroscopy test of "grab samples"
Actual # of Actual
Color "Contaminant" "Molecules" Conc. (pph)
Green PCB
Light Brown Pb
Dark Brown Fe
Red Chlorinated Doxin
Orange&Yellow Soil Matrix
Group Sample
Table for "sub-samples"
Actual # of Actual
Color "Contaminant" "Molecules" Conc. (pph)
Green PCB
Light Brown Pb
Dark Brown Fe
Red Chlorinated Doxin
Orange&Yellow Soil Matrix
Other
Analysis in Class
Draw conclusion regarding validity of you sample
1. Was either Group A "grab sample" representative of the actual sample
2. Why
3. Was Group B "grab sample" representative of the actual sample
4. Why
5 Combine both Group A "grab samples" and reevaluate
Speciation
6. In Group A what was the concentration of the two iron species?
Test Methods, Non-destructive, Destructive
7. What are the attributes of each?
8. Which can not be repeated?
Detection Limit
9. Evaluate the Detection limit
Sampling
10. Why should sample be mixed?
11. Why should sampler take a representative sample and not be allow to select by color?
12. What analytical step is collecting each color before counting analogous to?
Other Discussion
Color Key Representation
Green PCB
Light Brown Pb
Dark Brown Fe (chocolate =Fe+2, peanut butter =Fe+3)
Red Chlorinated Doxin
Orange & Yellow Soil Matrix
Other Unknown Larger
Notes on demonstration
One you can really sink you teeth into!
Reference Analytical Chemistry, vol. 64, no. 22, November 15, 92.
"Environmental Sampling for Trace Analysis" by Ray E. Clement, Ontario Ministry of the Environment.
3 Lb. mm,
(notes colors - yellow, orange, dk. brown, lt. brown, green, red)
2 Lb. Reese's Pieces
(notes colors - yellow, orange & dk brown)
(some large size coated candy as anomalies and low concentration contents or contaminants)
mm and Reese's Pieces Original Color code
Original Color code from article
Color Representation
Green PCB
Blue Pb
Brown Fe
Red Chlorinated Doxin
Purple & Pink Unknown Molecules
Orange & Yellow Soil Matrix
Key to mm and rees's pieces
Color Representation
Green PCB
Light Brown Pb
Dark Brown Fe (chocolate =Fe+2, peanut butter =Fe+3)
Red Chlorinated Doxin
Orange & Yellow Soil Matrix
(3 lb. mm and 1 lb. rees's pieces)
Points to bring out
similar to:
A sample is 25 mg and two 12 mg and one 1 mg sample is taken
inhomogeneity
fines in sample
different tests provide different information (chocolate =Fe+2, peanut butter =Fe+3)
Destructive vs. non- destructive
Mixing
moisture and wt. of sample
Taking a blind sample to prevent bias to favorite color.
Note-
Put in several of the large peanut butter mm in green, lt. brown and red as stray unknown molecules (contaminants)
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