Basic Sampling Techniques and Statistics

Basic Sampling Techniques and Statistics

WQT 134Aquatic Chemistry II

Standard Methods #1020, #1060 SamplingStandard Methods #1010 Statistics

WQT 134Aquatic Chemistry II

Standard Methods #1020, #1060 SamplingStandard Methods #1010 Statistics

Week 1 Objectives Week 1 Objectives

1. Proper Sample Collection

2. Understand basic statistical concepts

3. Grasp QA/QC

4. Understand IDL, MDL, and LDL, and how to calculate them

5. Use Excel spreadsheet for lab analysis

6. Understand the role of alkalinity in water and waste water

7. Understand how to measure alkalinity (SM #2010)

1. Proper Sample Collection

2. Understand basic statistical concepts

3. Grasp QA/QC

4. Understand IDL, MDL, and LDL, and how to calculate them

5. Use Excel spreadsheet for lab analysis

6. Understand the role of alkalinity in water and waste water

7. Understand how to measure alkalinity (SM #2010)

Reading assignment: American Public Health Association (APHA), American Water Works Association (AWWA) & Water Environment Federation (WEF). 1999.   Standard Methods for the Examination of Water and Wastewater, 20th edition

Reading assignment: American Public Health Association (APHA), American Water Works Association (AWWA) & Water Environment Federation (WEF). 1999.   Standard Methods for the Examination of Water and Wastewater, 20th edition

Sample Collection Sample Collection

WQT 134Environmental Chemistry II

STM. 20th edition. #1060

WQT 134Environmental Chemistry II

STM. 20th edition. #1060

Sample Collection #1060Sample Collection #1060

Grab Sample: Grab samples are single samples collected at a specific spot at a site over a short period of time (typically seconds or minutes). Thus, they represent a ‘‘snapshot’’ in both space and time of a sampling area

Composite Sample: Composite samples should provide a more representative sampling of heterogeneous matrices in which the concentration of the analytes of interest may vary over short periods of time and/or space .

Grab Sample: Grab samples are single samples collected at a specific spot at a site over a short period of time (typically seconds or minutes). Thus, they represent a ‘‘snapshot’’ in both space and time of a sampling area

Composite Sample: Composite samples should provide a more representative sampling of heterogeneous matrices in which the concentration of the analytes of interest may vary over short periods of time and/or space .

•Representative Sample: sample should represent the whole distribution sample

Sample Collection #1060Sample Collection #1060

Why is proper collection of a sample important?

•It is an old axiom that the result of any testing method can be no better than the sample on which it is performed.

Why do we care?

•The analysis will govern sample collection.

Why is proper collection of a sample important?

•It is an old axiom that the result of any testing method can be no better than the sample on which it is performed.

Why do we care?

•The analysis will govern sample collection.

Sample Collection #1060Sample Collection #1060Sample deterioration?

•Obtain a sample that meets the requirements of the sampling program and handle it so that it does not deteriorate or become contaminated or compromised before it is analyzed.

Sample collection?•Clean sample bottles especially when sampling and analyzing for very low analyte levels. •Collect a 1-L sample for most physical and chemical analyses. Keep cool•Representative sample•Pre-rinse only if no preservative added•Leave no head space

Sample deterioration?

•Obtain a sample that meets the requirements of the sampling program and handle it so that it does not deteriorate or become contaminated or compromised before it is analyzed.

Sample collection?•Clean sample bottles especially when sampling and analyzing for very low analyte levels. •Collect a 1-L sample for most physical and chemical analyses. Keep cool•Representative sample•Pre-rinse only if no preservative added•Leave no head space

Sample Collection #1060Sample Collection #1060Field Sampling

• Noncomposite samples for acidity, alkalinity, chlorine residual, nitrate, dissolved oxygen,

temperature, and pH. All on ice!• BOD analysis=composite=refrigerate• Microbial analysis= no composites=on ice

Note: Field Observations are critical!water temperature, weather conditions, water level, stream flow, post-collection conditions

Field Sampling

• Noncomposite samples for acidity, alkalinity, chlorine residual, nitrate, dissolved oxygen,

temperature, and pH. All on ice!• BOD analysis=composite=refrigerate• Microbial analysis= no composites=on ice

Note: Field Observations are critical!water temperature, weather conditions, water level, stream flow, post-collection conditions

Sample Collection #1060Sample Collection #1060Things to keep in mind….

•Avoid areas of excessive turbulence •Avoid sampling at weirs •Collect samples beneath the surface inquiescent areas and open sampling container below surface with the mouth directed toward the current •Composite samples are required, ensure that sample constituents are not lost during compositing. •Be safety conscious•Label samples adequately CHAIN OF CUSTODY!!

Things to keep in mind….

•Avoid areas of excessive turbulence •Avoid sampling at weirs •Collect samples beneath the surface inquiescent areas and open sampling container below surface with the mouth directed toward the current •Composite samples are required, ensure that sample constituents are not lost during compositing. •Be safety conscious•Label samples adequately CHAIN OF CUSTODY!!

1. Samples must be representative of the water distribution system.

2. Water taps used for sampling should be free of aerators, strainers, hose attachments, mixing type faucets, and purification devices.

3. Cold water taps should be used.

4. The service line must be cleared before sampling by maintaining a steady water flow for at least two minutes (until the water changes temperature).

5. At least 100 mL of sample must be collected, allowing at least a 1-inch air space to facilitate mixing of the sample by shaking.

6. Immediately after collection, a sample information form should be completed= CHAIN OF CUSTODY

1. Samples must be representative of the water distribution system.

2. Water taps used for sampling should be free of aerators, strainers, hose attachments, mixing type faucets, and purification devices.

3. Cold water taps should be used.

4. The service line must be cleared before sampling by maintaining a steady water flow for at least two minutes (until the water changes temperature).

5. At least 100 mL of sample must be collected, allowing at least a 1-inch air space to facilitate mixing of the sample by shaking.

6. Immediately after collection, a sample information form should be completed= CHAIN OF CUSTODY

Water Distribution Sample Collection

Water Distribution Sample Collection

· Name of system (public water system site identification number, if available)· Sample identification (if any)· Sample site location · Sample type (e.g., routine distribution system sample, repeat sample, raw or process water, other special purpose sample)· Date and time of collection· Analysis required· Disinfectant residual· Name of sampler and organization (if not the water system)· Sampler's initials· Person(s) transporting the samples from the system to the laboratory (if not the sampler) · Transportation condition (e.g., <10°C, protection from sunlight). If a commercial shipper was used, shipping records should be available.· Any remarks

· Name of system (public water system site identification number, if available)· Sample identification (if any)· Sample site location · Sample type (e.g., routine distribution system sample, repeat sample, raw or process water, other special purpose sample)· Date and time of collection· Analysis required· Disinfectant residual· Name of sampler and organization (if not the water system)· Sampler's initials· Person(s) transporting the samples from the system to the laboratory (if not the sampler) · Transportation condition (e.g., <10°C, protection from sunlight). If a commercial shipper was used, shipping records should be available.· Any remarks

Water Distribution Sample Collection

Water Distribution Sample Collection

Which of the following terms refers to the addition of chemicals to a sample in the field to prevent water

quality indicators from changing before final

measurements are performed?

Which of the following terms refers to the addition of chemicals to a sample in the field to prevent water

quality indicators from changing before final

measurements are performed?

Sta

ndardiza

tion

Buffe

r

Pre

serv

atio

n

Titr

atio

n

0% 0%0%0%

1. Standardization2. Buffer3. Preservation4. Titration

1. Standardization2. Buffer3. Preservation4. Titration

A ____ sample is a discrete sample that is collected

manually.

A ____ sample is a discrete sample that is collected

manually.

Gra

b

Com

posite

Flo

w p

roporti

onal

Tem

poral

0% 0%0%0%

1. Grab2. Composite3. Flow proportional4. Temporal

1. Grab2. Composite3. Flow proportional4. Temporal

A ________ sample consists of a collection of individual samples

collected at regular intervals throughout the day

A ________ sample consists of a collection of individual samples

collected at regular intervals throughout the day

Com

posite

Gra

b

Wei

ghted

ave

rage

Fin

al e

ffluen

t

0% 0%0%0%

1. Composite2. Grab3. Weighted average4. Final effluent

1. Composite2. Grab3. Weighted average4. Final effluent

A single sample of water taken at one time from one place is called

a _________ sample.

A single sample of water taken at one time from one place is called

a _________ sample.

Gra

b

Com

posite

Rep

rese

ntat

ive

0% 0%0%

1. Grab2. Composite3. Representative

1. Grab2. Composite3. Representative

Samples should only be collected where the water is

______ ____________.

Samples should only be collected where the water is

______ ____________.

Wel

l mix

ed

Ove

rflow

ing w

eirs

Bet

wee

n pro

cess

es

Sta

nding q

uietly

0% 0%0%0%

1. Well mixed2. Overflowing weirs3. Between processes4. Standing quietly

1. Well mixed2. Overflowing weirs3. Between processes4. Standing quietly

_______ of ________ is a legal term for an unbroken sequence

of possession from sample collection through analysis.

_______ of ________ is a legal term for an unbroken sequence

of possession from sample collection through analysis.

Chai

n Cust

ody

Chai

n Com

man

d

Chai

n Sam

ple

0% 0%0%

1. Chain Custody2. Chain Command3. Chain Sample

1. Chain Custody2. Chain Command3. Chain Sample

One mL is what fraction of a L?One mL is what fraction of a L?

1/10

1/100

1/1000

1/100000

0% 0%0%0%

1. 1/10

2. 1/100

3. 1/1000

4. 1/100000

1. 1/10

2. 1/100

3. 1/1000

4. 1/100000

What is the most common preservation method for

samples?

What is the most common preservation method for

samples?

Coolin

g to 4

deg

. C

Dec

hlorin

atio

n

Red

uctio

n

Aci

difica

tion

0% 0%0%0%

1. Cooling to 4 deg. C2. Dechlorination3. Reduction4. Acidification

1. Cooling to 4 deg. C2. Dechlorination3. Reduction4. Acidification

9/5(degrees C) + 32 = ______9/5(degrees C) + 32 = ______

Cel

sius

Fah

renhe

it

Kel

vin

0% 0%0%

1. Celsius

2. Fahrenheit

3. Kelvin

1. Celsius

2. Fahrenheit

3. Kelvin

•Given•Formula:•Solve:

•Given•Formula:•Solve:

Convert 16oF to oC? Convert 16oF to oC?

-23

OC

-9 O

C

26

OC

0% 0%0%

16 oF oC= 5 * (oF – 32) 9oC= 5 * (16-32)/9

oC= -9

16 oF oC= 5 * (oF – 32) 9oC= 5 * (16-32)/9

oC= -9

oC= 5 * (oF – 32) 9oC= 5 * (16-32)/9

oC= -9

oC= 5 * (oF – 32) 9oC= 5 * (16-32)/9

oC= -9

1. -23 OC

2. -9 OC

3. 26 OC

1. -23 OC

2. -9 OC

3. 26 OC

Samples taken for routine analysis should be preserved

by:

Samples taken for routine analysis should be preserved

by:

0% 0%0%0%

1. refrigerating

2. filtering

3. boiling

4. sterilizing

1. refrigerating

2. filtering

3. boiling

4. sterilizing

What is the maximum recommended holding time

for a sample that is to be analyzed for pH?

What is the maximum recommended holding time

for a sample that is to be analyzed for pH?

0% 0%0%0%

1. None; it must be analyzed immediately

2. 48 hours

3. 7 days

4. 14 days

1. None; it must be analyzed immediately

2. 48 hours

3. 7 days

4. 14 days

What is the minimum number of pH standards needed for calibration of a pH meter?

What is the minimum number of pH standards needed for calibration of a pH meter?

0% 0%0%0%

1. 1

2. 2

3. 3

4. 4

1. 1

2. 2

3. 3

4. 4

Basic Statistics Basic Statistics

WQT 134Environmental Chemistry II

STM. 20th edition. #1010 & 1020

WQT 134Environmental Chemistry II

STM. 20th edition. #1010 & 1020

Statistics Key Words/EquationsStatistics Key Words/Equations• Mean: is simply the sum of all values divided by the number of values

» µ = (∑ixi)/n

• Standard Deviation: is a measure of the spread of values » σ = [∑(x−µ)2/n]1/2.

• Coefficient of Variation: normalizes the standard deviation and sometimes facilitates making direct comparisons among analyses that include a wide range of concentrations σ/µ, with its estimate s/x

• Median: middle value of a sample population• Mode: most frequently occurring number in a sample population

• Mean: is simply the sum of all values divided by the number of values » µ = (∑ixi)/n

• Standard Deviation: is a measure of the spread of values » σ = [∑(x−µ)2/n]1/2.

• Coefficient of Variation: normalizes the standard deviation and sometimes facilitates making direct comparisons among analyses that include a wide range of concentrations σ/µ, with its estimate s/x

• Median: middle value of a sample population• Mode: most frequently occurring number in a sample population

Another word for the average is the ______________?

Another word for the average is the ______________?

Mea

n

Norm

Geo

met

ric m

ean

Hig

hest p

robab

ility

0% 0%0%0%

1. Mean

2. Norm

3. Geometric mean

4. Highest probability

1. Mean

2. Norm

3. Geometric mean

4. Highest probability

The mode is the most frequently occurring number in a data set?The mode is the most frequently occurring number in a data set?

Tru

e

Fal

se

0%0%

1. True

2. False

1. True

2. False

Statistics Key Words/EquationsStatistics Key Words/Equations• Accuracy: combination of bias and precision of an

analytical procedure, which reflects the closeness of a measured value to a true value.

• Precision: measure of the degree of agreement among replicate analyses of a sample, usually expressed as the standard deviation

• Accuracy: combination of bias and precision of an analytical procedure, which reflects the closeness of a measured value to a true value.

• Precision: measure of the degree of agreement among replicate analyses of a sample, usually expressed as the standard deviation

Statistics QA/QC KeyStatistics QA/QC Key

• Quality assessment: procedure for determining the quality of laboratory measurements by use of data from internal and external quality control measures

• Quality assurance: a definitive plan for laboratory operation that specifies the measures used to produce data of known precision and bias.

• Quality control: set of measures within a sample analysis methodology to assure that the process is in control.

• Quality assessment: procedure for determining the quality of laboratory measurements by use of data from internal and external quality control measures

• Quality assurance: a definitive plan for laboratory operation that specifies the measures used to produce data of known precision and bias.

• Quality control: set of measures within a sample analysis methodology to assure that the process is in control.

QA StepsQA Steps1. Appropriate signatures

2. Test Performed by Laboratory

3. Sample Handling Procedures Checklist

4. Standard Operating Procedures

5. Data Verification Practices

6. Chain of custody

1. Appropriate signatures

2. Test Performed by Laboratory

3. Sample Handling Procedures Checklist

4. Standard Operating Procedures

5. Data Verification Practices

6. Chain of custody

QC StepsQC Steps1. Show yearly results of MDL

2. Run Internal Blank

3. Run duplicates

4. Internal Standards

5. Blind Samples

6. Routine Calibration

1. Show yearly results of MDL

2. Run Internal Blank

3. Run duplicates

4. Internal Standards

5. Blind Samples

6. Routine Calibration

Quality control samples are analyzed for all of the following

reasons EXCEPT:

Quality control samples are analyzed for all of the following

reasons EXCEPT:

Chec

k fo

r Conta

min

...

Ver

ify p

reci

sion

Ver

ify a

ccura

cy

Det

erm

ine

if in

terfe

r...

To b

oost th

e eg

o of .

..

0% 0%

100%

0%0%

1. Check for Contamination

2. Verify precision

3. Verify accuracy

4. Determine if interferences are present.

5. To boost the ego of the analyst.

1. Check for Contamination

2. Verify precision

3. Verify accuracy

4. Determine if interferences are present.

5. To boost the ego of the analyst.

Normal DistributionNormal Distribution• Normal Distribution: If a measurement is repeated many times under essentially identical conditions, the results of each measurement, x, will be distributed randomly about a mean value (arithmetic average) because of uncontrollable or experimental error.

• Normal Distribution: If a measurement is repeated many times under essentially identical conditions, the results of each measurement, x, will be distributed randomly about a mean value (arithmetic average) because of uncontrollable or experimental error.

68.27% of the measurements lie between µ ± 1σ95.45% between µ ± 2σ, 99.70% between µ ± 3σ.

It is sufficiently accurate to state that 95% of the values are within ±2σ and 99% within ±3σ.

68.27% of the measurements lie between µ ± 1σ95.45% between µ ± 2σ, 99.70% between µ ± 3σ.

It is sufficiently accurate to state that 95% of the values are within ±2σ and 99% within ±3σ.

AverageAverage•Average: Two feet in bucket of ice water, two feet on hot coals.

On average I feel great?

•Average: Two feet in bucket of ice water, two feet on hot coals.

On average I feel great?

Accuracy and PrecisionAccuracy and Precision•Accuracy: refers to how closely a measured value agrees with the correct value.

•Precision: refers to how closely individual measurements agree with each other.

•Accuracy: refers to how closely a measured value agrees with the correct value.

•Precision: refers to how closely individual measurements agree with each other.

accurate(the average is accurate)not precise

accurate(the average is accurate)not precise

precisenot accurate

precisenot accurate

accurateand

precise

accurateand

precise

inaccuratenot precise inaccurate

not precise

**Assume aim is directed at bulls eye***Assume aim is directed at bulls eye*

Analytical PrecisionAnalytical PrecisionInstrumental detection level (IDL): the constituent concentration that produces a signal greater than five times the signal/ noise ratio of the instrument.

1.645 times the standard deviation of the blank

Method detection level (MDL): For seven replicates of the sample, the mean must be 3.14s above the blank where s is the standard deviation of the seven replicates. The method detection limit (MDL) is the only one designed to be determined in your laboratory using your chemicals, equipment, and technicians.

Compute MDL from replicate measurements one to five times the actual MDL. The MDL will be larger than the LLD because of the few replications and the sample processing steps and may vary with constituent and matrix.

Lower level of detection (LLD): the constituent concentration in reagent water that produces a signal 3.219s above the mean of blank analyses

Instrumental detection level (IDL): the constituent concentration that produces a signal greater than five times the signal/ noise ratio of the instrument.

1.645 times the standard deviation of the blank

Method detection level (MDL): For seven replicates of the sample, the mean must be 3.14s above the blank where s is the standard deviation of the seven replicates. The method detection limit (MDL) is the only one designed to be determined in your laboratory using your chemicals, equipment, and technicians.

Compute MDL from replicate measurements one to five times the actual MDL. The MDL will be larger than the LLD because of the few replications and the sample processing steps and may vary with constituent and matrix.

Lower level of detection (LLD): the constituent concentration in reagent water that produces a signal 3.219s above the mean of blank analyses

Analytical PrecisionAnalytical Precision

minimum quantitation level (MQL): the constituent concentration that produces a signal sufficiently greater than the blank that it can be detected within specified levels by good laboratories during routine operating conditions.

Typically it is the concentration that produces a signal 10s above the reagent water blank signal.

minimum quantitation level (MQL): the constituent concentration that produces a signal sufficiently greater than the blank that it can be detected within specified levels by good laboratories during routine operating conditions.

Typically it is the concentration that produces a signal 10s above the reagent water blank signal.

Both of these quality control samples can be used to measure

accuracy and precision.

Both of these quality control samples can be used to measure

accuracy and precision.

Sta

ndards

and

Dupl...

Bla

nks a

nd Sta

ndard

s

Bla

nks a

nd Dup

licat

es

Duplic

ates

and

Spik

es

36%

0%

9%

55%1. Standards and

Duplicates

2. Blanks and Standards

3. Blanks and Duplicates

4. Duplicates and Spikes

1. Standards and Duplicates

2. Blanks and Standards

3. Blanks and Duplicates

4. Duplicates and Spikes

This type of quality control sample is used to check for

interferences.

This type of quality control sample is used to check for

interferences.

Spik

es

Duplic

ate

Sta

ndards

Bla

nks

17%

50%

17%17%

1. Spikes

2. Duplicate

3. Standards

4. Blanks

1. Spikes

2. Duplicate

3. Standards

4. Blanks

Relative Standard DeviationRelative Standard DeviationRelative standard deviation (RSD): is a measure of precision, calculated by dividing the standard deviation for a series of measurements by the average measurement.

RSD= σ/µ CV = σ/µ *100

CV % Rule of Thumb For WQT 134 0-5% =excellent precision 5-10% =acceptable precision 10-20%= Poor precision

20%>=Houston we have a problem!

Relative standard deviation (RSD): is a measure of precision, calculated by dividing the standard deviation for a series of measurements by the average measurement.

RSD= σ/µ CV = σ/µ *100

CV % Rule of Thumb For WQT 134 0-5% =excellent precision 5-10% =acceptable precision 10-20%= Poor precision

20%>=Houston we have a problem!

Duplicates should agree with their original samples by this

margin.

Duplicates should agree with their original samples by this

margin.

Plu

s or

Min

us 2

0% R

e...

Plu

s or

Min

us 1

0% R

e...

Plu

s or

Min

us 2

0%

Plu

s or

Min

us 1

0%

20%

50%

0%

30%

1. Plus or Minus 20% Relative Percent Difference

2. Plus or Minus 10% Relative Percent Difference

3. Plus or Minus 20%

4. Plus or Minus 10%

1. Plus or Minus 20% Relative Percent Difference

2. Plus or Minus 10% Relative Percent Difference

3. Plus or Minus 20%

4. Plus or Minus 10%

The statistical calculation done to determine the spread of a set of measurements is called the

______________.

The statistical calculation done to determine the spread of a set of measurements is called the

______________.

Sta

ndard D

evia

tion

Rel

ativ

e Per

vasi

ve D

i...

Per

cent D

evia

tion

Sta

ndard E

rror

100%

0%0%0%

1. Standard Deviation

2. Relative Pervasive Difference

3. Percent Deviation

4. Standard Error

1. Standard Deviation

2. Relative Pervasive Difference

3. Percent Deviation

4. Standard Error

Problem #1Problem #1Some WQT 134 students measure pH on the same sample! The results are as follows:

AB= 7.2DO=7.0KO=6.9ML=5.5EC=7.3

Calculate mean= 7.2+7.0+6.9+5.5+7.3 = 6.78 5

Some WQT 134 students measure pH on the same sample! The results are as follows:

AB= 7.2DO=7.0KO=6.9ML=5.5EC=7.3

Calculate mean= 7.2+7.0+6.9+5.5+7.3 = 6.78 5

Problem #1 AVG, ExcelProblem #1 AVG, Excel

Problem #1, STDEV, Excel continued

Problem #1, STDEV, Excel continued

Calculate standard deviation= »σ = [∑(x−µ)2/n]1/2.

Calculate standard deviation= »σ = [∑(x−µ)2/n]1/2.

Problem #1, RSD, Excel continued

Problem #1, RSD, Excel continued

Calculate RSD RSD= σ/µ

Calculate RSD RSD= σ/µ

Problem #1, CV, Excel continuedProblem #1, CV, Excel continued

Calculate CVCV= σ/µ * 100

Calculate CVCV= σ/µ * 100

Problem #1, Final Analysis, Excel continued

Problem #1, Final Analysis, Excel continued

CV % Rule of Thumb For WQT 134 0-5% =excellent precision 5-10% =acceptable precision 10-20%= Poor precision

20%>=Houston we have a problem!

CV % Rule of Thumb For WQT 134 0-5% =excellent precision 5-10% =acceptable precision 10-20%= Poor precision

20%>=Houston we have a problem!

Problem #2, IDLProblem #2, IDL

Instrumental detection level (IDL): the lowest limit that the instrument can detect. It is determined on samples which have not gone through any sample preparation steps.

AB= .0024 mg/LDO=.0023 mg/LKO=.0026 mg/LML=.0027 mg/LEC=.0025 mg/L

Calculate IDL= 1.645 X standard deviation of the blank

IDL=1.645*.000158= .0026 mg/L

Instrumental detection level (IDL): the lowest limit that the instrument can detect. It is determined on samples which have not gone through any sample preparation steps.

AB= .0024 mg/LDO=.0023 mg/LKO=.0026 mg/LML=.0027 mg/LEC=.0025 mg/L

Calculate IDL= 1.645 X standard deviation of the blank

IDL=1.645*.000158= .0026 mg/L

Problem #3 MDLProblem #3 MDLOne of the procedures outlined in 40 CFR 136 for

determining the MDL is to prepare the analyte concentration at a level one to five times the estimated detection limit and run it multiple times.

1.Make solution of the analyte that is one to five times the estimated detection.

2. Test this solution seven or more times, then determine the standard deviation of the data set.

3. The method detection limit is calculated according to the formula:

MDL = Student’s t value (from a table) x standard deviation.

One of the procedures outlined in 40 CFR 136 for determining the MDL is to prepare the analyte concentration at a level one to five times the estimated detection limit and run it multiple times.

1.Make solution of the analyte that is one to five times the estimated detection.

2. Test this solution seven or more times, then determine the standard deviation of the data set.

3. The method detection limit is calculated according to the formula:

MDL = Student’s t value (from a table) x standard deviation.

Problem #3 MDLProblem #3 MDLA IDL for a phosphate procedure is 0.045 mg/L.Make a solution of 0.175 mg/L phosphate, which is

approximately four times the estimated limit 2. Results of multiple analysis (mg/L) 0.190, 0.194, 0.166, 0.174, 0.149, 0.183, 0.153,

0.144, 0.173

3. Determine STDEV 0.019 = mg/L.

4. Use MDL equation: MDL = Student’s t value (from table) x std. deviation

= 2.821 x 0.019 mg/L= 0.056 mg/L

A IDL for a phosphate procedure is 0.045 mg/L.Make a solution of 0.175 mg/L phosphate, which is

approximately four times the estimated limit 2. Results of multiple analysis (mg/L) 0.190, 0.194, 0.166, 0.174, 0.149, 0.183, 0.153,

0.144, 0.173

3. Determine STDEV 0.019 = mg/L.

4. Use MDL equation: MDL = Student’s t value (from table) x std. deviation

= 2.821 x 0.019 mg/L= 0.056 mg/L

Problem #3 Excel MDLProblem #3 Excel MDL

Problem #4 LDLProblem #4 LDL

The lowest limit is actually 2.5 times higher than the MDL.

1. Use LDL equation: LDL = 2.5 X MDL = 2.5 X 0.056 mg/L = 0.14 mg/L

The lowest possible value that can be detected with this method is 0.14 mg/L anything below this value is suspect!

The lowest limit is actually 2.5 times higher than the MDL.

1. Use LDL equation: LDL = 2.5 X MDL = 2.5 X 0.056 mg/L = 0.14 mg/L

The lowest possible value that can be detected with this method is 0.14 mg/L anything below this value is suspect!

Today’s objective: to become proficient with sample collection and statistical analysis has

been met.

Today’s objective: to become proficient with sample collection and statistical analysis has

been met.

Stro

ngly A

gree

Agre

e

Neu

tral

Dis

agre

e

Stro

ngly D

isag

...

17%

33%

8%

17%

25%1. Strongly Agree

2. Agree

3. Neutral

4. Disagree

5. Strongly Disagree

1. Strongly Agree

2. Agree

3. Neutral

4. Disagree

5. Strongly Disagree

To improve my knowledge pertinent to the subject matter

I would like to??

To improve my knowledge pertinent to the subject matter

I would like to??

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1. Have the instructor provide more math/stats blackboard homework assignments

2. Have data available on the webpage in Excel to practice my analysis

3. Have the instructor provide more blackboard reading assignments

4. Have a quiz to review the subject matter

5. None of the above

1. Have the instructor provide more math/stats blackboard homework assignments

2. Have data available on the webpage in Excel to practice my analysis

3. Have the instructor provide more blackboard reading assignments

4. Have a quiz to review the subject matter

5. None of the above