ANALYTICAL CHEMISTRY Chem 333

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ANALYTICAL CHEMISTRYChem 333
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Chapter 4Statistics
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Gaussian Distribution
Bell-Shaped Curve Described by

s standard deviation m mean
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Gaussian Curve
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Standard Deviation and Mean
Can never truly measure m or s. These are values
for an infinite data set (n infinity).
We can measure s and x. These are values for a
finite data set.
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Mean

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Standard Deviation

Degrees of Freedom n-1 Variance square of std.
dev. s2 Relative Std. Dev. 100s/mean
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Fishing Example
My wife and I went fishing at Lake Whatcom this
past weekend. We caught the following fish
Me 12 13.5 16 14 9 14.5
Wife 18 22 17 13 15 19
Me mean 13.17 s 2.42 Wife mean 17.33 s
3.14
Lake m 16.52 s 4.97
Learn to use your calculator!!! p. 71 Harris
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What Does the Std Dev Mean?
Overhead
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Gaussian Curve
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Understanding the Gaussian Shape
Pipet Calibration Overhead
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Normal Error Curve

A normal error curve is a Gaussian curve whose
area is unity.
Area 1
Enables one to calculate the probability of
observing a value in a particular range.
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Normal Error Curve
Express deviations from the mean as multiples of
the standard deviation.

Area 1

in Range

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Fishing Example
While fishing at Lake Whatcom, I caught fish
averaging 14 in length, with s 4.00. What are
the chances my next fish will be between 14 and
16?
Solution 1) Use Normalized Error Curve
2) Compute Area Under Curve for Specified Range
19.15 Probability fish is between 14 and 16.
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Fishing Example
What are the chances the next fish will be
between 12 and 16?
Solution Distribution Symmetric Around Mean
38.30 Probability fish is between 12 and 16.
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Fishing Example
What are the chances it will be between 16 and
18?
Solution 1) Solve for probability between
14-18 2) Solve for 14-16 and substract
14.98 Probability fish is between 16 and 18.
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Fishing Example
What are the chances it will be longer than 21?
You need to interpolate!

There is a 4 probability it will be longer than
21
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Uncertainty in a Measurement
3 Ways
Okay, but report N!!!
1.
2.
Better
3.
Best
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Standard Deviation of the Mean
Used occasionally to report uncertainty

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Confidence Intervals

Look up t for degrees of freedom (n-1) in
Students t table
Table 4-2
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Student t
Table 4-2
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What Do Confidence Limits Mean?
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Flintstone Vitamins
Seven measurements of the Zn content of
Flintstones vitamin-mineral supplements yielded
14.1, 15.2, 14.8, 15.5, 15.3, 14.6, and 14.9 mg
Zn per tablet.
Report the average value using each of the three
listed ways.
1) 14.9 0.5 mg Zn per tablet (N 7)
2) 14.9 0.2 mg Zn per tablet (N 7)
3) 14.9 0.4 mg Zn per tablet
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Blood Alcohol
Youre a Washington State Trooper and you arrest
an individual on the suspicion of driving while
under the influence of alcohol. You take him/her
to jail where a blood alcohol test is
administered. You measure the blood alcohol
level three times and find
0.084, 0.089, 0.079
Report the mean and uncertainty at the 95 C.L.
so that it may be introduced into court.
0.08 0.01 blood alcohol
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Comparing Tabulated Values
Case 1 Comparing results to a known value
Case 2 Comparing results to a known value
Case 3 Comparing individual differences
Only Consider Cases 1 2
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Glucose Sensor (Case 1)
You and your advisor have invented a new
non-prick blood glucose sensor. Youre excited
because you intend to patent this invention and
make enough money to pay off your school loans.
However, you must first see if the results are in
agreement with values obtained from accepted
methods.
Your GlucoSensor reads (mg/dL) 127, 125, 123,
130, 131, 126, 129.
Accepted Value 129.
Does your method gives results that differ
significantly at the 95 C.L.?
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Blood Cell Count (Case 2)
Red Blood Counts O.J. 5050, 5030,
5080 Glove 5090, 5120, 5130
Making millions off of your GlucoSensor, you
decide to pursue a self-financed career in film.
The knowledge gained in Chem 333 inspires you to
produce a PBS series on forensic science. In one
episode the red blood cell counts obtained from a
murder suspect and a bloody glove found at the
crime scene are compared.
Are the samples significantly different at the
95 C.L.?
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Blood Cell Count (Case 2)
Red Blood Counts O.J. 5050, 5030,
5080 Glove 5090, 5120, 5130
Equations Youll Need

Are the samples significantly different at the
95 C.L.?
Yes they are different at the 95 C.L., 3.2 gt 2.5
See p. 79 of text Eq (8), (9), (8a), (9a)
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Q-Test
Use to decide when to throw out inconsistent
datum

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Cold Fusion
After graduating from Western with honors, youre
now working in the laboratory of Dr. Martin
Fleischmann in the South of France. You make the
following power measurements from a Pd/D
electrochemical cell
0.3 W 0.1W 0.2W 0.2W 5.0W
You think the 5W reading is suspicious and want
to see if you should discard it at the 90 C.L.
Yes, it should be discarded based on Q gt 0.64
Cold Fusion Times
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NaOH Concentration
Dr. Emory, how do I calculate and report the
uncertainty in my NaOH concentration?
1. Perform replicate titrations and reject any
outlying points based on
(a) Q-Test (b) Other knowledge (e.g., spilling,
retainer fell into the beaker, etc.)
2. Calculate mean and std. dev. of the remaining
points
3. Report the mean 95 confidence interval
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QA/QC Program
QA/QC stands for Quality Assurance and Quality
Control
A QA/QC program is a set of guidelines developed
to ensure the validity of results.
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QA/QC Program
Typical Components
1) Chain of Custody
Keep track o f who, what, where, and when the
sample has been handled.
2) Sample Blank
Blank sample (e.g. water, sand) that accompanies
sample in its journey
3) Method Blank
This is a blank sample prepared during analysis
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QA/QC Program
Typical Components
4) Blank Spike (Method Spike)
A known amount of analyte is added to a blank
sample. A percent recovery for the analyte is
calculated.
5) Matrix Spike
A known amount of analyte is added (spiked) to
the sample. A percent recovery for the analyte
is calculated.
6) Check Standard
A standard from a source other than the standards
used to construct the calibration curve is
analyzed.
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Control Charts Process Monitoring
95.5 between m /- 2s
99.7 between m /- 3s
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Control Charts Matrix Spikes
Overhead