1. CHEM2017 ANALYTICAL CHEMISTRY
Mrs Billing
Gate House 8th floor, GH840

2. ANALYTICAL CHEMISTS IN INDUSTRY - INTERFACES
Other
chemists
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Supervisors
Health
&
Safety
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In field
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plants
Life
scientists
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chemist
Contract
labs
Sales
&
Marketing
Management
Suppliers
Professional
organizations
Engineers
Statisticians
Government
agencies

3. STATISTICAL TESTS AND ERROR ANALYSIS

5. PRECISION AND ACCURACY
PRECISION – Reproducibility of the result
ACCURACY – Nearness to the “true” value

6. TESTING ACCURACY
TESTING PRECISION

7. SYSTEMATIC / DETERMINATE ERROR
Reproducible under the same conditions in the same experiment
Can be detected and corrected for
It is always positive or always negative
To detect a systematic error:
Use Standard Reference Materials
Run a blank sample
Use different analytical methods
Participate in “round robin” experiments (different labs and people running the same analysis)

8. RANDOM / INDETERMINATE ERROR
Uncontrolled variables in the measurement
Can be positive or negative
Cannot be corrected for
Random errors are independent of each other
Random errors can be reduced by:
Better experiments (equipment, methodology, training of analyst)
Large number of replicate samples
Random errors show Gaussian distribution for a large number of replicates
Can be described using statistical parameters

9. For a large number of experimental replicates the results approach an ideal smooth curve called the GAUSSIAN or NORMAL DISTRIBUTION CURVE
Characterised by:
The mean value – x
gives the center of the distribution
The standard deviation – s
measures the width of the distribution

10. The mean or average, x
 the sum of the measured values (xi) divided by the number of measurements (n)
The standard deviation, s
 measures how closely the data are clustered about the mean (i.e. the precision of the data)
NOTE: The quantity “n-1” = degrees of freedom

12. Other ways of expressing the precision of the data:
Variance
Variance = s2
Relative standard deviation
Percent RSD / coefficient of variation

13. POPULATION DATA For an infinite set of data, n → ∞ : x → µ and s → σ
population mean population std. dev.
The experiment that produces a small standard deviation is more precise .
Remember, greater precision does not imply greater accuracy.
Experimental results are commonly expressed in the form:
mean  standard deviation

14. The more times you measure, the more confident you are that your average value is approaching the “true” value.
The uncertainty decreases in proportion to

15. EXAMPLE
Replicate results were obtained for the analysis of lead in blood. Calculate the mean and the standard deviation of this set of data.
Replicate
[Pb] / ppb 1
752 2
756 3 4
751 5
760

16. Replicate
[Pb] / ppb 1
752 2
756 3 4
751 5
760
NB DON’T round a std dev. calc until the very end.

17. The first decimal place of the standard deviation is the last significant figure of the average or mean.
754  4 ppb Pb
Also:
Variance = s2

18. Motor vehicle emissions Lead plumbing Pewter Lead-based paints
Lead is readily absorbed through the gastro intestinal tract. In blood, 95% of the lead is in the red blood cells and 5% in the plasma. About 70-90% of the lead assimilated goes into the bones, then liver and kidneys. Lead readily replaces calcium in bones.
The symptoms of lead poisoning depend upon many factors, including the magnitude and duration of lead exposure (dose), chemical form (organic is more toxic than inorganic), the age of the individual (children and the unborn are more susceptible) and the overall state of health (Ca, Fe or Zn deficiency enhances the uptake of lead).
European Community Environmental Quality Directive – 50 g/L in drinking water
World Health Organisation – recommended tolerable intake of Pb per day for an adult – 430 g
Pb – where from?
Motor vehicle emissions
Lead plumbing
Pewter
Lead-based paints
Weathering of Pb minerals
Food stuffs < 2 mg/kg Pb
Next to highways mg/kg Pb
Near battery works mg/kg Pb
Metal processing sites mg/kg Pb

19. CONFIDENCE INTERVALS
The confidence interval is the expression stating that the true mean, µ, is likely to lie within a certain distance from the measured mean, x – Student’s t test
The confidence interval is given by:
where t is the value of student’s t taken from the table.

20. A ‘t’ test is used to compare sets of measurements.
Usually 95% probability is good enough.

21. Example:
The mercury content in fish samples were determined as follows: 1.80, 1.58, 1.64, 1.49 ppm Hg. Calculate the 50% and 90% confidence intervals for the mercury content.
Find x = 1.63
s = 0.131
50% confidence:
t = for n-1 = 3
There is a 50% chance that the true mean lies between 1.58 and 1.68 ppm

22. x = 1.63 s = 0.131 90% confidence: t = 2.353 for n-1 = 3 90% 50%
1.68
1.48
1.58
1.78
90%
50%
90% confidence:
t = for n-1 = 3
There is a 90% chance that the true mean lies between 1.48 and 1.78 ppm

23. Confidence intervals - experimental uncertainty

24. APPLYING STUDENT’S T: 1) COMPARISON OF MEANS
Comparison of a measured result with a ‘known’ (standard) value
tcalc > ttable at 95% confidence level
 results are considered to be different  the difference is significant!
Statistical tests are giving only probabilities.
They do not relieve us of the responsibility of interpreting
our results!

25. 2) COMPARISON OF REPLICATE MEASUREMENTS
Compare two sets of data when one sample has been measured many times in each data set.
For 2 sets of data with number of measurements n1 , n2 and means x1, x2 :
Where Spooled = pooled std dev. from both sets of data
Degrees of freedom = (n1 + n2 – 2)
tcalc > ttable at 95% confidence level  difference between results is significant.

26. 3) COMPARISON OF INDIVIDUAL DIFFERENCES
Compare two sets of data when many samples have been measure only once in each data set.
e.g. use two different analytical methods, A and B, to make single measurements on several different samples.
Perform t test on individual differences between results:
d = the average difference between methods A and B
n = number of pairs of data
Where
tcalc > ttable at 95% confidence level  difference between results is significant.

27. Are the two methods used comparable?
Example:
(di)
Are the two methods used comparable?

28. ttable = 2.571 for 95% confidence
tcalc < ttable
 difference between results is NOT significant.

29. F TEST COMPARISON OF TWO STANDARD DEVIATIONS
Fcalc > Ftable at 95% confidence level
 the std dev.’s are considered to be different  the difference is significant.

31. Q TEST FOR BAD DATA The range is the total spread of the data.
The gap is the difference between the “bad” point and the nearest value.
Example:
Gap
Range
If Qcalc > Qtable  discarded questionable point

32. Arrange in increasing order:
EXAMPLE:
The following replicate analyses were obtained when standardising a solution: M, M, M and M. One value appears suspect. Determine if it can be ascribed to accidental error at the 90% confidence interval.
Arrange in increasing order:
Q =
Gap
Range