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CHEM2017. ANALYTICAL CHEMISTRY. Mrs Billing Gate House 8 th floor, GH840 Caren.Billing@wits.ac.za 011 717-6768. ANALYTICAL CHEMISTS IN INDUSTRY - INTERFACES. Other chemists. Colleges Universities. Lawyers. Health & Safety. Peers, Supervisors. Production plants.

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chem2017
CHEM2017

ANALYTICAL CHEMISTRY

Mrs Billing

Gate House 8th floor, GH840

Caren.Billing@wits.ac.za

011 717-6768

slide2

ANALYTICAL CHEMISTS IN INDUSTRY - INTERFACES

Other

chemists

Colleges

Universities

Lawyers

Health

&

Safety

Peers,

Supervisors

Production

plants

Technical reps

In field

Contract

labs

Life

scientists

Analytical

chemist

Management

Sales

&

Marketing

Professional

organizations

Suppliers

Engineers

Statisticians

Government

agencies

precision and accuracy
PRECISION AND ACCURACY

PRECISION– Reproducibility of the result

ACCURACY – Nearness to the “true” value

slide6

TESTING ACCURACY

TESTING PRECISION

slide7

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)
slide8

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

slide9

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

slide10

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

slide12

Other ways of expressing the precision of the data:

  • Variance

Variance = s2

  • Relative standard deviation
  • Percent RSD / coefficient of variation
population data

For an infinite set of data,

n → ∞ :x → µands → σ

population mean population std. dev.

POPULATION DATA

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

slide14

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

slide15

EXAMPLE

Replicate results were obtained for the analysis of lead in blood. Calculate the mean and the standard deviation of this set of data.

slide17

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

slide18

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 20-950 mg/kg Pb

Near battery works 34-600 mg/kg Pb

Metal processing sites 45-2714 mg/kg Pb

slide19

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

CONFIDENCE INTERVALS

The confidence interval is given by:

where t is the value of student’s t taken from the table.

slide20

A ‘t’ test is used to compare sets of measurements.

Usually 95% probability is good enough.

slide21

Find x = 1.63

s = 0.131

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.

50% confidence:

t = 0.765 for n-1 = 3

There is a 50% chance that the true mean lies between 1.58 and 1.68 ppm

slide22

90%

1.78

x = 1.63

s = 0.131

1.68

50%

1.63

1.58

1.48

90% confidence:

t = 2.353 for n-1 = 3

There is a 90% chance that the true mean lies between 1.48 and 1.78 ppm

slide24

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!

slide25

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.

slide26

Where

3) COMPARISON OF INDIVIDUAL DIFFERENCES

Compare two sets of data whenmany 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

tcalc > ttable at 95% confidence level  difference between results is significant.

slide27

Example:

(di)

Are the two methods used comparable?

slide28

ttable = 2.571 for 95% confidence

tcalc < ttable

 difference between results is NOT significant.

slide29

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.

slide31

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:

12.2 12.4 12.5 12.6 12.9

Gap

Range

If Qcalc > Qtable discarded questionable point

slide32

Gap

Q =

Range

EXAMPLE:

The following replicate analyses were obtained when standardising a solution:0.1067M, 0.1071M, 0.1066M and 0.1050M. One value appears suspect. Determine if it can be ascribed to accidental error at the 90% confidence interval.

Arrange in increasing order: