Error Analysis. The big questions are: - What value best represents a set of measurements and how reliable is it?

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2 The big questions are: - What value best represents a set of measurements and how reliable is it?

3 An ICP analysis yields LOTS of data typically, 9 individual measurements for each analyte for each sample (3 replicates * 3 runs) the report sequence or ASCII data file gives you the mean (average) of the replicates and the standard deviation of the replicates What does that REALLY mean?

4 Assuming a normal (gaussian) distribution of the data: 1st question - what is the most probable value for the population? 1st approach - take the mean (average) 2nd approach - take the median useful if there are few measurements and asymmetry is involved

5 Mean: x = Ʃ(x i ) / n Median = the value of the middle item, or the mean of the values of the two middle items, when the data are arranged in an increasing or decreasing order of magnitude

6 E.g. 42, 39, 31, 35, and 38 Median = 38

7 Generally speaking, the median of a set of n items, where n is odd, is the value of the n +1 / 2 th largest item E.g. The median of 25 numbers is the value of the (25 +1) /2 = 13 th largest number

8 By definition, the mean is heavily influenced by extreme values while the median is not Outliers strongly effect the mean value, but show little to no effect on median E.g.: xi = 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 8, 9, 9, 17 Median = 6 Mean = 6.867

9 Dispersion of a population Ok, you ve decided to take the mean - How reliable is it? Two measures to judge reliability of the mean: - Range and Standard Deviation

10 Range: R = x max x min strongly influenced by extreme values with n being sufficiently large (> 9), you can use quantiles to buffer the range against outliers n = 10, cast out high and low. Left with n = 8, the range of which is called the 10-90% range if n is large enough, can bracket the data in the 17-83% range (will bound ~2/3 of all data)

11 Taking the mean (or median) of the bounded range should provide a good estimate of the true value Why 17 th and 83 rd quantiles? Encompasses ~2/3 of the data points, which is very close the interval of the mean +/- 1 standard deviation (SD)

12 The Standard Deviation most common measure of dispersion robust statistic - will provide meaningful data even if the population does not strictly meet the definition of the normal population

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14 Relative standard deviation (or coefficient of variation c.o.v.) RSD (%) = 100*sx / mean

15 Predominant sources of error in ICP-MS analysis: weighing/volume error error in standard concentration instrument error

16 How does one evaluate the true error or uncertainty associated with an ICP-MS analysis? Sample preparation errors are probably greater than instrument error

17 SO...strictly speaking, replicates should be conducted by preparing multiple aliquots of the same sample and running them multiple times However, this is generally impractical to do for all samples A better idea is to do this for maybe one or two samples

18 Reproducibility and Repeatability Reproducibility = standard deviation of a method over a long time frame Repeatability = standard deviation of a method over a short time frame (with all controllable conditions being the same)

19 Reporting ICP Data due to systematic and random errors, ICP data should rarely, if ever, be reported to greater than 3 or 4 significant digits

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21 Multicollector(MC)-ICP-MS Models: - NuPlasma from Nu Instruments, UK - Neptune Plus, Thermo Scientific, Germany Primary use Determination of the isotopic composition of elements from geological materials in both solution or laser ablation mode

22 Analytical Advantages of an ICP- MC-ICP-MS instrument Rapid isotopic analysis compared to TIMS (thermal ionisation mass spectrometry) Higher ionization efficiency compared to TIMS Very low detection limits (i.e. most elements << 1 ppm) Spectral simplicity Very few interferences, and the overlaps that do occur are predictable; thus these are corrected by evaluating other isotopes of the same element

23 NuPlasma Instrument Outline Doublefocusing mass spectrometer Electrostatic analyser Plasma & Introduction system Transfer lenses Laminated Magnet Zoom lens Detectors

24 Production of flat top peak shapes

25 Zoom lenses LENS 1 LENS 2

26 Detectors

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29 Ion counters (3) discrete dynode electron multipliers

30 ISIS New generation MC-ICP- MS instrument from Nu Instruments Collector configuration array shall contain more ion counters (4 or 5) instead of 3