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Experimental Errors Just because a series of replicate analyses are precise does not mean the results are accurate

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- Experimental Errors
- Just because a series of replicate analyses are precise does not mean the results are accurate
- Sometimes less precise results for a series of analyses are more accurate than a more precise series of replicates
- See Figure 2-3 in FAC7, p. 15

- Consider three situations that give results producing scatter in data or deviations from the true value
- Determinate error sometimes called systematic error that produces a deviation in the results of an analysis from the true value
- Indeterminate error sometimes called random error that produces uncertainty in the results of replicate analyses
- Results in scattering in the observed measurements or results
- The uncertainty is reflected in the quantitative measures of precision

- Gross errors which occur occasionally and often are large in magnitude

- Experimental Errors
- Determinate Errors are inherently determinable or knowable
- Instrumental errors are produced because apparatus is not properly calibrated, not clean or damaged
- Electronic equipment can often give rise to such errors because contacts are dirty, power supplies degrade, reference voltages are inaccurate, etc.

- Method errors result from non-ideal behavior of reagents and reactions used for analysis
- Interferences
- Slowness of reactions
- Incompleteness of reactions
- Species instability
- Nonspecificity of reagents
- Side reaction

- Personal errors involve the judgement of the analyst
- Bias in reading an instrument
- Number bias - preference for certain digits

- Instrumental errors are produced because apparatus is not properly calibrated, not clean or damaged

- Experimental Errors
- Effect of determinate errors on the results of an analysis
- Constant error example: Suppose there is a -2.0 mg error in the mass of A containing 20.00% A
- Examine the effect of sample size on %A calculated
- The result is that for a constant error, the relative quantity of A approaches the true value at high sample masses.

- Constant error example: Suppose there is a -2.0 mg error in the mass of A containing 20.00% A

- Experimental Errors
- Effect of determinate errors on the results of an analysis
- Proportional error example: Suppose there is a + 5 ppt relative error in the mass of A for a sample that’s 20.00 % in A
- Effect of sample size on %A
- The %A is independent of sample size if a proportional error of constant size exists in the mass of A

- Proportional error example: Suppose there is a + 5 ppt relative error in the mass of A for a sample that’s 20.00 % in A

- Experimental Errors
- Mitigating determinate errors
- Instrument errors can be reduced by calibrating one’s apparatus
- Personal errors can be reduced by being careful!
- Method errors can be reduced by
- Analyzing standard samples
- The NIST has a wide variety of standard samples whose analyte concentrations are well established

- The effect of interferences can often be accounted for by spiking the analytical sample with a known quantity of analyte or performing a standard additions analysis
- The effect of the interferences on the added analyte should be the same as that on the original analyte

- Independent analysis of replicates of the same bulk sample by a well proven method of significantly different design can check for determinate errors
- Blank determinations may indicate the presence of a constant error
- Carry out the analysis on samples that contain everything but the analyte

- Vary the sample size in order to detect a constant error

- Analyzing standard samples

- Experimental Errors
- Gross errors - such as arithmetic mistakes, using the wrong scale on an instrument can be cured by being careful!
- Indeterminate or random errors producing uncertainty in results
- Arise when a system is extended to its limit of precision
- There are many, often unknown, uncontrolled, opportunities to introduce small variations in each measurement leading to an experimental result

- One way to examine uncertainty is to produce a frequency distribution
- Example: examine the frequency distribution for a measurement that contains four equal sized uncertainties, u1, u2, u3, u4
- The combinations of the u’s give certain numbers of possibilities:

- Arise when a system is extended to its limit of precision

This data is plotted in Figure FAC7 3-1, p 22.

- Experimental Errors
- One way to examine uncertainty is to produce a frequency distribution
- If the number of equal sized uncertainties is increased to 10
- only 1/500 chance of observing + 10u or -10u

- If the number of indeterminate uncertainties is infinite one expects a smooth curve
- The smooth curve is called the Gausian error curve and gives a normal distribution

- Conclusions about the normal distribution
- The mean is the most probable value for normally distributed data
- This is because the most probable deviation from the mean is 0 (zero)

- Large deviations from the mean are not very probable
- The normal distribution curve is symmetric about the mean
- The frequency of a particular positive deviation from the mean is the same and the same sized but negative deviation from the mean

- Most experimental results from replicate analyses done in the same way form a normal distribution

- The mean is the most probable value for normally distributed data

- If the number of equal sized uncertainties is increased to 10

- Experimental Errors
- Examine the data for the determination of the volume of water delivered by a 10.00 mL transfer pipet - FAC7, Table 3-2, p. 23 and Table 3-3, p. 24 and Figure 3-2, p. 24
- 26% of the 50 results are in the 0.003 mL range containing the mean
- 72% of the 50 measurements are within the range ±1s of the mean
- The Gaussian curve is shown for the smooth distribution having the same s=s and the same mean as this 50 sample set of data