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

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

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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


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  • 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


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  • 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.


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  • 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


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  • 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


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  • 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:


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


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  • 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


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  • 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


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