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


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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

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Presentation Transcript
slide1

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
slide2

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
slide3

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.
slide4

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
slide5

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
slide6

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:
slide8

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
slide9

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