Experimental Errors

1

• 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

2

• 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

3

• 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.

4

• 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 thats 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

5

• Experimental Errors
• Mitigating determinate errors
• Instrument errors can be reduced by calibrating
  ones 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

6

• 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 us give certain numbers
  of possibilities

7
This data are plotted in Figure FAC7 3-1, p 22.
8

• 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

9

• 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 ss and the same
  mean as this 50 sample set of data