Accuracy and Precision

1
Lecture 3

• Accuracy and Precision

2
Section 3.1

• Accuracy and precision already defined in Section
  1.3
• Good precision generally means good accuracy
• See Section 3.2 for an exception
• Poor precision generally means poor accuracy
• Some students seem to get lucky, with their mean
  coinciding with accepted value even with poor
  precision

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Section 3.2

• Determinate (systematic) errors
• These errors affect accuracy
• Can have good precision but poor accuracy
• You make the same mistake every time
• Include instrument errors, operative (personal)
  errors, method errors
• Zauggs 1st Law of Analytical Chemistry Your
  chances of getting 0 error are 0

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Determinate Errors

• Instrument errors
• Faulty equipment, poor calibration
• Operative errors
• Poor technique, math errors
• Some operative errors, like spilling a sample on
  the bench, are gross errors that arent really
  determinate errors. They result in outliers.
  See Section 3.14
• Method errors
• Most serious, sometimes can be corrected by
  running a reagent blank

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Section 3.6

• Example You analyze a sample to contain 0.135 g
  Cu, it actually contains 0.145 g Cu
• Absolute error your value accepted value
• 0.135 g 0.145 g -0.010 g
• Relative error (percent error) Absolute error
  as a percentage of accepted value
• (-0.010 g/0.145 g)100 -6.9 or -69 ppt
• Keep the sign! It tells you whether you are
  above or below the accepted value
• Ignore relative accuracy we wont use

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Section 3.3

• Indeterminate (random) errors affect precision
• You wont get the same answer every time you do
  the experiment no matter how careful you are
• Zauggs 2nd Law of Analytical Chemistry
  Randomness Happens
• Especially with a grade on the line

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Figure 3.2

• A plot of an infinite number of results plotted
  as result (x axis) versus frequency of obtaining
  a particular result (y axis)
• The standard deviations, from -3s to 3s, are
  superimposed on the plot
• Lets add a little to Figure 3.2

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Population Standard Deviation s

• Make an infinite number of measurements
• 68.3 of them will be within 1s
• 95.0 of them will be within 1.96s
• 95.4 of them will be within 2s
• 99.0 of them will be within 2.58s
• 99.7 of them will be within 3s
• Add this to Figure 3.2
• Compare (later) with Table 3.1, last line
• So what is standard deviation really?

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Section 3.7

• Population (s) and sample (s) standard deviations
• Know and understand Equations 3.1 and 3.2 and why
  they are different
• Know how to obtain each type of standard
  deviation on your calculator
• Practice doing Example 3.7 using your
  calculators statistical functions
• Know how to do it longhand as in Example 3.7, but
  for routine work just use your calculator
• You will use sample standard deviation in all of
  your lab work (unless you do 30 or more replicate
  trials!)

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Section 3.7 continued

• Ignore Equation 3.3 and Example 3.8
• An alternate longhand way to calculate s
• Its easier for longhand determination of s
• Standard deviation of mean standard error
• Smeans/vN (Equation 3.4)
• A modified standard deviation that takes into
  account the extra reliability of a large number
  of measurements
• We will generally use just s instead of smean

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Section 3.7 continued again

• Relative standard deviation (rsd)
• Also called coefficient of variation (cv)
• Divide standard deviation by mean, express as a
  percentage
• rsd
• This is the basis of your precision grade in lab
• See example 3.9 for calculation of rsd or cv

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A Common Mistake

• If you are reporting the Cu in an unknown, for
  example, the mean and the standard deviation
  already have units of . The rsd is then a of
  a , so to speak. Be careful!
• Suppose mean 54.23, s 0.2
• What is rsd? rsd 0.4
• Usually round s to one significant figure

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Section 3.7 goes on and on

• Variance square of standard deviation
• We will use it soon
• Some important final points
• Increase N, decrease s but must consider time and
  cost. Is it worth it?
• Many ways to express precision
• 54.23 0.2 Cu. What does the 0.2 mean?
• Zauggs 3rd Law of Analytical Chemistry
• Careful analysts avoid 2nd Law better than sloppy
  analysts

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Section 3.8

• You must become comfy with Excel
• If you are not, see tutorial on web site and/or
  work through Section 3.8
• A couple of points not in text
• To get rows and columns to print, click on
  Sheet on Page Setup and check Row and column
  headings
• STDEV sample standard deviation
• STDEVP population standard deviation

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Section 3.4

• Mostly a review of Chem 105 sig fig rules
• Introduces relative and absolute uncertainty
  needed for Section 3.9
• Serious errors in my text in last sentence on p.
  69. Should read
• For example, the relative uncertainty without
  regard to the decimal point of 0.0344 is 1 part
  in 344, and of 5.39 is 1 part in 539.
• The key number has the greatest uncertainty
• 0.0344 is the key number in above example

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Section 3.4 continued

• Relative uncertainty is independent of decimal
• Used in multiplication and division
• 344 1 has a relative uncertainty of 1/344 or
  0.291
• 0.344 0.001 has a relative uncertainty of
  0.001/0.344 or 0.291
• 999 1 has 3 sig figs, whereas 1001 1 has 4
  sig figs, but both have essentially the same
  relative uncertainty (about 1 part in 1000)
• Chem 105 sig fig rules fail to address this issue

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Section 3.4 again

• Example 3.3 Can you see why 35.63 is the key
  number and not 0.5481 or 0.05300?
• And can you see that the answer (88.55) has an
  uncertainty of about 2.5 parts in 8900?
• 1/3563 2.5/8855
• Relative uncertainty in answer must be at least
  as big as relative uncertainty in key number

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Section 3.4 ad infinitum

• Example 3.4 Rounding the answer to 547 (as per
  Chem 105 rules) produces too much uncertainty in
  the answer
• 1/547 is MORE uncertain than the uncertainty in
  the key number (891)
• Can write 546.6 to convey more certainty than
  547, but less than 546.6
• To be given more teeth in Section 3.9

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Section 3.4 nearly done

• Absolute uncertainty used in addition and
  subtraction
• Line up decimals, so relative uncertainty is
  irrelevant
• No key number
• This is essentially the Chem 105 addition and
  subtraction sig fig rule
• Section 3.9 will modify this

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Sections 3.4, 3.5

• Uncertainties with logarithms
• This is the Chem 106 approach and is a rough
  approximation
• Well do this again after Section 3.10
• Rounding The even-number rule
• Same as 105 text
• 4.75 rounds to 4.8, 4.85 rounds to 4.8
• But 4.8500001 rounds to 4.9!
• Rarely does a number ending in 5 need to be
  rounded back just one place. Hardly ever use the
  even-number rule

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Lecture 4 assignment

• Read Sections 3.9 through 3.11