1. INTRODUCTION TO METROLOGY

2. lseidman@matcmadison.edu DEFINITIONS Metrology is the study of measurements Measurements are quantitative observations; numerical descriptions

3. lseidman@matcmadison.edu OVERVIEW This longer lecture explores general principles of metrology Next 3 shorter lectures apply principles to specific measurements: weight, volume, pH Later will talk about measuring light transmittance (spectrophotometry)

4. lseidman@matcmadison.edu WE WANT TO MAKE “GOOD” MEASUREMENTS Making measurements is woven throughout daily life in a lab. Often take measurements for granted, but measurements must be “good”. What is a “good” measurement?

5. lseidman@matcmadison.edu EXAMPLE A man weighs himself in the morning on his bathroom scale, 172 pounds. Later, he weighs himself at the gym,173 pounds.

6. lseidman@matcmadison.edu QUESTIONS How much does he really weigh?

7. lseidman@matcmadison.edu Do you trust one or other scale? Which one? Could both be wrong? Do you think he actually gained a pound?

8. lseidman@matcmadison.edu Are these “good measurements”?

9. lseidman@matcmadison.edu NOT SURE We are not exactly certain of the man’s true weight because:  Maybe his weight really did change – always sample issues  Maybe one or both scales are wrong – always instrument issues

10. lseidman@matcmadison.edu DO WE REALLY CARE? Do you care if he really gained a pound? How many think “give or take” a pound is OK?

11. lseidman@matcmadison.edu ANOTHER EXAMPLE Suppose a premature baby is weighed. The weight is recorded as 5 pounds 3 ounces and the baby is sent home. Do we care if the scale is off by a pound?

12. lseidman@matcmadison.edu “GOOD” MEASUREMENTS A “good” measurement is one that can be trusted when making decisions. We just made judgments about scales. We make this type of judgment routinely.

13. lseidman@matcmadison.edu IN THE LAB Anyone who works in a lab makes judgments about whether measurements are “good enough” –  but often the judgments are made subconsciously  differently by different people Want to make decisions  Conscious  Consistent

14. lseidman@matcmadison.edu QUALITY SYSTEMS All laboratory quality systems are concerned with measurements All want “good” measurements Some language is quoted in your lab manual

15. lseidman@matcmadison.edu NEED Awareness of issues so can make “good” measurements. Language to discuss measurements. Tools to evaluate measurements.

16. lseidman@matcmadison.edu METROLOGY VOCABULARY Very precise science with imprecise vocabulary  (word “precise” has several precise meanings that are, without uncertainty, different) Words have multiple meanings, but specific meanings

17. VOCABULARY Units of measurement Standards Calibration Traceability Tolerance Accuracy Precision Errors Uncertainty

18. lseidman@matcmadison.edu UNITS OF MEASUREMENT Units define measurements Example, gram is the unit for mass What is the mass of a gram? How do we know?

19. lseidman@matcmadison.edu DEFINITIONS MADE BY AGREEMENT Definitions of units are made by international agreements, SI system  Example, kilogram prototype in France  K10 and K20 at NIST

20. lseidman@matcmadison.edu EXTERNAL AUTHORITY Measurements are always made in accordance with external authority Early authority was Pharaoh’s arm length

21. lseidman@matcmadison.edu A standard is an external authority Also, standard is a physical embodiment of a unit

22. lseidman@matcmadison.edu STANDARDS ARE: Physical objects, the properties of which are known with sufficient accuracy to be used to evaluate other items.

23. lseidman@matcmadison.edu STANDARDS ARE AFFECTED BY THE ENVIRONMENT Units are unaffected by the environment, but standards are  Example, Pharaoh’s arm length might change  Example, a ruler is a physical embodiment of centimeters Can change with temperature But cm doesn’t change

24. lseidman@matcmadison.edu STANDARDS ALSO ARE: In chemical and biological assays, substances or solutions used to establish the response of an instrument or assay method to an analyte See these in spectrophotometry labs

25. lseidman@matcmadison.edu STANDARDS ALSO ARE: Documents established by consensus and approved by a recognized body that establish rules to make a process consistent  Example ISO 9000  ASTM standard method calibrating micropipettor

26. lseidman@matcmadison.edu CALIBRATION IS: Bringing a measuring system into accordance with external authority, using standards For example, calibrating a balance  Use standards that have known masses  Relate response of balance to units of kg  Do this in lab

27. lseidman@matcmadison.edu PERFORMANCE VERIFICATION IS: Check of the performance of an instrument or method without adjusting it.

28. lseidman@matcmadison.edu TOLERANCE IS: Amount of error that is allowed in the calibration of a particular item. National and international standards specify tolerances.

29. lseidman@matcmadison.edu EXAMPLE Standards for balance calibration can have slight variation from “true” value  Highest quality 100 g standards have a tolerance of + 2.5 mg  99.99975-100.00025 g  Leads to uncertainty in all weight measurements

30. lseidman@matcmadison.edu TRACEABILITY IS: The chain of calibrations, genealogy, that establishes the value of a standard or measurement In the U.S. traceability for most physical and some chemical standards goes back to NIST

32. TRACEABILITY Note in this catalog example, “traceable to NIST”

33. lseidman@matcmadison.edu VOCABULARY Standards Calibration Traceability Tolerance Play with these ideas in labs

34. ACCURACY AND PRECISION ARE: Accuracy is how close an individual value is to the true or accepted value Precision is the consistency of a series of measurements

35. lseidman@matcmadison.edu EXPRESS ACCURACY % error = True value – measured value X 100% True value Will calculate this in volume lab

36. lseidman@matcmadison.edu EXPRESS PRECISION Standard deviation  Expression of variability  Take the mean (average)  Calculate how much each measurement deviates from mean  Take an average of the deviation, so it is the average deviation from the mean Try this in the volume lab

37. lseidman@matcmadison.edu ERROR IS: Error is responsible for the difference between a measured value and the “true” value

38. lseidman@matcmadison.edu CATEGORIES OF ERRORS Three types of error:  Gross  Random  Systematic

39. lseidman@matcmadison.edu GROSS ERROR Blunders

40. lseidman@matcmadison.edu RANDOM ERROR In U.S., weigh particular 10 g standard every day. They see:  9.999590 g, 9.999601 g, 9.999592 g …. What do you think about this?

41. lseidman@matcmadison.edu RANDOM ERROR Variability No one knows why They correct for humidity, barometric pressure, temperature Error that cannot be eliminated. Called “random error”

42. lseidman@matcmadison.edu RANDOM ERROR Do you think that repeating the measurement over and over would allow us to be more certain of the “true” weight of this standard?

43. lseidman@matcmadison.edu RANDOM ERROR Yes, because in the presence of only random error, the mean is more likely to be correct if repeat the measurement many times Standard is probably really a bit light Average of all the values is a good estimate of its true weight

44. lseidman@matcmadison.edu RANDOM ERROR AND ACCURACY In presence of only random error, average value will tend to be correct With only one or a few measurements, may or may not be accurate

50. Mean Median Mode

51. lseidman@matcmadison.edu THERE IS ALWAYS RANDOM ERROR If can’t see it, system isn’t sensitive enough Less sensitive balance:10.00 g, 10.00 g, 10.00 g Versus 9.999600 g…

52. lseidman@matcmadison.edu SO… Can we ever be positive of true weight of that standard? No There is uncertainty in every weight measurement

53. lseidman@matcmadison.edu RELATIONSHIP RANDOM ERROR AND PRECISION Random error –  Leads to a loss of precision

54. lseidman@matcmadison.edu SYSTEMATIC ERROR Defined as measurements that are consistently too high or too low, bias Many causes, contaminated solutions, malfunctioning instruments, temperature fluctuations, etc., etc.

55. lseidman@matcmadison.edu SYSTEMATIC ERROR Technician controls sources of systematic error and should try to eliminate them, if possible  Temperature effects  Humidity effects  Calibration of instruments  Etc.

56. lseidman@matcmadison.edu In the presence of systematic error, does it help to repeat measurements?

57. lseidman@matcmadison.edu SYSTEMATIC ERROR Systematic error –  Does impact accuracy Repeating measurements with systematic error does not improve the accuracy of the measurements

59. lseidman@matcmadison.edu ANOTHER DEFINTION OF ERROR IS: Error = is the difference between the measured value and the “true” value due to any cause Absolute error = “True” value - measured value Percent error is: “True” value - measured value (100 %) “True” value

60. lseidman@matcmadison.edu ERRORS AND UNCERTAINTY Errors lead to uncertainty in measurements Can never know the exact, “true” value for any measurement. Idea of a “true” value is abstract – never knowable. In practice, get close enough

61. lseidman@matcmadison.edu UNCERTAINTY IS: Estimate of the inaccuracy of a measurement that includes both the random and systematic components.

62. lseidman@matcmadison.edu UNCERTAINTY ALSO IS: An estimate of the range within which the true value for a measurement lies, with a given probability level.

63. lseidman@matcmadison.edu UNCERTAINTY Not surprisingly, it is difficult to state, with certainty, how much uncertainty there is in a measurement value. But that doesn’t keep metrologists from trying …

64. lseidman@matcmadison.edu METROLOGISTS Metrologists try to figure out all the possible sources of uncertainty and estimate their magnitude One or another factor may be more significant. For example, when measuring very short lengths with micrometers, care a lot about repeatability. But, with measurements of longer lengths, temperature effects are far more important

65. lseidman@matcmadison.edu REPORT VALUES Metrologists come up with a value for uncertainty You may see this in catalogues or specifications  Example: measured value + an estimate of uncertainty

66. lseidman@matcmadison.edu UNCERTAINTY ESTIMATES Details are not important to us now But principle is: any measurement, need to know where the important sources of error might be

67. lseidman@matcmadison.edu SIGNIFICANT FIGURES One cause of uncertainty in all measurements is that the value for the measurement can only read to a certain number of places This type of uncertainty. It is called “resolution error”. (It is often evaluated using Type B methods.)

68. lseidman@matcmadison.edu SIIGNIFICANT FIGURE CONVENTIONS Significant figure conventions are used to record the values from measurements Expression of uncertainty Also apply to very large counted values  Do not apply to “exact” values Counts where are certain of value Conversion factors

70. lseidman@matcmadison.edu ROUNDING CONVENTIONS Combine numbers in calculations Confusing Look up rules when they need them

71. lseidman@matcmadison.edu RECORDING MEASURED VALUES Record measured values (or large counts) with correct number of significant figures Don’t add extra zeros; don’t drop ones that are significant With digital reading, record exactly what it says; assume the last value is estimated With analog values, record all measured values plus one that is estimated Discussed in Laboratory Exercise 1

72. lseidman@matcmadison.edu ROUNDING A Biotechnology company specifies that the level of RNA impurities in a certain product must be less than or equal to 0.02%. If the level of RNA in a particular lot is 0.024%, does that lot meet the specifications?

73. lseidman@matcmadison.edu The specification is set at the hundredth decimal place. Therefore, the result is rounded to that place when it is reported. The result rounded is therefore 0.02%, and it meets the specification.

74. lseidman@matcmadison.edu Look at all the problems for chapter 13.

75. lseidman@matcmadison.edu GOOD WEB SITE FOR SIGNIFICANT FIGURES http://antoine.frostburg.edu/cgi- bin/senese/tutorials/sigfig/index.cgi

78. Match these descriptions with the 4 distributions in the figure: Good precision, poor accuracy Good accuracy, poor precision Good accuracy, good precision Poor accuracy, poor precision

79. lseidman@matcmadison.edu THERMOMETERS Look at the values for the thermometers on the board. Significant figure conventions can guide us in how to record the value that we read off any measuring instrument. With these thermometers, correct number of sig figs is _______.

80. lseidman@matcmadison.edu THERMOMETERS Were they accurate? How could we figure out the “true” value for the temperature?

81. lseidman@matcmadison.edu REPEATING MEASUREMENTS Would repeating measurements with these thermometers, assuming we did not calibrate them, improve our ability to trust them? Is their error an example of random or systematic error?

82. lseidman@matcmadison.edu CALIBRATION Calibration of the thermometers could lead to increased accuracy This is a type of systematic error In the presence of systematic error, repeating the measurement will not improve its accuracy

83. lseidman@matcmadison.edu TOLERANCE Here is a catalog description of mercury thermometers. Are these thermometers out of the range for which their tolerance is specified?

84. lseidman@matcmadison.edu PRECISION Were they precise? How could precision be measured? Would calibration help to make them more precise?

85. lseidman@matcmadison.edu CALIBRATION Calibration would probably not improve their precision

86. lseidman@matcmadison.edu RETURN TO OUR ORIGINAL TYPE OF QUESTION Are our temperature measurements “good” measurements? How do you make that judgment? Can we trust them?

87. lseidman@matcmadison.edu THERMOMETERS – GOOD ENOUGH? Are times that we need to be very close in temperature measurements. For example PCR is fairly picky. Other times we can be pretty far off and process will still work.

88. lseidman@matcmadison.edu EXPLORE SOME OF THESE IDEAS In lab:  Calibrate instruments  Use standards  Check performance of micropipettes  Record measurement values  Calculate per cent errors  Calculate repeatability