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Ideal Measurement Model

Discussion

• Every measurement involves random error.
• The ideal measurement model:
   
       actual measurement = true measurement + random error.
• Symbolically the ideal measurement model is written as:
   
       x_i = μ + e_i
• In practice, measurements also usually involve bias:
   
  actual measurement = true measurement + random error + bias
   
  or x_i = μ + e_i + b_i.
• Bias is systematic unknown error.
• See this website for the difference between bias and precision (small random error):
   
  www.mathisfun.com/accuracy-precision.html
• High precision = low variance; low precision = high variance. We will define variance mathematically later in this lecture.

Official Definitions of Meter, Second, and Kilogram

• Currently the meter is officially defined as the distance that light travels in 1/299,272,458 of a second.
• Grace Hopper (1906 - 1992) had a long career in the navy. She used to carry a wire that was one foot in length to her popular computer lectures.
• One foot is the distance that light travels in one nanosecond.
• Historical Definitions of the Meter
• Originally, the second was defined as 1/86,400 of a solar day.
• In 1960, the second was defined as 1/86,400 of the solar day in 1900.
• In 1968, second was defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition of the two hyperfine periods of the ground state of the cesium-133 atom. The value of the duration is interpolated to an atom chilled to absolute zero.
• The kilogram is defined as the weight of the one-kilogram prototype weight stored in a vault in a lab outside of Paris.
• Many countries have prototype weights. Here is the one kilogram prototype weight of the United States.

The NIST 10 Gram Prototype Weight

• The National Institute of Standards and Technology (NIST), formerly called the National Bureau of Standards (NBS), is responsible to maintaining the accuracy of the nations weights and measures.
• In 1940, NBS acquired a 10 gram prototype weight, which it used to calibrate its scales. It was weighed once a week for many years after 1940.
• We look at 100 such weighings. Here are the first 5 weighings:
   
       9.999591 grams
       9.999600 grams
       9.999594 grams
       9.999601 grams
       9.999598 grams
• Here is the complete list of 100 weighings: nist-10.txt.