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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.

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.