The Ideal Measurement Model
- Every measurement involves random error.
- The ideal measurement model:
actual measurement = true measurement + random error.
- Symbolically the ideal measurement model is written as:
- In practice, measurements also usually involve bias:
actual measurement = true measurement + random error + bias
- Bias is systematic unknown error.
- See this website for the difference between bias and precision
(small random error):
- 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) 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 NBS 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
- 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
- We will look at 100 such weighings. Here are the first 5 weighings:
- Here is the complete list of 100 weighings: