Ideal Measurement Model

## The 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:

xi = μ + ei

• In practice, measurements also usually involve bias:

actual measurement = true measurement + random error + bias

or

xi = μ + ei + bi.

• 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.

### 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 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 will 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: nbs-10.xls.