Question

This assessment though concerns in particular the dispersion of random errors which occurs when repeated tests are performed on the same sample, and it takes into account all the possible factors that can affect it. It should be pointed out that the awareness of such variability does not reduce, but instead it improves the knowledge about the measured value. It follows that the uncertainty does not represent the difference between the measured and the true value (which will always be unknown), but it is an estimated interval that includes all the possible results of the measurement – including the true value – at the chosen confidence level.

Explain this theory in 300 words?

Answer 1

If we make a measurement, we expect that the measurement will be approximately (but not exactly) equal to the true value. If we make a very large number of measurements, some will be larger and some smaller than the true value. If we took an infinite number of measurements, they would be distributed about the true value. A distribution defines how they will be distributed. When many independent random factors act in an additive manner to create variability, data will follow a bell-shaped distribution called the Gaussian distribution. This distribution is sometimes also called a Normal distribution.

We need to take account of how the uncertainties in our measurements will affect other parameters. The derivations of the specific formulas below require calculus, so we will not derive them in class. However, if you wish, you could verify that the formulas actually work, but testing them with actual numbers.

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