Error and Uncertainty

The precision to which we can measure something is limited by experimental factors, leading to uncertainty. The uncertainty depends on various factors including environmental, process, man or machine. The better control of these various factors, better the uncertainty.

The deviation of a measurement from the "correct" value is termed the error, so error is a measurement of how inaccurate our results are. 
There are two general types of errors.

. Systematic Errors - A error that is constant from one measurement to another, for example, an incorrectly marked ruler would always make the same mistake measuring something as either bigger or smaller than it actually is every time. These errors can be quite difficult to eliminate!

. Random Errors - Random errors in your measurement occur statistically, ie. they deviate from the correct value in both directions. These can be reduced by repeated measurement.

But here is where it gets confusing… When you estimate the uncertainty of your measurement, as you will do frequently in the lab component of this course, you should consider the possible sources of error that contribute to the uncertainty. This way if there are large sources of error in your experiment, you will have a large uncertainty which will not exclude the accurate value of the quantity you are trying to measure.

Why is error and uncertainty so important?
An accurate estimate of the uncertainty in an experiment is the only way to determine whether an experiment is consistent or inconsistent with a theory.

If the theoretical prediction lies within the estimate of the uncertainty of the experiment then we can say the theory is consistent with the experiment. Another way of stating this would be that the measured value is consistent with the theoretical one if the error is less than the uncertainty. However, if the uncertainty is very large this this may be a meaningless statement! If we estimate the uncertainty to be smaller than it really is we may discard a valid theory (and perhaps an important discovery).

Our aim is therefore always to accurately estimate the uncertainty of our results and strive to improve it!

Averaging and Standard Deviation
When a leading cause of uncertainty in our measurement is random error we can lower the uncertainty in our measurement by repeated measurement and averaging (if the main sources of error are random). If we can assume that our measurements are governed by a typical statistical distribution then the standard deviation becomes a useful measurement of the variance of our data.

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