## General Resources

## Notes on measurement error estimation.

In experiments it is very important to give a numerical value for the error in a measurement. In this page, we describe shortly the methods for error estimation. A detailed explanation (in Hebrew) can be found here as PDF or doc:

**Errors when Reading Scales**- The error is the smallest tic size. For example, if your ruler has 1mm ticks on it than you can say that your pen is 15cm long with a 1mm error.-
**Errors of Digital Instruments**- The error is half the smallest digit. For example, if you measure the weight of salt in a four digit semi analytical scale, you can say that you have 0.5682 gr salt with a 0.00005 gr error. -
**Statistical Errors**- When you measure the same variable several times, you get a statistical scatter of the result. In order to estimate the error, we assume that the results are distributed normally and take their standard deviation to be the measurement error. -
**Propagating Errors**- If you are interested in the error of a function of a measured variable, or a function of several measured variables you need to know how to propagate the error. The general function is error(F)= error(Fx)+error(Ft) = sqrt( (|df/dx|*error(x))^2+(|df/dt|*error(t))^2). For example, if I want to know the error in the velocity of running man that ran for 1 min (error 1 s) a distance of 200 meters (error 20 cm) then:

v = x/t -> error(v)/v = sqrt((error(x)/x)^2+(error(t)/t)^2)

-> v = 200 m/min error(v) = 200*sqrt((0.2/200)^2+(1/60)^2) = 3.3393 m/min.