As we saw before, physics is an experimental science and every inquiry into Nature starts by making observation and taking measurements. Let us do a simple experiment. Pick up a pendulum in your house. Any object of some length with a mass at the tip will do. (For example, an antique pocket watch like you can see on the side, or more easily a rock tied on a string) The pendulum oscillates because of the force of gravity. The period is just a function of the length of the pendulum and of a constant of nature
You want to check whether your prediction agrees with experiments.
To make sure you are doing things right, you take multiple measurements. I did it at home and here are my results for my own pocket watch whose length I measured to be 20 cm.
|Period (s)|Length(m)| Gravitational constant "g" (
You have just seen the most typical type of error: the statistical error. As its name implies, it is due to the random fluctuations in the measurements. It's source is often easily identifiable and experimentalists work very hard to reduce this ever-present source of uncertainty.
The most important thing about statistical random errors is that they are random. So once you have tried everything you can to minimize them, you can still reduce their effects by making many, many measurements. Sometimes you will measure a bigger value, sometimes a smaller value; by taking the average, you reduce the error.
Sample size is really important in science and when deciding whether or not to trust a study it is important to look at whether there was a large or small sample and if there were uncontrolled random errors. Another example: If you ask ten of your friends what their favorite color is, and you find a big preference for blue, you cannot conclude that this is true for the whole world's population, your sample size is too small.
The most dangerous source of error is the non-random one. These systematic (one way or the other) errors cannot be eliminated by taking many many measurements. They don't average out. If you don't know what they are, or what is causing them, it is very hard to eliminate them or even quantify their size. Here is an example:
In the measurement of the pendulum above, I never specified how exactly I measured the length. From the tip of the chain to the top of the watch or to the middle of the watch? The standard formula for predicting the period from
Thinking about sources of errors is something physicists, and scientists spend a great deal of time thinking about and understanding. It is very important for scientists to design experiments with these sources of errors in mind, and they do!