Errors and Uncertainty

If it don't have errors, it ain't real! Errors are a way of saying how well a quantity is or is not known.

In science, there are different kinds of errors or uncertainties associated with data or measurements that can influence one's interpretation of what is occurring.

1. Measurement errors - Suppose you wish to measure the length of the wall and find it to be 100 feet. Is the wall perfectly straight? Was the ruler that was used laid exactly end-to-end all the time? Were you measuring to the nearest foot or the nearest inch or what? A measurement of the length of the wall should have some associated error that takes these different issues into account, for example one might say the wall is 100 foot plus or minus half an inch due to measurement error.

2. Statistical errors - Suppose I drop 50 pencils on the floor. They hit the floor and scatter around, but the pencils mostly fall around some central position. The question becomes, if I drop one more pencil, where is it likely to land and with what confidence? Well, the 51st pencil is most likely to land at the central spot (assuming I drop it in the same way that I dropped the other 50). However, if the 1st 50 are scattered all over the room, I'm not very confident that the 51st will actually land on the central spot. It could end up anywhere. On the other hand, if the 1st 50 all fell in a nice neat pile on top of the central spot, then I am pretty confident that one more pencil might land there too!

3. Interpretative errors - Suppose I ask you to measure the distance between two people who are standing apart. Seems simple enough, but what does that mean? Is it from nose to nose? Big toe to big toe? Maybe from the nose of one person to the big toe of the other? This is different from the other two errors, because in effect it represents human error. It can still be an issue.

   Another kind of interpretative error has to do with unknown influences. For example, if when viewed through a telescope, a star is seen to move back and forth, is that because the star was really moving back and forth, or is the telescope just shaky, or could the Earth have suffered a tremor? Interpretative errors can be difficult to assess. Repeating a measurement and getting a similar answer can sometimes be helpful.