Standard Deviation vs Uncertainty measurement?

[stevensfo]

Any statisticians around?

One of my responsibilities for many years has been checking the accuracy of certain laboratory balances. Although in practice, the precision doesn't have to be super sharp, we're required to follow certain procedures.

I more or less understand the difference. S.D. shows the variation of the balance when a weight is used to test it, e.g. ten times.

However, the weights themselves have been checked by an accredited lab, and uncertainty takes into consideration the error of the weights themselves, in addition to the error of the balance. The uncertainty measure is currently very fashionable! But I have to admit that I don't really understand the figures. Unlike some of the more traditional statistical measurements, they seem very difficult to interpret.

I appreciate how uncertainty can be important when a process has many steps, each with its own error, but is it really important for checking a balance where the error of the weights is almost non-existent or at least five decimal places below where we'd even notice?

Steve

PS The meaning of Standard Error rather than S.D. has completely eluded me for the moment. I grew up preferring to look at raw data and simple variance graphs.

[Maroochydore]

The meaning of Standard Error rather than S.D. has completely eluded me for the moment.

As far as I can recall - it's been many a year - SD is the deviation from the mean of a dataset. SE is the deviation from the mean of a series of datasets.

So, if you have 10 datasets and you set the mean for each dataset as a dataset in it's own right, then the SE is, if you like, the SD of that 'new' data set.

I hope I've explained that correctly.

[hiriskpaul]

In your context standard error is the error on the mean. If you take multiple measurements of something then you can calculate the mean and standard deviation of those measurements. The standard error is calculated as the standard deviation divided by the square root of the number of measurements. The standard error gives you an estimate of the accuracy of the mean. So let's say the mean is 100 and standard error is 1. This means you can consider that the true value has a 68% probability of being between 99 and 101, a 95% probability being between 98 and 102, etc. The assumption here is that the errors on the measurements are normally distributed, which is often a reasonable assumption.

In practice with simple measurements such as a weight you may get exactly the same measurement every time you take it, eg because your scales only go to 2dp, and so end up with zero standard error, which is unhelpful. In that case you may have to make do with the precision of your scales as an estimate of uncertainty in the weight. Then you might reasonably say that the weight of something is between 99.9g and 100.1g with 100% certainty. There is no precise statistic called "Uncertainty". Sometimes this may refer to an absolute range, and sometimes it may refer to an error on the mean. It can have other meanings as well, but if a number is being quoted for uncertainty it should really be made clear what is meant by the number.