How to Convert Error to Standard Deviation?

[intervoxel]

How to convert error to standard deviation?

I explain my simple question:

I have a program that requests the standard deviation of a physical measurement.

But I only have the error, let's say v=-3.445643 +- 1.5%. How do I make the conversion?

Please

 

[mathman]

Usually the standard deviation has the same dimension as the average. In your case it would be .015 x 3.445643.

 

[dav2008]

You don't have enough information to make that statement.

An error only needs a single measurement to apply and says that "the actual value is somewhere in an interval from a-b to a+b".

If, however, you take N measurements, you can talk about standard deviations. If the data are normally distributed (usually a good assumption) then what a standard deviation s is saying is "68.27% of the time, my measurement is within a-s to a+s. 95.45% of the time, my measurement is within a-2s to a+2s. 99.73% of the time, my measurement is within a-3s to a+3s" and so on. These percentages are tabulated and a graphical representation can be seen here: http://en.wikipedia.org/wiki/File:Standard_deviation_diagram.svg

Now if you're not too familiar with where the error is actually coming from, I think a good rule of thumb would be to say your error is equal to 3 standard deviations. In other words, you would be saying that your measurement is within +/- 1.5% 99.73% of the time.

Edit: And like mathman said, your standard deviation should be in the same units as your measurement. You don't want to say your standard deviation is .5%.

 

[intervoxel]

I thank you for the answers.

 

[dav2008]

Actually let me clarify one point a bit:

An error says "the actual value is somewhere in an interval from a-b to a+b" but it doesn't say with what certainty. That certainty has to exist though but you just don't know it right off the bat. It may be 99% of 99.999%, but it's that certainty that will dictate what the standard deviation is. That's where it goes back to making a lot of measurements.

 

[mathman]

Usually when an error is specified it is assumed to be "standard error", which means the error as given by one standard deviation. It all boils down to definition of "error" in the given context.