- #1
kwah
- 17
- 0
Hi,
For an experiment I have a value for the error in time t (s) to be +-0.13s but I'm having difficulty getting from this to an error in t^-2 for the error bars drawn onto a graph.
My values for t are in the range 36.84 - 24.88seconds.
The range for t^-2 is 0.0007368 - 0.0016155 s^-2.
My initial thought is that the error would simply follow the algebvraic manipulation of t, but that would give values such as 0.0008 +-59.172s which seems ridiculous.
Secondly I thought maybe work with the error % instead. The percentage error in t is approximately 0.42% (100 * 0.13/{mean of t values}).
(0.42%)^2 = 0.00176% and
(0.42%)^-2 ~5670000%.
This definitely leads me to believe that the error for a reciprocal should not also be a reciprocal but doesn't really get me much closer to getting the error values.
A rough attempt at sticking some nice numbers in doesn't help too much:
100 +-10
100^2 = 90^2 to 110^2
= 8100 to 12100
= 10100 +-2000
(same again for cubing it and base 10 but on paper).
From that I can somewhat see that the ^2 & +-2000 and ^3 & +-301000 might be related somehow but none of it seems immediately intuitive / obvious.
Searches for 'error squared' (and variations thereof) show many results for mean square error and root mean square and a few results I found here point to error propogation but I didn't find the brief look at error propogation accessible - maybe its simply lack of sleep but it just went in one eye and out the other.
So yeah, basically just a very long winded way of asking:
How should errors get manipulated? Specifically, how does an error in a variable get affected if the variable is raised to a power?
I don't mind reading up about it if you point me to somewhere that the answer is definitely at as I'm not normally one to ask for answers to be served to me but on a short deadline I'd like something pretty quick and accessible please :)
Thanks,
kwah
PS, apologies if this is in the wrong section but I think that the issue I'm having is simply just a simple math / manipulation issue :) .
For an experiment I have a value for the error in time t (s) to be +-0.13s but I'm having difficulty getting from this to an error in t^-2 for the error bars drawn onto a graph.
My values for t are in the range 36.84 - 24.88seconds.
The range for t^-2 is 0.0007368 - 0.0016155 s^-2.
My initial thought is that the error would simply follow the algebvraic manipulation of t, but that would give values such as 0.0008 +-59.172s which seems ridiculous.
Secondly I thought maybe work with the error % instead. The percentage error in t is approximately 0.42% (100 * 0.13/{mean of t values}).
(0.42%)^2 = 0.00176% and
(0.42%)^-2 ~5670000%.
This definitely leads me to believe that the error for a reciprocal should not also be a reciprocal but doesn't really get me much closer to getting the error values.
A rough attempt at sticking some nice numbers in doesn't help too much:
100 +-10
100^2 = 90^2 to 110^2
= 8100 to 12100
= 10100 +-2000
(same again for cubing it and base 10 but on paper).
From that I can somewhat see that the ^2 & +-2000 and ^3 & +-301000 might be related somehow but none of it seems immediately intuitive / obvious.
Searches for 'error squared' (and variations thereof) show many results for mean square error and root mean square and a few results I found here point to error propogation but I didn't find the brief look at error propogation accessible - maybe its simply lack of sleep but it just went in one eye and out the other.
So yeah, basically just a very long winded way of asking:
How should errors get manipulated? Specifically, how does an error in a variable get affected if the variable is raised to a power?
I don't mind reading up about it if you point me to somewhere that the answer is definitely at as I'm not normally one to ask for answers to be served to me but on a short deadline I'd like something pretty quick and accessible please :)
Thanks,
kwah
PS, apologies if this is in the wrong section but I think that the issue I'm having is simply just a simple math / manipulation issue :) .