Hi all,
Please forgive the slightly long winded explanation, I could really do with some help here.
I have a computer simulation which contains multiple variables to which I have applied random perturbations in order to simulate the possible error. The random perturbations are in the form of a normal distribution. I perform an experiment (1) where I do this 250 times and end up with a mean and variance as the result.
I know perform experiment 2 where the random perturbations are only applied to one variable and output another mean and varience of the 250 simulations.
If I want to know the effect that this variable is having on the overall distribution is it mathematically correct to divide the variance obtained by experiment 2 by the varience obtained by experiment 1?
If I then do another experiment (3) where I include perturbations to only 2 variables (The first will be the same variable as used in experiment 2 and an additional variable) can I subtract the varience obtained by experiment 2 from the varience obtained in experiment 3 to give me the error associated with the additional variable and then divide this by the varience obtained in experiment 1 to give me the amount that this variable is contributing to the overall error. Is this mathematically correct?
I can then repeat the experiment several times clumping variables together in terms of their origins in order to determine which groups contribute to the overall error.
I have tried this but when summing up the variences always get an answer bigger than the original varience obtained in experiment 1. I think that this is due to the perturbations applied to each variable cancelling each other out and thus giving a smaller overall varience for experiment 1 than the sum of all the individual components. If anyone can help with this problem I would be most grateful. I am trying to work out how to disentangle the errors without running lots and lots of experiments, ie one for each individual variable.
Thank you in advance
David
Please forgive the slightly long winded explanation, I could really do with some help here.
I have a computer simulation which contains multiple variables to which I have applied random perturbations in order to simulate the possible error. The random perturbations are in the form of a normal distribution. I perform an experiment (1) where I do this 250 times and end up with a mean and variance as the result.
I know perform experiment 2 where the random perturbations are only applied to one variable and output another mean and varience of the 250 simulations.
If I want to know the effect that this variable is having on the overall distribution is it mathematically correct to divide the variance obtained by experiment 2 by the varience obtained by experiment 1?
If I then do another experiment (3) where I include perturbations to only 2 variables (The first will be the same variable as used in experiment 2 and an additional variable) can I subtract the varience obtained by experiment 2 from the varience obtained in experiment 3 to give me the error associated with the additional variable and then divide this by the varience obtained in experiment 1 to give me the amount that this variable is contributing to the overall error. Is this mathematically correct?
I can then repeat the experiment several times clumping variables together in terms of their origins in order to determine which groups contribute to the overall error.
I have tried this but when summing up the variences always get an answer bigger than the original varience obtained in experiment 1. I think that this is due to the perturbations applied to each variable cancelling each other out and thus giving a smaller overall varience for experiment 1 than the sum of all the individual components. If anyone can help with this problem I would be most grateful. I am trying to work out how to disentangle the errors without running lots and lots of experiments, ie one for each individual variable.
Thank you in advance
David