I see that I have so much more to learn! Thank you so much for the detailed answer and the example worksheet. I have been evaluating my electrical designs for years using Jacobian matricies to calculate the total uncertainty and the "Effect" of each of the contributors so that I could verify that my design meets my design goals. By examining the "Effect" of each contributor, I could then make appropriate component changes as required to meet my goals (e.g. change a resistor from a 1% to a 0.1% resistor, use a better opamp, etc.) or change the design specifications.
Using the Jacobian matricies, I am able to predict an uncertainty that matches the value returned by the SEA combine(f(),errors) function:
Using the Jacobian I am essentially calculating the following:
uncertainty = sqrt( (diff(y, a) * sa)^2 + (diff(y, b)* sb)^2 + ...)
Using the Jacobian I can also calculate the worst case uncertainty as follows:
worst case uncertainty = abs(diff(y, a) * sa) + abs(diff(y, b) * sb) + ...)
In generally I list both of the results for my clients. The worst case results are exceedingly conservative since in practice it is unrealistic to expect every parameter to be at its worst case value.
I really like the SEA app and by your explanation, I can see how I can also use it to see the effects of each contibutor. My next step (after I review a bit of statistics that you response alerted me to) will be to compare the SEA vs Jacobian matricies implementation efforts.