I have a set of results from mathimatical model along 1000 m for every100 m and for different dates. What is the best way to statistically compare the performance of this model with the standard model?
Would you be so kind as to provide a few more details.
1) What are the different models?
Are you comparing Y=X1+X2^2 versus Y=(X1 * Log(X2))/(X1-X2)?
Are you comparing Y=X1+X2 in July versus Y=X1+X2 in December?
Are you comparing Y=X1+X2 versus Y=X7+X9?
Is one model a computer simulation and the other field data?
2) Do you have the raw data for all models or is one model a published model and you have the data for the other model?
3) What do you hope for in your answer? What is the goal?
4) What is your sample size? Can you get more samples?
As asked my answer would be this: I assume that you have a standard model and that you gathered data to create a new model. The best way to compare them is to go back to the field and do another experiment. Then you can analyze the data with both models and see how different they are both quantitatively and qualitatively. It is possible that Y(standard) = X1 + X2 + X3, and Y(new) = X6 + X12 + (X15)^2. However with the new data you find that Y(standard) is statistically indistinguishable from Y(new). This is a qualitative difference without quantitative consequence.
If you cannot gather new data, consider a simulation.
1) Simulate your system using something like a cellular automata model: http://mathworld.wolfram.com/CellularAutomaton.html shows one example, but these can be far more complex.
2) Use your raw data to get a mean and standard deviation. Use a random number generator with that mean and standard deviation to generate new values. Compare model output. Do this 100,000 times and look at the distribution of outcomes between the two models.
Dear Timothy A Ebert , first thanks a lot, I will send it to you to have better idea. by the way I found the answer and now I am working on that, thanks for your kind help and may God bless you.
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