Methods for correlation and error analysis (statistical)

[rodder58]

1. A system of 7 objects each have one measurement taken of them. These measurements are to be compared with two theoretical models, which theoretical model does the data fit best?[br]The machine used to measure the values has an extremely small error, so the data gathered does not have significant any error in the numbers I am interested in ( hence no standard deviation ). All numbers measured depend on each other. There are no multiple measurements done on the objects as error in machine is so small, thus no giant spread of data.



2. Example: => Experimental data : Object 1 (OJ1): 93.8, OJ2: 81.3, OJ3: 72.7, OJ4: 38.9, OJ5: 62.9, OJ6: 76.0 OJ7: 43.6 [br]
Theoretical Model 1: OJ1: 107.97, OJ2: 116.85, OJ3: 127.52, OJ4: 160.40, OJ5:132.10, OJ6: 121.03, OJ7: 155.14[br]
Theoretical Model 2: OJ1: 110.03, OJ2: 116.86, OJ3: 128.20, OJ4: 156.72, OJ5: 135.37, OJ6: 125.24, OJ7:153.99[br]



3. The data does not fit a normal curve, thus the Chi-squared method does not apply to it. It does not fit any other form of curve. A modified matched-pair analysis was attempted, but the lack of a standard deviation did not lead to a true meaningful answer. I have searched for a method, but to not avail. The Kolmogorov-Smirnov test was suggested, but I don't know if it can be applied to this system?

 

[D H]

Please don't write your entire post in bold. It makes it hard to read.

See how much better this looks?

If the measurement errors are indeed "very small" (presumably on the order of 1/10, given the numbers you posted), both models are bad. Make that incredibly, incredibly bad.

You need to do something completely different here. Check your models (did you do the math right?), check your measurements (did you perform the procedure properly?), check everything. No statistical hypothesis test applied to observations and models this far in disagreement will have any validity whatsoever.

Edited to add:
You didn't say anything about the model uncertainties. If these differ between the two models then you can say one model is better than the other. I assumed small model uncertainties because of the precision you used in specifying the model values. If the uncertainty in some value is 40 for example, it is silly (at best) to say the expected value is 156.72.