How to check statistical significance for 2 non-linear trend lines?

[#1]

Dear JMP Community,

I have a question for your advise.

Case Study:

1. We are measuring the surface contour of an object.

2. The object is 150 cm long.

3. There are 2 measurement method, called (Method A) & (Method B).

Below is a simple graph showing:

X-Axis (Discreet Integer)  = The object length.

Y-Axis (Continuous Data) = The measurement of object contour (measured at each increment of X).

Questions:

How do I check check if there is any statistical difference between these 2 trend lines?

Take note, here we cannot do statistical test on 2 groups of data (on the measurement results alone between Method A &B) , since the data is tied to the specific length of the objects.

For example :

If the object surface is totally flat, the trend line recorded by both method (A and B) should be a flat line.

In my case, the object is curve (smiley face), so both method (A and B) shows a curve as in the graph.

Is there a method to check statistical difference for 2 or more non-linear trend lines?

Appreciate your thoughts on this. Thanks a lot.

B.r,

Chris

[#2]

Hi @ChrisLooi ,

  Since you are comparing method A and method B to measure the same thing, this sounds like it's perfectly fit for a Bland-Altman analysis. You can read the wiki on it here and from the NIH here.

  Presumably, you have a method (maybe A?) that is the standard and you're wanting to compare if the alternative test method (B?) results in the same results. You can do this by considering the Bland Altman analysis that compares the difference in the two measures to the average of the two measures. You can then plot this with the scaled standard deviation to see if there are systematic differences between the two methods.

  Another option is that if method A and B are measuring the same thing and should result in more or less the same measurements other than maybe noise, then you could always plot the results of A vs results of B one as the Y-axis and one as X-axis. If they were perfectly matching, you would get a line at 45-degrees, but they won't be, however, they should be close. The slope should be near 1 and the y-intercept should be near 0. Evaluating this fit can also give you an idea of how well one method maps to the other.

Hope this helps!,

DS

[#3]

Just one other thought...simply looking at the graph you provided, how much of a difference in the measures is of Practical Significance?  How much of a difference would matter from a scientific or engineering perspective?  Have you tried both methods measuring the same exact object twice?  This would provide an estimate of precision repeatability.  I might be more interested in which method has the better repeatability in a comparison of methods.