We are trying to evaluate the differences between measured data against an ideal baseline; in this case we're comparing the shape / magnitdue / quality of force displacement curves.
We've in the past compared the various slopes, peaks and valleys to do this, but are finding this doesnt capture all the variation we are seeing.
Is there a way to compare the entire "shape" of one curve against that of a baseline (for example comparing red vs blue in my attached plot)?
Is your goal to just characterize the magnitude of the delta at various locations along the x axis? If so I'd just create a simple run chart at predetermined x values and find the delta between one curve and the other. That will capture turning points, magnitude of delta, etc.
I think there a multiple ways that you could compare a 'master' curve to others. Some are more exploratory data analysis based like the correlation...some are more modeling based so I think some thought around what your criteria are for comparison is warranted before we offer more specific guidance. And also perhaps some insight around the practical purpose of the comparison and what decisions or actions it would lead to is helpful. Is it to explain, predict or something else? Reason I'm bringing all this up is the famous Anscombe's Quartet data set has 'curves' if you will, that have many identical 'statistics'...but the insight from each element of the quartet are very different. See Anscombe.jmp which is in the JMP Sample Data Directory.
If I'm interpreting your question correctly then the Functional Data Explorer in JMP Pro is likely what you're looking for.
Here are some resources for learning more about the Functional Data Explorer:
@abdulj, a sanitized (all IP removed) data table for the data representing your two curves would be a good example to test several of the options for the Functional Data Explorer platform, for example DTW, dynamic time warping, and column functions, etc.
If possible and you have time please post.
Sure - see attached table with a script to show the graph. Basically how can i quantify how different each of these curves are from one another. And if I designated one of these curves as a "master", how can compare how closely each of the other ones compares to the master?
I did this in just a few minutes with Functional Data Explorer, FDE (requires JMP Pro 14) and without knowing your data, so it's not in any sense definitive. But it does confirm Jeff's suspicion that this might be an approach worth investigating.
It looked like ID1, ID2 and ID3, taken together, identify a unique trace. Using FDE showed that the first functional principal component accounted for nearly 95% of the variability between the traces, so might be a good measure of similarity or distance:
Take a look at the scripts within the updated table.
I think you will find the answer to that in the resources that @Jeff_Perkinson shared.
But, briefly, this is a functional principal components analysis. One of way of thinking about functional principal components is that they are characteristic curves that describe the variation from the mean curve.