Comparing offset between curves

Question

I have two populations of data on a Y-by-X plot. I want to quantify the difference between the two populations somehow, but have a couple of issues.

* The populations have different distributions of x-values, making it difficult to compare averages without chopping off some of the data.
* The trends curve, so I can't compare the equations easily.

Ideally, I'm looking for a way to quantify the 'average' difference in Y at a given X. Is there a way I can do this easily within JMP?

Y-by-X plot attached.

Untitled.png

brady_brady · Answer

Hi, here is one easy approach.

1) Right-click in your graph and select Smoother > Save Formula.

2) Look at the formula in the data table... it will have 2 "Spline Eval" pieces, one for each member in the group.... something like this:

3) Copy + paste each individual piece, so that it operates on all rows, not just rows belonging to a specific group, into a new formula column.

***** NOTE: this may involve extrapolation in your case, so heed the relevant interpretive cautions. Each formula will look something like this:

This will produce something like the last 2 columns, which I've named Curve 1 and Curve 2, in your table:

Next, compute the difference in these 2 columns, using a new formula column or a 1-click transform from within Graph Builder, and graph the difference column and the 2 formula columns you previously created vs. x, to view the results:

I've attached a table with illustrative table scripts and formula columns.

Cheers,

Brady

ExampleTable.jmp

Dan_Obermiller · Answer

Here is a thought. Your curves look like they can be described quite well by a quadratic model. So have your data set up as 3 columns: Group, X, and Y.

Use Fit Model.

Y goes in as Y.

Build a model with effects for Group, X, X*X, Group*X, and Group*X*X.

Run the model and look at the parameter estimates.

The estimate for Group will give you the offset in the intercepts for the models.

The estimate for Group*X will give you the change in the slopes between the two models.

The estimate for Group*X* will give you the change in the quadratic terms between the two models.

By breaking it up this way, you have a better description of what and how the groups differ without having to explore EVERY possible X and calculating a difference. But, you could still do that by using the profiler. Place the slider for X at your desired location and look at the change in the Group profile.