Linear and quadratic contrasts with unequally spaced treatments

[#1]

I am using the contrasts specification window with + and - buttons. However, when treatments are unequally spaced, the simple + and - isn't working. Here's my specific example:

Treatment doses: 0, 1, 2, 4 

These doses are NOT equally spaced so we can not use the typical 4 level linear and quadratic contrasts. I calculated appropriate coefficients as shows in this link. 

https://real-statistics.com/one-way-analysis-of-variance-anova/trend-analysis-polynomial-contrast-co...

From my calculations, the linear coefficients should be -7, -3, 1, 9. In JMP, -0.7, -0.3, 0.1, and 0.9 satisfy the JMP requirements of adding up to 0 and absolute value less than 2. 

My issue is with quadratic coefficients. From my calculations, the quadratic coefficients should be 224, -128, -256, 160. How do I get these quadratic coefficients into JMP 16 Pro?

Thank you for any and all advice!! 

[#2]

Yes, it can be confusing.  It is how the model is parameterized. Yes, it looks funny...but once you realize how the model is parameterized it's just addition to get the contrasts/comparisons/estimates/etc. of interest.

Here is some detail: https://www.jmp.com/support/help/en/17.1/index.shtml#page/jmp/nominal-factors.shtml#ww65535.

Now, you can also see another parameterization if you look at the "indicator function parameterization" results in the Fit Model platform (compare those to the "parameter estimates"). They look different, but they are equivalent. That, however, won't change the parameterization in the Custom Test dialog. I'd take some time looking at your parameter estimates to make sure you understand them, and their respective p-values (i.e., what the null hypotheses are).  One way to help is to select "Show Prediction Expression" to see how the model actually looks.

[#3]

Not knowing the details of your experiment makes this challenging, but can you treat dose as a continuous factor and model it via ANCOVA?  Yes, you only have 4 levels (0, 1,2, 4) but it may not be a bad way to at least visualize what is going on.