How to interpret the results from a paralellism test of two non linear curves - F test

[#1]

Hi

I need to prove, statistically, that these two curves are parallel. I have made a data table, fit a non linear 4PL curve and ran a parallelism test. Unfortunately my statistical knowledge is limited and I don´t know how to interpret the results. I would assume since the Prob value of the F test is below 0,05 the result is significant and therefore the null hypotheses is correct and and the lines are parallel. However the Prob value shows up orange, which confuses me.

Could someone help me make sense of this? And also explain the importance of the Prob ChiSq.

Thank you

[#2]

Good question. But, you have it backwards. If p-value < 0.05 then there is evidence of non-parallelism. You're testing the null  hypothesis of equal lower and upper asymptotes and slopes. To that end, either an F or Chi2 test statistic is used. Lack of statistical significance (p > alpha) at a preselected level (alpha=0.05, for example) is viewed as indicative of parallelism (i.e., can not reject the null hypothesis). Conversely, if p < alpha then then the hypothesis of parallelism is rejected. 

[#3]

The example you shared will be poorly modeled by a 4PLC. You have observed a narrow range that does not exhibit the four features of a sigmoid curve, so it is difficult to estimate all four parameters well. A quadratic polynomial will be better.

Also, parallelism tests are provided for compatibility. They are legacy tests that are still commonly used today, but they are indefensible. An inferential test works in one direction only. They are used to establish the alternative hypothesis with data. The parallelism tests use an alternative hypothesis that there is a difference. Failure to reject the null hypothesis (i.e., they are parallel) cannot be used as an argument for parallelism. It is invalid. You must use inference where the alternative hypothesis is an equivalence (parallel) and reject the null hypothesis that they are different (non-parallel) to conclude parallelism.

The equivalence test fails, as expected by inspection of the plot of the data and the fits. They do not have the same shape.

[#4]

Hi Mark: Thanks for introducing the Fit Curve platform to me! I had no idea of its existence. It is a great set of tools, and is a great addition to JMP!

[#5]

Thanks for the reply Mark.

I can see the mistake in choosing a 4PL as the curve does not have the sigmoidal shape. Noted, actually look at the shape of your curve! I am learning.

Regarding the equivalence test, it fails because all factors (intercept, slope and quadratic) are out of limit? Would it fail if only the slope is within limits? Could you give further instruction on how to interpret the results of this test?

[#6]

In the case of the quadratic example, for parallelism slopes and quadratics must be equivalent. So, to answer your question, yes it would fail if only the slope is  within limits. The difference in intercepts is an offset between the two curves, so it has no effect on parallelism. 

A pretty good discussion is here.

https://www.researchgate.net/publication/225064005_Implementation_of_Parallelism_Testing_for_Four-Pa...

[#7]

What does it mean to be parallel? It means the same shape but a shift left or right from the standard curve. So one parameter can vary, but the others must remain 'fixed.'