Ratio Statistics / Fieller's Method

[_john_97]

What inspired this wish list request? 

When evaluating the ratio of two data sets, for example, product 1 and product 2, the most well accepted method for determining the confidence interval of this ration is Fieller's method/theorem. This analysis is currently not available in JMP and R must be used.

https://en.wikipedia.org/wiki/Fieller%27s_theorem

What is the improvement you would like to see? 

I would like to see an option in the Oneway analysis fit y by x platform to perform this analysis.

Why is this idea important? 

This is needed when making comparisons between two things expressed as a ratio, for example, product 1 is X% better than product 2. 

[JMP-Andy]

The R library mratios has a ttestratio() function that tests if the ratio of 2 sample means are statistically different from a null hypothesis ratio, rho (e.g., H0: rho = 1).  You can specify if the variances are equal or unequal (Satterthwaite d.o.f. approximation) and do a 1-sided or 2-sided test.  It uses Fieller's Theorem to calculate the confidence interval of the ratio.     

https://cran.r-project.org/web/packages/mratios/index.html 

There is no python package that does this for integration with JMP 18 as far as I know.  It would be great to have this added to Fit Y by X, or even more generally to Fit Model. Testing the ratios of any linear combinations from a GLM is also possible with mratios:

"With this package, it is possible to perform (simultaneous) inferences for ratios of linear combinations of coefficients in the general linear model. In particular, tests and confidence interval estimations for ratios of treatment means in the normal one-way layout and confidence interval estimations like in (multiple) slope ratio and parallel line assays can be carried out. Moreover, it is possible to calculate the sample sizes required in comparisons with a control based on relative margins. For the simple two-sample problem, functions for a t-test for ratio-formatted hypotheses and Fieller confidence intervals are provided assuming homogeneous or heterogeneous group variances."

[SarahGilyard]

Thank you for posting this suggestion _john_97.  We are investigating this method for possible inclusion in the Oneway platform. Thanks!