Measurement Error Bars

Question

Hey all!

Got a puzzler here... I've got a customer that would like to include a measurement uncertainty in a linear fit - i.e. multiple tools measuring in a manufacturing environment, tool A has an uncertainty of +/-0.01 units, and tool B has an uncertainty of +/-0.05 units.  It is impractical to capture the uncertainty around each datapoint within the data set by replication (measuring the same sample several times) or the data is unavailable due to on tool aggregation of the raw data.  Assume that we have a column of data with the uncertainty for each data point provided - i.e. data col, uncertainty col.

So here's the question.  Is there a way to  first display the uncertainty around each data point, when it is provided in this manner, in the Bivariate or Fit Model Platform and can the uncertainty be included in the analysis?  Lets assume for the moment that Graph Builder using a range isn't an option - the customer found that method too complicated.  My gut says I should be able to do it using a weight (more uncertainty = lower weight), but I'd like the group's thoughts.

Thanks!

M

MikeD_Anderson · Answer

chris.kirchberg  - I've done this before too back in the day.  Back then I did it using the experimental data analysis package for Mathematica (my pre-JMP days).   The customer that asked this is also a materials chemist, so the context is definitely an experimental chem/physics question.  I also had this question back at my old job, but couldn't figure out how to do it before I went into another role.

phil.kay​ - I hadn't thought of simulating!  Cool idea, the customer in question is pretty new to the software (< 3 months), so its probably a bit complex to propose for him.  But I'm going to have to remember that one...

A column property would definitely be a step in the right direction.  There is a column property for sigma, but that's more for a historical sigma for SPC applications.  It sounds like, based on the comments so far, that there isn't a capability built in for this.

danielvalente​ Is this something that can we get into the pipeline for JMP13?  It is actually a customer request and I could imagine that there would be a lot of application and need for it.

I could image a 3 part solution here.

1.  Need the ability to plot user provided error bars in x and y for measurement errors from a column.  (Since, in a production setting two tools might not have the same measurement error... it does happen - a lot).  This could look like a Measurement Uncertainty field in the platform dialog.

2.  Need the ability to provide a measurement error as a column property for single tool or unknown measurement error situations (a default error).

3.  Need to propagate the measurement uncertainty through the calculations.

Phil_Kay · Answer

Hi Mike,

I have done this before for a measurement uncertainty problem. There are algebraic approaches to propagation of uncertainty. However, I find it easier to use the brute force approach of Monte Carlo simulation. You could simulate 1000 versions of the data with simulated variability according to the uncertainty in Y and X. You would then fit Y = B0 + B1*X for each of these 1000 data sets. You then have a distribution of 1000 values for B0 and B1 and hence can create confidence intervals. It requires a bit of table manipulation but it could always be scripted if they need to do this a lot.

I agree it would make sense uncertainty to be a column property.

I think Ian Cox had a scripted solution for displaying uncertainty in Y and X.

Phil

Chris_Kirchberg · Answer

Hi Mike, Basically they want to propagate error of measurement into the modeling of regression. I have done this in chemistry by hand and it is a painfully long process. I would have thought that a column property would have been a great place to capture known variability (or error of measurement like you stated, another way to put it as known standard deviation for the measurement). However, I do not see away to enter this for a column or propagate this standard error/variation within Fit Model or Fit Y by X. Chris Kirchberg JMP Technical Enablement Engineer Worldwide Technical Enablement Team SAS Institute, Inc. 100 SAS Campus Drive | Building T | Cary, NC 27513 Tel: +1-919-531-9927 Mobile: +1-303-378-7419 E-mail: chris.kirchberg@jmp.com Unsubscribe