Chemist needs help - Data analysis of critical micellar concentration

[borodin]

Hi!

How are you?

 

I'm doing a project on chemistry and i need some help on analysis of data, if possible. I think i can get more help from a mathematician then a chemist. I'm studying a property (CMC, critical micellar concentration) of a solution, and to treat data i trace a plot of concentration (m) Vs specific conductivity (k), like this.

 

 

Then with a linear fit i get two straight lines, and the intersection is the CMC:

 

 

The problem begins when the variation isn't relevant, like this:

 

 

Now, i've found this paper where get a complicated data treatment and get a derivate-like result:

 

 

Paper: http://www.scienceforums.net/forum/attachment.php?attachmentid=2562&stc=1&d=1277950968

 

On page 138, in Results and Discussion, they said:

The problem of estimating the derivatives of the regression curve has beenvresolved by implementing the local polynomial regression estimator in the programming language Matlab, using the quartic kernel and plug-in optimal AMSE bandwidth. The calculation of hopt(x0) was achieved by estimating σε2 using a local polynomial regression, with a pilot bandwidth; the Parzen-Rosenblatt kernel estimator for f(x0) was also obtained by using a pilot bandwidth, and a parametric regression and a local polynomial regression were used for m(p+1)(x0). To avoid the problem of choosing an initial value h0, an iterative ap- proach was taken starting with a large h0. This initial pilot bandwidth produces another bandwidth, and this last one produces another, and so on. The iteration is continued to convergence.

 

This is chinese for me. I've never work in mathlab,so..it's sound very difficult to me to replicate this method, i just know the basics of math to work. But i would like give it a try. I've done the first and the second dervivative (dk/dm) ant it didn't worked. Its difficult to work with mathlab and this plugins? Is doable to a non-expert? Do you have any sugestion of a method to do the analysis of my data?

 

Thank you!

 

I

A nonparametric approach to calculate critical micelle concentrations- the local polynomial regr.pdf

Edited July 1, 2010 by borodin

[borodin]

There's an excel sheet with a plot, if you would like to check!

Thanks again:)

 

PS - sorry my bad english..

Exemplo.xlsx.zip

[Xittenn]

You've probably moved on already.... I just read this...

 

So what you are saying here is that when the two lines intersect but at near equal slopes you cannot see the intersection because you are not applying any mathematics to the process and are solely relying on sight to visualize the point of interception?

 

It looks to me as though you should be using least of squares linear regression for arbitrary data points, assuming you are only expecting linear type data.... otherwise use the non-linear(log-linear) equivalent...

 

I may be misinterpreting your post :/