Birge ratio

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Sun, 03/01/2009 - 07:41 am

Has anyone dealt with the comparison of measurement results ? I want to calculate the Birge ratio for a set of measurements with given uncertainty estimates. If anyone has already written a function that does this sort of analysis, I would be glad not to have to reinvent the wheel. And in case there are more knowledgeables out there - are there, perhaps, other criteria to identify outliers or data heterogenity ?
You are really not providing enough information about your problem.

If you want to calculate the Birge ratio you really need to have a Chi-square from somewhere. This would typically be available if you ran curve fitting or have some way of comparing and summing differences between data sets. Since you are not telling us what kind of data you have or how many data sets are involved, it is impossible to give you more specific advice about computing the ratio.

If you are dealing with a single set of data there are other criteria for finding outliers. It could be as simple as using a box plot. Simply run your data through the 1D statistics report (Analysis Menu->Statistics).

If you have more than one data set and you are looking for homogeneity (of variances) you might want to check out StatsVariancesTest. You might also find the StatsContingencyTable appropriate.

I hope this helps,

A.G.
WaveMetrics, Inc.

March 2, 2009 at 03:47 pm - Permalink

Igor wrote:
You are really not providing enough information about your problem.

If you want to calculate the Birge ratio you really need to have a Chi-square from somewhere. This would typically be available if you ran curve fitting or have some way of comparing and summing differences between data sets. Since you are not telling us what kind of data you have or how many data sets are involved, it is impossible to give you more specific advice about computing the ratio.



A.G. thanks for looking after it. Well, I will try to explain what I want to do. I have N published measurement results for a quantity (speed of light, for example). These results are collected from different publications together with their error estimates (standard deviation). I then want to find a weighted average if the data sets are compatible. In order to test for compatibility one can look at the Birge ratio, which is related to some chi^2(x,N-1) distribution function. I have started to write a function that does this, using the data and their errors as input waves.

I just wanted to know whether others have already tackled/encountered this problem, and or whether there are alternative testing methods for finding out the compatibility of individual data. I know that there are other tests out there (Cochrans, ...), but they always demand several sets of samples that can then compared to each other. The key problem is that my literature data do not give individual samples, but only estimated parameters from distributions that are not necessarily gaussian or known. I also don't know the effective number of degrees of freedom of these measurements.

March 4, 2009 at 06:50 am - Permalink

It sounds as if some form of ANOVA test is in order. If you have all the data from all experiments you can use StatsANOVA1Test and/or the Tukey test (HSD) in StatsTukeyTest. If you don't have the individual measurements leading to the means and variances you can still compute the relevant quantities for ANOVA. This is discussed, for example on page 199 of the fifth edition of Zar's book (Biostatistical Analysis, Prentice Hall NY 2009).

A.G.

March 9, 2009 at 01:12 pm - Permalink