- #1

Mikeldon

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**Combine several measures: "consensus mean" or a sampling problem?**

Dear all,

I have this problem:

the work aims to test the value (mean and error) of several sensors (with a different measure for each) in a subjects group, and then to have a single global value (a single mean and error) from all the sensors used to test the group. All sensors measure the same molecule with different specificity. The normality of the sensors measure in unknown.

More in details: I have 20 subjects (a,b,c,...,n). For each subject I can use different sensors (A, B, C,...M) , each resulting in a measure. The interest is focused on the value of each sensor (reflecting a biological parameter ) and then on the complessive value of all sensor measures.

The value provided by each sensor is interesting, so for the subjects I have the value of each sensor measurement. Not all measures ar reliable and some must be discarded, so each sensor measures a different subset of the 20 subjects.

I calculated the mean value, and variance of sensor A, B, C,...M using available measures from the group for each of the sensors.

**So this is the available data:**

Sensor A -> values from subjects (a,c,d,f,h,j...,n) ===> mean(A), variance(A)

Sensor B -> values from subjects (c,d,e,g,...,l) ===> mean(B), variance(B)

Sensor C -> values from subjects (a,b,d,e,j,k,...,n) ===> mean(C), variance(C)

...

Sensor M -> values from subjects (b,c,d,g,h,...,K) ===> mean(M), variance(M)

Each mean and variance calculated upon a different (sometimes equal) set of subjects, because of discarding of some bad values.

**Now the problem:**

I want to have a single measure from all my means, and relative variance, and I find difficult to decide which method to use, and under which reasons (heteroskedasticity, correlation of samples, ecc ecc).

The global measure should account for variability between and within each sensor, giving at the end a single mean value and a single error.

In particular I tend to consider two approaches: the calculation of a "consensus mean" or -considering each sensor as a strata- treat my work as a stratified sampling (where each sensor would be a strate) and weight each sensor by the number of subjects from which measures are available.

The theoretical approach of "consensus mean" is described here: http://www.fire.nist.gov/bfrlpubs/build02/PDF/b02027.pdf (page 26)

and here:

http://www.itl.nist.gov/div898/software/dataplot/refman1/auxillar/consmean.htm

And I would use Dataplot with the Mandle-Paule approach.

While for stratified sampling approach I am considering the formula described here:

http://www.spsstools.net/Tutorials/WEIGHTING.pdf (page 9)

Which approach do you think is more suitable for my needs, and why?

Thank you very much!

Michael.