The scientific method is always accompanied by a description of the standard experiment that holds everything constant except the variable of interest, [math]x[/math]. Suppose it would be very difficult to design an experiment that separates [math]x[/math] from [math]y[/math], so your experiment instead quantifies the effect of [math]x + y[/math]. Am I right to think the problem is solved if you can run experiments to quantify [math]y[/math] or alternatively [math]x + z[/math] and [math]x + y + z[/math]? If the scientist can verify that there's no interaction, it should be simple math. There might also be the option to decompose [math]x[/math] into simpler variables that could be tested independently.

 

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x + y= 6

y = 4

 

x = 6 - 4 = 2

 

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x + y + z = 12

x + z = 8

x + y = 6

 

z = 12 - 6 = 6

x = 8 - 6 = 2

or

y = 12 - 8 = 4

x = 6 - 4 = 2

 

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Edited September 13, 201411 yr by MonDie

The technique you require is called two way analysis of variance.

 

Here are some references

 

https://www.google.co.uk/search?q=two+way+analysis+of+variance&hl=en-GB&gbv=2&oq=&gs_l=