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Which statistical tools are best suited for this problem:

Team A goes and measures 3 magnitudes in 200 locations (let's imagine the volume of a room, the insulation coefficient and the average temperature outside the room). For each room they calculate the energy this room will consume to keep the desired temperature for a week.

So after the measurement campaign they have measured these 3 magnitudes in 200 different rooms (each room is only measured once). So the data looks like:

 (Room_volume, r_coefficient, T, estimated_energy)

Team A is assumed to be very good at getting their results. Now team B measures the same 200 rooms, and calculates all the estimated energies for each room.

How should we measure the performance of team B vs team A (where A is assumed to be accurate)?

Forgetting the physics, as it's just an illustrative example, how do you compare the accuracy of a measurement campaign measuring 3 values from which a 4th one can be calculated deterministically? Note that none of these values are distributed in any special way among the 200 samples (they don't look gaussian)

I started looking at the distribution of errors, so:

 {Estimated_energy_Ai - Estimated_energy_Bi} with i = 1..200

And seeing how many results are within a standard deviation. What other tools are appropriate?

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If you are 100% sure your data is non-normal, then you can perform a T-test to say if the two results are significantly different.

if your data sets have equal sample and variance

try using scipy.stats.ttest_rel

http://docs.scipy.org/doc/scipy-0.13.0/reference/generated/scipy.stats.ttest_rel.html

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  • $\begingroup$ Unfortunately the two data sets have different variance. Is there a version that can account for that? $\endgroup$
    – Massagran
    Commented Jun 12, 2014 at 13:07
  • $\begingroup$ You if variance are different then you can try a two sample t test. you can try t test for unequal variance. Check the examples from scipy stat ttest independent $\endgroup$
    – Sri
    Commented Jun 12, 2014 at 15:04

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