# Normalize across groups, individuals or population?

I would like to compare sensors of a manufacturer A with those of a manufacturer B. As they provide different measurement magnitudes, I want to scale the variables such that it makes more sense to compare them:

But I'm not sure how exactly this should be done: Shall I scale the sensors

1. individually
2. among the manufacturers
3. or across the population?

The latter probably makes no sense but the others? The upper four belong to manufacturer A and the lower four to manufacturer B.

This is how it looks when scaling per manufacturer:

• Could the different magnitudes be due to differences in units? – Dave Aug 27 '20 at 10:36
• All the units are of resistance. Is that what you mean? – Ben Aug 27 '20 at 11:11
• Are all of the units Ohms? – Dave Aug 27 '20 at 11:34
• Yes, everything is measured in Ohms. – Ben Aug 27 '20 at 14:21
• What property of the sensors do you want to compare? Independent scaling will destroy the possibility of some comparisons, so it's essential that we know your objective. – whuber Aug 28 '20 at 18:21

First, my understanding of what the product actually does, to quote a reference:

A resistive sensor is a transducer or electromechanical device that converts a mechanical change such as displacement into an electrical signal that can be monitored after conditioning. They are commonly used in instrumentation.

Second, assume you can construct a representative population of displacements that could be generated in practice or that comprise areas of interest (appropriately repeated to reflect relative importance).

For each known value of displacement in the constructed test population, obtain the generated electrical signal (whose precise value is known) by the manufacturer's product.

You now have a basis to compare manufacturers in performance, or how to weight each manufacturer to construct a super population for select goals.

• That's interesting but I didn't quite get it. For an easier understanding: The device, a sensor, is converting an applied gas concentration to a related resistance value (through physical-chemical processes). These values are read out electronically afterwards. – Ben Aug 27 '20 at 11:10
• Ben: Good background. In this context, various commonly tested gaseous in varying volumes are tested by comparison to the known volume of gas using a select manufacturer's product. This results in a precision estimate by product across a range of gaseous and volumes. If most of the commonly performed tests occur for gas x at volume y, then one could 'standardized' the product performance at these values for different manufacturer's product, as one conceivable option. – AJKOER Aug 27 '20 at 20:52
• Exactly, but how to compare the performance? – Ben Aug 28 '20 at 5:00
• In the case of physical displacement per a gas displacement, take a known volume (or weight converted to moles of say CO2, where 1 mole of any gas at standardized temperature and pressure occupies the same volume relative to the moles of the gas present) of, for example, say Dry Ice (solid frozen CO2), in a medium in which CO2 (gas) at room temperature does not dissolve. Test gas volume/wt on a product to estimate, by electrical resistance measurements, its opinion of the amount of gas present. Repeat the tests. The different measuring products should agree after adjusting for volume (moles). – AJKOER Aug 28 '20 at 11:53

Doesn't the main objective of normalization imply that you should normalize your whole dataset? Meaning, assuming you have the same variables for both manufacturers, you create a dataset with all your observations, and scale it accordingly?

I think it would be useless to scale the data per manufacturer; to make sense, I believe you need to scale all the observations in your dataset simultaneously.

• I did that just to find out - and the populations/differences look all the same but on a scaled axis now. Hence, I guess, this isn't useful. – Ben Aug 27 '20 at 11:13
• Maybe I misunderstood your problem / objective. But if you want to compare the manufacturers, aren't you exactly supposed to retain the differences, but on the same scale? – Johanna Aug 27 '20 at 11:33
• I guess the answer is yes :) Question is how do I do exactly this? – Ben Aug 27 '20 at 14:22
• What I have done in the past is what I suggested (scale the whole dataset all togheter), but if this is wrong I'd also like to know! – Johanna Aug 27 '20 at 14:38
• I didn't say it is wrong but visually nothing changed. So, at least, I would say it doesn't provide more information. – Ben Aug 27 '20 at 14:46