Comparing companies - which method should I use

#1
Hi everyone,
I would like to compare 5 companies regarding the average price of 3 product categories. The average price has already been calculated as a weighted average.
The objective of this analysis is to compare the companies on the three product categories despite the price difference and to be able to quantify how much each company is above or below the others.
Ideally, I should be able to place all new values within a single chart.The main problem is that the average price differs significantly among the 3 categories.

On the Internet I've found three scaling methods:
1. Min-max normalization
2. Z-score Normalization
3. Mean normalization (deviation from the mean, divided by MAX-MIN)

Unfortunately, none of them convince me completely:
Min-max normalization sets the minimum value equal to 0 as a new value
Z-score Normalization I'm afraid is not intuitive enough for my interlocutors
Mean normalization is a little better, I just don't understand the added value of dividing by MAX-MIN instead of directly the mean itself. I'm just not sure if dividing by the mean has other drawbacks that I can't see.

Can you please give your opinion on the techniques considered and suggest whether there are any further approaches for this case?
Thank you very much
Best regards
David


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Karabiner

TS Contributor
#2
1. Min-max normalization
2. Z-score Normalization
3. Mean normalization (deviation from the mean, divided by MAX-MIN)
(...)
Z-score Normalization I'm afraid is not intuitive enough for my interlocutors
Mean normalization is a little better, I just don't understand the added value of dividing by MAX-MIN instead of directly the mean itself.
Both in 2) and 3), the mean is subtracted from each value, hence the mean
of the normalized data is zero. The difference between 2) and 3) is how the
variability is handled. There is no division by the mean in both approaches.
Can you please give your opinion on the techniques considered and suggest whether there are any further approaches for this case?
Well, you did not state the research question behind this, which goals should
be achieved by the chart. For example, is it is clearly unimportant if companies
differ up to 400 unit in Cat3, but only 8 units in Cat1?

With kind regards

Karabiner
 
#3
you did not state the research question behind this, which goals should
be achieved by the chart. For example, is it is clearly unimportant if companies
differ up to 400 unit in Cat3, but only 8 units in Cat1?
Hi Karabiner, thank you for your reply.
For example I should be able to state something like: Company 3 has a price 30% higher than the average of competitors on categories 1 and 2, but 40% lower on category 3.
I thought that by converting these deviations into relative terms the 3 categories, which have significantly different means and standard deviations, would be somewhat comparable.
I hope I added a little more context and answered the question.

David