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I would like to emphasize the percentage change in the treatment cost by the percentage changes in the share of non-hazard waste.

Can I say "Every 10 percentile increment in the share of non-hazard waste in total waste leads to a 10-percentile decrement in the unit treatment cost"

If not accurate, how to describe the trend in the figure?

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  • You mean "every 10 percent", not percentile. A percentile is a grouping into one of 100 groups.
    – stangdon
    Commented Sep 10, 2021 at 11:43
  • Every 10% increment in the share of non-hazard waste in total waste leads to a 10% decrement in the unit treatment cost? I was afraid people might be confused by the base of each 10% increment because an increase from 10% by 10% is 11%, not 20%...
    – Elizabeth
    Commented Sep 10, 2021 at 14:00
  • That's true, "a 10% increment" could be ambiguous. But my point was that percentile is definitely wrong.
    – stangdon
    Commented Sep 10, 2021 at 14:09
  • Ok, no percentile. Do you have any idea how to make the sentence more clear?
    – Elizabeth
    Commented Sep 10, 2021 at 14:47

3 Answers 3

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There are many alternatives. The key idea is that an increase by 10 percentage points results in a decrease of one dollar.

One possibility is to reverse this and say

A decrease of ten percentage points in the share of non-hazard waste increases the unit treatment cost by one dollar.

The difference between a ten percent decrease, and a ten percentage point decrease is that the change from 30% to 15% is a 50% decrease (it is halving) but a 15 percentage point decrease. See a comical take on this.

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The suggested wording will emphasize the treatment cost benefit as a function of the percentage of non-hazard waste, which i think is the intention of the question.

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The math relationship you are describing is an 'inverse-ratio', which describes an output (waste) that gets smaller as the input (cost) gets larger. In your example, this is a 'proportional inverse-ratio', where every new unit of cost results in the same amount of new reduction in waste.

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