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What is the meaning of this sentence:

With any other averaging method, the relative position of every city in the sample would be worse.

Using the proposed method has better relative position or worse position among methods? What is meaning of "With any other" here?

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    'Better' or 'worse' position does not describe the methods but the cities measured. Using the averaging method in question gives values which put the cities in a better relative position (we are not told relative to what) than they would be using other averaging methods. – StoneyB on hiatus Jun 2 '15 at 19:44
  • It is comparing this method with other averaging methods. So here this averaging method is better than others? – user2991243 Jun 2 '15 at 19:46
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    It is not comparing the methods, it is comparing the results of the methods. – StoneyB on hiatus Jun 2 '15 at 19:46
  • That's true :-). yes. so here the results of this averaging method is better than others (better position of cities in the ranking)? – user2991243 Jun 2 '15 at 19:48
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    Sort of. It doesn't mean this is a better method--it may in fact be wildly inaccurate--but it yields better positions relative to the standard for the cities you are "averaging". – StoneyB on hiatus Jun 2 '15 at 20:05
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Suppose you have a new method "M" for "averaging" a particular value for cities -- for instance, "cultural diversity"-- which you measure against some standard ... perhaps the value of New York, which you define as 100.

With this method—that is, using this method—you come up with the following values for three cities:

            measured with
              Method M
  Toledo         84% of New York
  London        103% of New York
  Delhi         117% of New York

There are also other averaging methods, A, B and C. With these methods, you have the following values

            measured with   measured with   measured with
              Method A        Method B        Method C
  Toledo         65              75             72
  London         93              94             89
  Delhi          98             101             98

Your method, Method M, gives higher values relative to New York than any other method. That doesn't mean it's a better method, or a worse method—it just gives different results.

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It sounds like it means this model is the best.

Let's simplify the sentence a little to understand it better:

With any other [model], the [result] would be worse.

With can be thought of as short for if we did it with:

If we did it with any other model, the result would be worse.

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