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What's a very concise, pithy but formal way (register is scientific English) to say that two methods identify the same set of factors involved in a process but that one method identifies more factors on top of the shared results?

In essence, I want a short statement that captures the following:

Method X and Method Y identifiy a shared set of factors; however, Method X also identifies some additional factors

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  • Your question is clear enough as it is, but it might help stimulate some ideas if you could give some example sentences, fill-in-the-blank style.
    – Dan Bron
    Aug 13 '14 at 14:24
  • I know I asked for an example sentence, but that one simply reprises your question. Can you provide a sentence you'd like to write in your actual paper (or whatever), and show us what word(s) in that sentence you'd like us to fill in? In other words, provide a template sentence as you'd actually want to write it, with blanks for the sought word(s).
    – Dan Bron
    Aug 13 '14 at 14:45
  • I guess the sentence structure that captures the quoted statement is one of the moot points. I'd want that statement to be rephrased in as concise a way as possible.
    – lybarin
    Aug 13 '14 at 14:49
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    While method Y identifies some of the factors involved, method X identifies all these plus others. Aug 13 '14 at 15:23
  • @Edwin Ashworth: I suggest you make your Comment an Answer. Jan 12 '15 at 8:43
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You're looking for "proper subset", although other terms could also apply. Here's a summary of your choices:

1) subset relation, also called set inclusion: a derived binary relation between two sets. If all the members of set A are also members of set B, then A is a subset of B, denoted A ⊆ B. From this definition, it is clear that a set is a subset of itself. (these use the same data pool and one can be less than the other but the problem with using this term is it won't be clear that one set contains less data than the other, since the term can mean either less than or equal data)

2) proper subset: A is called a proper subset of B if and only if A is a subset of B, but B is not a subset of A. (clear that you mean one set has less data, and both use the same data pool).

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