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I was suddenly bombarded with a new topic at the end of my dissertation which other student was supposed to do and its related to statistics which was not my field till now but I am reluctantly entering it. So please dont mind if the question here is rather stupid. The problem I have is: I need to rank a set of items based on "validity". The item ranked 1 in this case would be more "valid" than the item which is ranked 2 and so on. To decide the ranks, there are 9 different criteria with different ranges. Each criterion measures something different and on a different scale. However, I make sure that each criterion is positively related to validity. Higher the "score" more the "validity".

For example,

  • Criteria_1 : Scores presence of an element "a" in item x as 0.5,

  • Criteria_2 : Scores presence of another element "b" in the item x as 1.0,

  • Criteria_3 : Scores presence of another element "c" in the item x as 0.7,
  • ...,
  • Criteria_N : Scores presence of another element "z" in the item x as 5.0

Some criteria just score the presence of absence of an element with "1.0" or "0.0", respectively.

To make a summary score like Criteria_Sum, I need to add up all these criteria. BUT to do it I need to make the apples and pears comparable. In this case should I "normalize" the scores or "standardize" them? If the answer is "either" why "normalize" or why "standardize"?

For further information: The items to be ranked in this case are graphs and we need to check if the graphs are valid or not valid. If the connections between nodes and edges are valid or not valid.

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  • $\begingroup$ At the moment your different criteria all have different weights (if you just add them). Is that what you want? If so no need to normalise them. If you want them to have equal weight then convert them all onto the same scale. If I have completely misunderstood your question then you need to provide a bit more detail. $\endgroup$
    – mdewey
    Jun 3, 2016 at 14:52
  • $\begingroup$ You got the question right. I need to being the data to same scale. Is there a specific way to do it or just use mean centering method? $\endgroup$
    – AnjaniKD
    Jun 6, 2016 at 10:01

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At the moment each criterion has two values, one of them is zero, the other varies. To put them all on the same scale it would be simplest to convert them all to have values zero and unity. So multiply the first one by 2, leave the second one, and so on. The last one N needs dividing by 5. Centering by subtracting the mean will still leave them with different ranges.

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