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What does the standardized anomaly [(x-mean)/standard deviation] really represent? From Wikipedia, the standardized anomaly (SA) represents the number of standard deviations above or below the mean that a specific observation falls.

Does this mean that:

  1. The SA indicates the dispersion of the data?
  2. The SA is dimensionless. As it is dimensionless, I am able to apply the SA to different time series (with different units) and compare different time series at once. For this, I will estimate the trend of the SA time series for the different time series and compare their trend values. What does this comparison actually represent? What does it mean when one of the time series indicates a trend?
  3. Next question, I am interested in comparing the time series before and after the SA is applied. To do this, I estimated the trend in the original time series (y1) and its standardized anomaly time series (y2). What does it mean when the trend in y2 > y1? The trend is estimated using the least-square regression method.
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    $\begingroup$ Should be (x $-$ mean) / SD. Of your questions: #1: No, because you have scaled by SD, the measure of dispersion. #2: The scaling is how many SDs you are above or below the mean. #3 I am not clear what you mean there. $\endgroup$
    – Nick Cox
    Mar 18 at 10:22
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    $\begingroup$ Maybe you are interested in a specific problem with specific data. In that case it is probably better if you explain this rather than asking an abstract question that doesn't really make clear what you have in mind. $\endgroup$
    – Christian Hennig
    Mar 18 at 10:57
  • $\begingroup$ Can you add a link for your reference to Wikipedia? $\endgroup$
    – Firebug
    Mar 18 at 11:01
  • $\begingroup$ I couldn't find 'anomaly' in the linked Wikipedia page. Perhaps you mean the Standard score (or Z-score)? $\endgroup$
    – Firebug
    Mar 18 at 11:09
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    $\begingroup$ Not to be too flippant, but what do you mean by meaning? The scaling does not transform to a normal distribution but researchers often use a comparison with the normal to guide interpretation, as whenever values on this scale are above 2 in absolute value (a moderate deal) or above 3 (a bigger deal). $\endgroup$
    – Nick Cox
    Mar 18 at 13:28

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