**Edit: (10/26/13) More clear (hopefully) mini-rewrites added at the bottom**
I'm asking this from a theoretical/general standpoint - not one that applies to a specific use case.
I was thinking about this today:
Assuming the data does not contain any measurement errors, if you're looking at a specific observation in your data and one of the measurements you recorded contains what could be considered an outlier, does this increase the probability (above that of the rest of the observations that do not contained measured outliers) that the same observation will contain another outlier in another measurement?
For my answer I'm looking for some sort of theorem, principle, etc. that states what I'm trying to communicate here much more elegantly. For clearer explanations see Gino and Behacad's answers.
Let's say you're measuring the height and circumference of a certain type of plant. Each observation corresponds to 1 plant (you're only doing this once).
For height, you measure:
Obs 1 | 10 cm Obs 2 | 9 cm Obs 3 | 11 cm Obs 4 | 22 cm Obs 5 | 10 cm Obs 6 | 9 cm Obs 7 | 11 cm Obs 8 | 10 cm Obs 9 | 11 cm Obs 10 | 9 cm Obs 11 | 11 cm Obs 12 | 10 cm Obs 13 | 9 cm Obs 14 | 10 cm
Since observation 4 contains what could be considered an outlier from the rest of the data, would the probability increase that measured circumference also contains an outlier for observation #4?
I understand my example may be too idealistic but I think it gets the point across...just change the measurements to anything.
Edited in attempts to make more clear:
Version 1 Attempt of Abbreviated Question:
In nature and in general, is there a tendency (even a weak one) that the probability is greater that the "degree of variance from the mean in any attribute(s) of an observation" will be similar to the "degree of variance from the mean in any other* specific attribute of that same observation" in comparison to the probability that it will INSTEAD be more similar to the "degree of variance from the mean in that same* specific attribute of any other observation."
* next to a word means I was pairing what they reference.
"Quotes" used above mean nothing and are used simply to help section parts together/off for clarity.
Version 2 Attempt of Abbreviated Question:
In nature and in general, is variance from the mean across observations for one attribute¹ correlated (even with extremely loose correlation) to the variance from the mean across observations for all attributes¹?
¹Attribute meaning measurement, quality, presence-of-either of these, and/or nearly anything else that the word "attribute" could even slightly represent as a word. Include all synonyms of the word "attribute" as well.