What does it mean when you say that two variables are
In general mathematics, two variables are considered "related" if
changing the value of one changes the value of the other. This is a very
general concept, so do not make it over-complicated. For example, Y= X+2.
The variables X and Y are related by the equation: Y= X+2.
In statistics, the concept of "related-ness" is more subtle. In this
case "related" is often used to mean "correlation". Here, if a collection
of some observations (X's) changes in some way, and another collection of
observations of some other variables (Y's) also changes in some way -- the
two variables are said to be "correlated"-- and there are formulas that
measure how well the variables are correlated. The caution here is that
"correlation" does not necessarily imply "causation". That is, two
variables can be correlated without one "causing" the other. Both may be
changing due to some other variables that have not even been identified,
so you have to be very careful.
A fanciful example is the following: I have a magic bell. It protects me
from tigers in my back yard. Every morning I ring it three times, and look
to see how many tigers are in my back yard. I have done this every morning
for 3 years, and not once have I ever seen a tiger. Therefore, my magic bell
is 100% effective in protecting me from tigers in my back yard. The fallacy
here is transparent, but often that transparency is not so self-evident.
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Update: June 2012