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Symmetric measures are reported separately for
customers who did and did not have contact with a
store representative. These measures are based on the
chi-square statistic.
Phi is the
ratio of the chi-square statistic to the weighted
total number of observations. It is the most
"optimistic" of the symmetric measures, and unlike
most association measures, does not have a theoretical
upper bound when either of the variables has more than
two categories.
Cramer's V
is a rescaling of phi so that its maximum possible
value is always 1. As the number of rows and columns
increases, Cramer's V becomes more conservative with
respect to phi.
The contingency
coefficient takes values between 0 and
SQRT[(k-1)/k], where k = the number of rows or
columns, whichever is smaller.
It becomes more conservative with respect to phi as
the associations between the variables become
stronger.
The significance values of all three measures are 0.012, indicating a statistically
significant relationship.
However, the values of all three measures are under 0.3, so although the relationship
is not due to chance, it is also not very strong.
While these measures give some sense of the strength
of the association, they do not, in general, have an intuitive
interpretation. To develop a clearer sense of this, look at the
directional measures.
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Symmetric Measures |