Symmetric measures

Figure 1. Symmetric measures for Store by Service satisfaction, controlling for Contact
Symmetric measures for Store by Service satisfaction, controlling for Contact

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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