Editing Contingency table (section)

===Cramér's ''V'' and the contingency coefficient ''C''===
{{Main|Cramér's V}}
Two alternatives are the ''contingency coefficient'' ''C'', and [[Cramér's V]].

The formulae for the ''C'' and ''V'' coefficients are:

: <math>C=\sqrt{\frac{\chi^2}{N+\chi^2}}</math> and

: <math>V=\sqrt{\frac{\chi^2}{N(k-1)}},</math>

''k'' being the number of rows or the number of columns, whichever is less.

''C'' suffers from the disadvantage that it does not reach a maximum of 1.0, notably the highest it can reach in a 2&nbsp;×&nbsp;2 table is 0.707&nbsp;. It can reach values closer to 1.0 in contingency tables with more categories; for example, it can reach a maximum of 0.870 in a 4&nbsp;×&nbsp;4 table. It should, therefore, not be used to compare associations in different tables if they have different numbers of categories.<ref>Smith, S. C., & Albaum, G. S. (2004) ''Fundamentals of marketing research''. Sage: Thousand Oaks, CA. p. 631</ref>

''C'' can be adjusted so it reaches a maximum of 1.0 when there is complete association in a table of any number of rows and columns by dividing ''C'' by <math>\sqrt{\frac{k-1}{k}}</math> where ''k'' is the number of rows or columns, when the table is square {{citation needed|date=June 2020}}, or by <math>\sqrt[\scriptstyle 4]{{r - 1 \over r} \times {c - 1 \over c}}</math> where ''r'' is the number of rows and ''c'' is the number of columns.<ref>Blaikie, N. (2003) ''Analyzing Quantitative Data''. Sage: Thousand Oaks, CA. p.&nbsp;100</ref>