This correlation is used to measure the association for the data where one or both variables have nominal scale and it is computed from a contingency table. In contingency table, we have to find the expected value from each cell. The bigger of the difference between expected value and observed value, the bigger of the relationship degree between two variables that meant that Cramer coefficient has also bigger value. When the data are ordinal scale then the relationship degree can be found by using Spearman correlation or Kendall Tau correlation, and when the data are quantitative form (in interval or ratio scale) and both variables have followed normal distribution then the relationship degree can be found by using Pearson correlation. Spearman, Kendall Tau, and Pearson correlation will be explained in other writing sessions. The formula of Cramer coefficient is
Cramer coefficient cannot be negative, interval score is between 0 and 1, because the statistic measures the relation between categorical variables which have no inherent order to them.
Example: by using contingency table of banking sample below, calculate Cramer coefficient to see the assosiation between age borrowers and their loan returning status
So the relationship degree between age borrowers and their loan returning status is 0.2504
This testing is used to determine the significance of relationship between two qualitative variables measured as nominal or categorical scaling. The null hypothesis being tested is
H0 : No association between two variables in the population
The statistic test uses the chi-square test as follow
Conclusion: There is significant assosiation between age borrowers and their loan returning status with the 95 percent level of confidence.
Note: The chi-square test should not be used if more than 20 percent of the expected frequencies are less than 5.
See you in other writing sessions, have enjoying statistics.
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*) Writer is a lecturer in The Institute of Statistics,Jakarta,Indonesia.
Bachelor of Statistics from TheInstituteofStatistics,Jakarta,Indonesia.
Master of Science in Experimental Statistics from NMSU, USA.