In the Chi-Square Test of Independence, the Test Statistic Used $\chi ^ { 2 } = \Sigma \frac { ( \mathrm { O } - \mathrm { E } ) ^ { 2 } } { \mathrm { E } }$

Essay

In the chi-square test of independence, the test statistic used is $\chi ^ { 2 } = \Sigma \frac { ( \mathrm { O } - \mathrm { E } ) ^ { 2 } } { \mathrm { E } }$ . Discuss the meaning of $\mathrm { O }$ and $\mathrm { E }$ and explain the circumstances under which the $\chi ^ { 2 }$ values will be smaller or larger. What is the relationship between a significant $\chi ^ { 2 }$ value and the values of $\mathrm { O }$ and $\mathrm { E }$ ?