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In the Chi-Square Test of Independence, the Test Statistic Used χ2=Σ(OE)2E\chi ^ { 2 } = \Sigma \frac { ( \mathrm { O } - \mathrm { E } ) ^ { 2 } } { \mathrm { E } }

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In the chi-square test of independence, the test statistic used is χ2=Σ(OE)2E\chi ^ { 2 } = \Sigma \frac { ( \mathrm { O } - \mathrm { E } ) ^ { 2 } } { \mathrm { E } } . Discuss the meaning of O\mathrm { O } and E\mathrm { E } and explain the circumstances under which the χ2\chi ^ { 2 } values will be smaller or larger. What is the relationship between a significant χ2\chi ^ { 2 } value and the values of O\mathrm { O } and E\mathrm { E } ?

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