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

question 19

Essay

In the chi-square test of independence, the formula used is $\chi ^ { 2 } = \frac { \Sigma ( \mathrm { O } - \mathrm { E } ) ^ { 2 } } { \mathrm { E } }$ . 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 O and E?

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Definitions:

Generalization

The process of formulating general concepts by abstracting common properties of instances.

Power

The capacity or ability to direct or influence the behavior of others or the course of events.

Entire Block

A term used in logic or mathematics to refer to the entirety of a set, structure, or piece of data.

Generalization

A broad statement or concept obtained by inference from specific cases, often used to make predictions or to simplify complex ideas.