Changes

  Each cell has an expected frequency of at least five.

  Each cell has an expected frequency of at least five.

*The <math>\chi^2</math> test first calculates a <math>\chi^2</math> statistic using the formula:

*The <math>\chi^2</math> test first calculates a <math>\chi^2</math> statistic using the formula:

<math>\chi^2 = \sum_{i=1}^{columns} \sum_{j=1}^{rows} \frac{(observed _ij-expected _ij)^{2}}{grand total}</math>

<math>\chi^2 = \sum_{i=1}^{columns} \sum_{j=1}^{rows} \frac{(observed _{ij}-expected _{ij})^{2}}{grand total}</math>

*<math>observed ij</math> is the array of the observed values in a given set of values

*<math>observed _{ij}</math> is the array of the observed values in a given set of values

*<math>expected ij = \frac{(column _i total)*(row _j total)}{grand total} </math>

*<math>expected _{ij} = \frac{(column _i total)*(row _j total)}{grand total} </math>

*observed and expected must have the same number of rows and columns and there must be atleast 2 values in each.

*observed and expected must have the same number of rows and columns and there must be atleast 2 values in each.

*A low result of <math>\chi^2</math> is an indicator of independence.

*A low result of <math>\chi^2</math> is an indicator of independence.

*From the formula of <math>\chi^2</math> we will get <math>\chi^2</math> is always positive or 0.

*From the formula of <math>\chi^2</math> we will get <math>\chi^2</math> is always positive or 0.

*0 only if <math>observed _ij = expected _ij</math> for each <math>i</math> and <math>j</math>.  

*0 only if <math>observed _{ij} = expected _{ij}</math> for each <math>i</math> and <math>j</math>.  

*CHITEST uses the <math>\chi^2</math> distribution with the number of Degrees of Freedom df.

*CHITEST uses the <math>\chi^2</math> distribution with the number of Degrees of Freedom df.

*where <math>df=(r-1)(c-1),r>1</math> and <math>c>1</math>.

*where <math>df=(r-1)(c-1),r>1</math> and <math>c>1</math>.