# ChiSquaredTest Command

From GeoGebra Manual

- ChiSquaredTest[ <Matrix> ]
- Performs a chi-squared test that compares the given matrix of observed counts against the matrix of expected counts determined by the hypothesis of independence.
- The matrix of expected counts is calculated internally. Each expected count is found from the row and column totals of the given matrix of observed counts using the rule:
- Results are returned in list form as
*{Probabilty value, chi-squared test statistic}*. **Example:**`ChiSquaredTest[{{1, 2, 1}, {3, 2, 3}}]`

yields*{0.69, 0.75}*.

- ChiSquaredTest[ <List>, <List> ]
- Performs a Goodness of Fit test that compares the given list of observed counts against the given list of expected counts.
- Results are returned in list form as
*{Probabilty value, chi-squared test statistic}*. **Example:**`ChiSquaredTest[{1, 2, 3, 4}, {3, 2, 4, 2}]`

yields*{0.31, 3.58}*.

- ChiSquaredTest[ <Matrix>, <Matrix> ]
- Performs a chi-squared test that compares the given matrix of observed counts against the given matrix of expected counts.
- Results are returned in list form as
*{Probabilty value, chi-squared test statistic}*. **Example:**`ChiSquaredTest[{{1, 2, 1}, {3, 2, 3}}, {{2, 3, 2}, {4, 2, 3}}]`

yields*{0.45, 1.58}*.