The use of this research test aims to verify if the distributions of two or more unrelated samples differ significantly in relation to the given variable.

## Conditions for test execution

Exclusively for nominal and ordinal variables;

Preferably for large samples, <30;

Independent observations;

Not applicable if 20% of observations are less than 5

There can be frequencies below 1;

In the latter two cases, if there are such incidences, it is advisable to group the data according to a specific criterion.

## Procedure for Test Execution

Determine H_{0}. The variables are independent, or the variables are not associated;

Establish the significance level (µ);

Determine the rejection region of H_{0}. Determine the value of degrees of freedom (φ), where φ = (L - 1) (C - 1), where L = table row numbers and C = number of columns… Find the value of Chi-square tabulated;

Calculate the Chi Square using the formula:

_{ }

To find the expected value (E), use the following formula:

_{ }

Since the calculated Chi Square, higher than the tabulated, rejects H_{0} in favor of H_{1}.

There is dependency or the variables are not associated.

### Example

A researcher wants to identify if there is dependence on the consumption of their chocolates and the cities of their region.

Taquari Valley Towns | |||||

Chocolate flavor | Lajeado | Holy Cross | Star | Taquari | ∑ |

Cashew Chocolate | 60 | 30 | 20 | 40 | 150 |

Peanut Chocolate | 45 | 35 | 20 | 10 | 110 |

Chocolate with flakes | 55 | 25 | 47 | 13 | 140 |

Chocolate with raisins | 70 | 35 | 25 | 20 | 150 |

∑ | 230 | 125 | 112 | 83 | 550 |

H_{0}: The preference for flavors is independent of the city

H_{1}: The preference for flavors depends on the city.

µ = 0,05

φ = (4 - 1) (3 - 1) = 6, where tabulated chi square is 12.6.

Calculation of expected values (E). | Taquari Valley Towns | |||

Chocolate flavor | Lajeado | Holy Cross | Star | Taquari |

Cashew Chocolate | 62,7 | 34,1 | 30,5 | 22,6 |

Peanut Chocolate | 46,0 | 25,0 | 22,4 | 16,6 |

Chocolate with flakes | 58,5 | 31,8 | 28,5 | 21,1 |

Chocolate with raisins | 62,7 | 34,1 | 30,5 | 22,6 |

Χ_{2} = (60 - 62,7)2/62,7 + (30 - 34,1) 2/34,1… (20 - 22,6) 2/22,6 =

_{ }

0,11+0,49+3,61+13,39+0,02+4+0,25+2,62+0,21+1,45+12+3,11+0,85+0,32+0,99+0,29 = 43,72

It is concluded that the calculated Chi square (43.72) is higher than the tabulated (12.6), rejects H_{0} in favor of H_{1}.

## Contingency Coefficient (CC)

CC is an indicator of the degree of association between two variables analyzed by Chi square.

The closer to 1, the better the contingency coefficient, which ranges from 0 to 1.

In the example given above the coefficient would be 0.3442.

_{ } Next: T Test for Two Unrelated Samples