Chi-Square-Tests

The chi-square distribution depends on the number of degrees of freedom.

• There is a family of chi-square distributions.
• It is skewed to the right.
• It is non-negative.
  

Chi-square test of independence is used to determine if there is a significant relationship between two qualitative (categorical) variables.

A contingency table is used to investigate whether two traits or characteristics are related.

1. H0: X and Y are independent
   Ha: X and Y are dependent

2. Assumption: The excepted cell frequencies are > 5

3. Set the level of significance

4. Critical value is , with degrees of freedom (r-1)(c-1)
5. Test statistic:

where:
= observed frequency in cell
= expected frequency in cell
= number of rows
= number of columns
6. Reject H0 if

Chi-squared test of goodness of fit:

d.f. = k - 1

Chi-squared test of independence in a contingency table:

d.f. = (r - 1)(c - 1)

These formulas and degrees of freedom calculations are fundamental to performing chi-squared tests in statistics.