A distribuição qui-quadrado é uma probability distribution that arises in statistics when analyzing the variability of categorical data. It is particularly useful in testes de hipóteses, especially for tests of independence and ajuste do modelo.
A Chi-Square test evaluates how well the observed data fits a specific distribution model, comparing the observed frequencies to the expected frequencies under the hipótese nula. The distribution is characterized by a single parameter, the degrees of freedom (df), which is determined by the number of categories or groups in the data.
The Chi-Square Distribution is defined only for non-negative values, and its shape changes based on the degrees of freedom. With lower degrees of freedom, the distribution is skewed to the right, while as the degrees of freedom increase, it approaches a distribuição normal. This makes it a versatile tool for various statistical analyses, including assessing relationships in contingency tables and testing variance in populations.
Em aplicações práticas, os pesquisadores frequentemente use the Chi-Square test to determine if there is a significant association between two categorical variables or to test the fit of observed data to a theoretical model. The resulting Chi-Square statistic is then compared to a critical value from the Chi-Square distribution to determine the statistical significance of the results.