The chi-square (χ²) distribution is a probability distribution that arises in statistics and is commonly used in hypothesis testing and confidence interval construction.
Uses of the Chi-Square Distribution:
- Hypothesis Testing for Variances: it is used in the chi-square test for variance to compare sample variances with known or hypothesized population variances.
- Model Fit Assessment: the chi-square statistic is used to assess how well the observed data fit the expected model.
- In contingency table, the chi-square test for independence is used to determine whether there is a significant association between two categorical variables.
The results of chi square distribution in cdc diabetes 2018 dataframe is shown below :
When k is one or two, the chi-square distribution is a curve shaped like a backwards “J.” The curve starts out high and then drops off, meaning that there is a high probability that Χ² is close to zero.