e-Statistics

## Chi-square Distribution

The chi-square distribution has the number of degrees of freedom (df) = . The curve lies on the positive line, and its shape is skewed to the right particularly when df is small. The critical point, denoted by , is provided for the upper tail.

 Level (p-value) Upper-tailed region

When the sample variance  is obtained from the data of observations which satisfies the normality assumption, the statistic with true variance  has the chi-square distribution with degrees of freedom.

Conversely when the statistic is given, we can find the corresponding so that the value belongs to the critical region, and call it p-value.