p-value for Chi-square test

p-value for Chi-square test

If the test statistic $\chi^2$ has chi-square distribution with $n$ degrees of freedom and the observed value of the test statistic is $\chi^2_{obs}$, then the $p$-value of the test for testing

a. left-tailed alternative is $p$-value = $P(\chi^2_{n}\leq \chi^2_{obs})$.

b. right-tailed alternative is $p$-value = $P(\chi^2_{n}\geq \chi^2_{obs})$.

c. two-tailed alternative is $p$-value = $2P(Z\geq \chi^2_{obs})$.

Formula

The $p$-value of chi-square test for left tailed alternative is

$p$-value = $P(\chi^2_{n}\leq \chi^2_{obs})$

The $p$-value of chi-square test for right tailed alternative is

$p$-value = $P(\chi^2_{n}\geq \chi^2_{obs})$

The $p$-value of chi-square test for two tailed alternative is

$p$-value = $2P(Z\geq \chi^2_{obs})$

where,

• $\chi^2_{obs}$ is the value of test statistic