Tech Tips: Chi-Square Distributions

Calculating Heights of Points on the Graph of a $\chi^2$ Function

To find the height at $x$ of the graph of a $\chi^2$ function associated with $df$ degrees of freedom (and centered at $0$),


Calculating Probabilities Associated with the $\chi^2$ Distribution

To find the probability that a random variable following a $\chi^2$ distribution with $df$ degrees of freedom results in a value less than $x$ (i.e. the area under the chi-square distribution to the left of $x$.)


Inverse Calculations Related to the $\chi^2$ Distribution

To find the $x$ value for which a random variable following a chi-squared distribution with $df$ degrees of freedom will produce an outcome less than $x$ with some given probability of $p$ (or equivalently, the $x$ value where there is an area of $p$ to the left of $x$ and under the related chi-squared distribution curve) ...


Goodness of Fit Tests

To conduct a goodness-of-fit test,


Tests of Independence / Homogeneity of Proportions

To conduct a test for independence or homogeneity of proportions,