The chi-square statistics are defined by the following formula:

Here, n is the size of the sample, s is the standard deviation of the sample, and σ is the standard deviation of the population.

If we repeatedly take samples and define the chi-square statistics, then we can form a chi-square distribution, which is defined by the following probability density function:

Here, Y₀ is a constant that depends on the number of degrees of freedom, Χ₂ is the chi-square statistic, v = n - 1 is the number of degrees of freedom, and e is a constant equal to the base of the natural logarithm system.

Y₀ is defined so that the area under the chi-square curve is equal to one.