Chi Square Distribution

Chi square was first utilized by Karl Pearson in 1900. It is denoted by the Greek letter χ². This contains only one parameter, called the number of degrees of freedom (d-f), whereas term degree of freedom represents the number of independent random variables that express the chi square

Properties

1. Its critical values vary along with the degree of freedom. For every raise in the number of degrees of freedom there is a new χ² distribution.

2. This possesses additional property then that when χ²₁ and χ²₂ are independent and have a chi square distribution along with n1 and n2 degrees of from χ²₁ + χ²₂ will be distributed also as a chi square distribution along with n1 + n2 degrees of freedom

3. Where the degrees of freedom are 3.0 and less the distribution of χ² is skewed. However, for degrees of freedom greater than 30 in a distribution, the values of χ² are generally distributed

4. The χ ² function has simply one parameter, the number of degrees of freedom.

5. χ² distribution is a continuous probability distribution that has the value zero at its lower limit and extends to infinity in the positive direction. Negative value of χ² is not possible since the differences between the expected and observed frequencies are usually squared.