Chi Square Calculations
The probability density function (PDF), f(x), of the Chi-Square distribution is:
Here, ν is a positive integer, and Γ is the Gamma function. The shape parameter ν is usually known as the degrees of freedom or dimension of the distribution. This distribution arises in many areas of statistics, including reliability applications. Particularly, it is used for assessing the goodness-of-fit of models, tests of significance, and finding confidence intervals.
The cumulative probability is defined as:
In the General Statistics Calculator, the F(x) is entered or displayed in percentages. For example, F(x) = 0.9 is entered or displayed as 90%. The value of x is called the Chi-Square parameter. Thus, the General Statistics Calculator calculates the following:
1. Cumulative probability, which is the F(x) for the given values of x and ν.
2. Chi-Square parameter, which is x for the given values of F(x) and ν.
The Chi-Square distribution is also used in statistical hypothesis testing. In such cases, the objective is to find the x value, which is called the critical value, at a given significance value. In other words, the objective is to find x for a given (1 - F(x)) value. For example, to find the critical value for the 0.05 significance test, for the cumulative probability, you must enter 95:
100 * (1-0.05)=95