Stats: Chi-Square Distribution The chi-square ( ) distribution is obtained from the values of the ratio of the sample variance and population variance multiplied by the degrees of freedom. This occurs when the population is normally distributed with population variance sigma^2. Properties of the Chi-Square • Chi-square is non-negative. Is the ratio of two non-negative values, therefore must be non-negative itself. • Chi-square is non-symmetric. • There are many different chi-square distributions, one for each degree of freedom. • The degrees of freedom when working with a single population variance is n-1. Chi-Square Probabilities Since the chi-square distribution isn't symmetric, the method for looking up left-tail values is different from the method for looking up right tail values. • Area to the right - just use the area given. • Area to the left - the table requires the area to the right, so subtract the given area from one and look this area up in the table.
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This note was uploaded on 01/26/2012 for the course MATH 1070 taught by Professor Akbas during the Spring '08 term at Georgia State University, Atlanta.