The Chi-Square Distribution: Summary of Formulas 1.4 2008/06/23 12:48:13 GMT-5 2008/07/15 10:15:12.949 GMT-5 Barbara Illowsky illowskybarbara@deanza.edu Susan Dean deansusan@deanza.edu Connexions cnx@cnx.org elementary statistics This module provides an summary on formulas used in Chi-Square Distribution as a part of Collaborative Statistics collection (col10522) by Barbara Illowsky and Susan Dean. The Chi-square Probability Distribution μ=df and σ=2⋅df Goodness-of-Fit Hypothesis Test Use goodness-of-fit to test whether a data set fits a particular probability distribution. The degrees of freedom are number of cells or categories - 1. The test statistic is Σ n ( O − E ) 2 E , where O = observed values (data), E = expected values (from theory), and n = the number of different data cells or categories. The test is right-tailed. Test of Independence Use the test of independence to test whether two factors are independent or not. The degrees of freedom are equal to (number of columns - 1)(number of rows - 1). The test statistic is Σ ( i ⋅ j ) ( O - E ) 2 E where O = observed values, E = expected values, i = the number of rows in the table, and j = the number of columns in the table. The test is right-tailed. If the null hypothesis is true, the expected number E = (row total)(column total) total surveyed . Test of a Single Variance Use the test to determine variation. The degrees of freedom are the number of samples - 1. The test statistic is ( n - 1 ) ⋅ s 2 σ 2 , where n = the total number of data, s2 = sample variance, and σ2 = population variance. The test may be left, right, or two-tailed.