One of the most common uses for this test is to assess whether two categorical variables are significantly related or not. The formula for a Chi-Square statistic is The Chi-Square test of independence is right-tailed The Chi-Square distribution is one of the most important distributions in statistics, together with the normal distribution and the F-distribution The distribution of the test statistic is the Chi-Square distribution, with \((r-1)\times(c-1)\) degrees of freedom, where r is the number of rows and c is the number of columns The main properties of a Chi-Square test of independence are: The idea of the test is to compare the sample information (the observed data), with the values that would be expected if the two variables were indeed independent. Sometimes, a Chi-Square test of independence is referred as a Chi-Square test for homogeneity of variances, but they are mathematically equivalent. Book traversal links for 15.Chi-Square of independence is a test used for categorical variables in order to assess the degree of association between two variables. This is the crucial result of a Chi-square test. Once you calculate a Chi-square value, you use this number and the degrees of freedom to decide the probability, or p-value, of independence. Therefore, the probability that a chi-square random variable with 10 degrees of freedom is greater than 15.99 is 1−0.90, or 0.10. The degrees of freedom for a Chi-square grid are equal to the number of rows minus one times the number of columns minus one: that is, (R-1)(C-1). The table tells us that the probability that a chi-square random variable with 10 degrees of freedom is less than 15.99 is 0.90.
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