The chi-square distribution There are three major properties The chi-square distributions are a family of of a chi-square distribution distributions that take only positive values and are skewed to the right. A specific chi- Chi-square is either 0 or positive, never square distribution is specified by giving its degrees of freedom A chi-square distribution in not symmetrical The chi-square test for a two-way table Its skewness is positive. As the number of with r rows and c columns uses critical degrees of freedom increases, chi-square values from the chi-square distribution with (r-1)(c-1)degrees of freedom. The P-value approaches a symmetric distribution is the area to the right of x under the chi- There is a particular distribution for each quare density curve degree of freedom Figure 1 shows the density curves for three z/X members of the chi-square family of Table e distributions gives critical values distributions to find p for a 出##出 test 需15 29 The chi-square distribution • The chi-square distributions are a family of distributions that take only positive values and are skewed to the right. A specific chi￾square distribution is specified by giving its degrees of freedom. • The chi-square test for a two-way table with r rows and c columns uses critical values from the chi-square distribution with (r-1)(c-1) degrees of freedom. The P-value is the area to the right of under the chi￾square density curve. 2 χ 30 Figure 1 shows the density curves for three members of the chi-square family of distributions. 16 31 There are three major properties of a chi-square distribution • Chi-square is either 0 or positive, never negative. • A chi-square distribution in not symmetrical. Its skewness is positive. As the number of degrees of freedom increases, chi-square approaches a symmetric distribution. • There is a particular distribution for each degree of freedom. 32 Table E gives critical values for chi-square distributions. Use Table E to find P￾value for a chi-square test