Chi-square significance test from software. The results of the chi-square significance test for the vaccination example appear in the computer outputs in Figure 9.1 (pages 928–930), labeled Pearson (JMP) or Pearson Chi-square (Minitab and SPSS). Because all the expected cell counts are large (5 or more), the distribution provides an accurate -value. We see that , , and Note that Minitab and SPSS report the -value as 0.000 or .000. These are rounded numbers and potentially misleading. The -value is small, but it is not zero. For this reason, we prefer to report As a check, we verify that the degrees of freedom are correct for a table:
The chi-square test confirms that the data provide evidence against the null hypothesis that there is no relationship between political party preference and vaccination opinion. Under , the chance of obtaining a value of greater than or equal to the calculated value of 12.29 is small, less than 0.0001—fewer than 1 time in 10,000.