The chi-Square Test The chi-square statistic is a sum of term one for each cell in the table. In the The statistical test that tells us whether cocaine example, 14 of the D group those differences are statistically succeeded in avoiding a relapse. The significant compares the observed and expected count for this cell is 8. So the expected counts. The test statistic that component of the chi-square statistic from makes the comparison is the chi-square this cell is statistic (observed count-expected count) expected count (14-8)36 88 Chi-square statistic Think of the chi-square statistic z as a measure of the distance of the observed The chi-square statistic is a measure of counts from the expected counts. Like any how far the observed counts in a two-way distance, it is always zero or positive, and table are from the expected counts. The it is zero only when the observed counts formula for the statistic is are exactly equal to the expected counts arge values of x are evidence against H (observed count-expected count)- because they say that the observed counts are far from what we would expect if h. were tru13 25 The Chi-Square Test • The statistical test that tells us whether those differences are statistically significant compares the observed and expected counts. The test statistic that makes the comparison is the chi-square statistic. 26 Chi-square statistic • The chi-square statistic is a measure of how far the observed counts in a two-way table are from the expected counts. The formula for the statistic is 2 2 (observed count expected count) expected count χ − = ∑ 14 27 • The chi-square statistic is a sum of terms, one for each cell in the table. In the cocaine example, 14 of the D group succeeded in avoiding a relapse. The expected count for this cell is 8. So the component of the chi-square statistic from this cell is 2 2 (observed count expected count) expected count (14 8) 36 4.5 8 8 − − = == 28 • Think of the chi-square statistic as a measure of the distance of the observed counts from the expected counts. Like any distance, it is always zero or positive, and it is zero only when the observed counts are exactly equal to the expected counts. Large values of are evidence against because they say that the observed counts are far from what we would expect if were true. 2 χ 2 χ H0 H0