Interpreting chi-square

To interpret our observed chi-square statistic of 235.53, we refer to a table of chi-square probabilities which provides expected values for chi-square from the theoretical chi-square distribution for tables with different degrees of freedom at different alpha levels.

Looking at the table, with 2 degrees of freedom, the probability of attaining a chi-square of 235.53 is much lower than our selected alpha of .05 (which has an expected chi-square value of 5.991). On this basis we can reject the null hypothesis that there is no significant difference in median income between census tracts with few African-Americans and census tracts with 50 percent or more African-Americans. Another way of saying this is that in the population from which our sample was drawn, median income does vary by the minority status of a tract. Based on census data, the more African-Americans in a tract, the lower the median income of that tract is likely to be. (And this, where over 80 percent of all tracts in MA report median incomes that are $40,000 or higher!)