In Interpreting the results of chi-squared. Does this relationship appear to be linear or non-linear? Problem: People with more education are often stereotyped as being more liberal than people with less education and therefore might be more likely to attribute inequality to discrimination. Is there a relationship between educational degrees attained (degree) and attitudes about discrimination (racdif1)? The table below shows the correctly percentaged table with χ2 and the associated p-value for 2010: Chart given: < Was able to get a lot of information such as: $$df = 2 $$ $$\alpha = 0.05$$ $$\chi^2_{critical} = 5.991 $$ $$\chi^2_{achieved} = 8.1784 $$ Because the achieved is greater than the critical, we can reject the null hypothesis. What I am wondering is in interpreting the chi-square (including a substantive interpretation of the results). Does this relationship appear to be linear or nonlinear? Please help Thank you

The Chi-Square Test for Independence has nothing to do with a relationship being linear or non-linear. It is simply a test to determine if one categorical variable is associated with another categorical variable. The hypotheses are as follows:

$$H_0: \text{Highest degree and attributing inequality to discrimination are independent}$$

$$H_a: \text{Highest degree and attributing inequality to discrimination are associated}$$

In your case, as you correctly determined, you would reject the null hypothesis at $\alpha=0.05$ and conclude that we have significant evidence of an association.