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: https://i.stack.imgur.com/FBchB.jpg
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.