A Chi-Square Test of Independence With Studs Terkel’s American Dreams: Lost and Found
In American Dreams: Lost and Found, historian Studs Terkel interviewed 98 different individuals and asked them to talk about their conception of the American Dream. The interviewees ranged from wealthy to poor, urban to rural, famous to unheard of, and are meant to offer a diverse survey of people as well as a unique perspective into how Americans understand their country and their dreams. The interviews also varied as to the focus of their content. Some people spoke more of their family’s accomplishments while others spoke more directly of their own. Some spoke of broader issues, such as unions or social justice, and used “we” language while others typically relied on a first-person narrative. Further, many people exhibited certain self-concepts, in which they revealed whether they felt positive or negative about themselves. In an attempt to determine whether the focus of an interview (either self- or family/we-focused) was related to someone’s self-concept (positive, negative, or neutral/ambivalent), I conducted a textual analysis of each interview and placed each one in a cell. To determine whether the two nominal labels were independent, I then conducted a Chi-Square Test of Independence:
χ^2=∑(O_i- E_i)^2/E_i
Where O_i is each total number of observations for a specific cell and E_i is the expected total for each cell. E_i is calculated, in this case, by taking the sum of a column, multiplying it by the sum of a row, and dividing the product by the total sample size, or:
E_i=(R_i C_j)/N
After calculating the obtained χ^2, I compared it to a χ^2 critical value. The degrees of freedom are calculated by multiplying the number of rows minus one by the number of columns minus one:
df=(r-1)(c-1)
The χ^2 obtained in this case was 3.10 and the χ^2 critical value was 5.99, leading to a failure to reject the null hypothesis that interview focus and self-concept are independent. This leads to the conclusion that there is not enough evidence to determine whether or not the two variables are related or not. It could be the case that these variables are indeed independent, but further analysis should be conducted first before drawing that conclusion.
