Categorical Data Analysis: Methods and Models

The question of whether there is equality in the US education system is a matter of debate. Until the late 1960s, minority races in the US were educated in segregated schools (Darling-Hammond, 2016). Despite the conspicuous achievements following the end of segregation in the 1970s, it is essential to continually evaluate the distribution of educated people and employment across different races. The research seeks to establish whether race affiliation influences the level of educational qualifications. The research question is: What effect does race have on the level of educational qualifications. 

Hypothesis 

The research will test the significance of the association between race and degree. The null hypothesis assumes no significant association between race and degree, while the alternative assumes a significant association between race and degree. 

The null hypothesis, H0: There is no association between race and degree 

The alternative hypothesis, H1: There exists an association between race and degree. 

Research Design 

The Chi-square test is an effective research design for testing the association between two categorical variables. In testing the association, chi-square tests compare the observed frequencies relative to the expected frequencies calculated under the assumption that the variables are not associated (Frankfort-Nachmias & Leon-Guerrero, 2016). For example, expected frequencies when using chi-square to evaluate the association between race and degree assume that the race and degree are not associated, and hence the frequencies are the same for the various racial groups. 

Crosstabs 

Dependent variable 

The research seeks to test the effect of race on the educational level. Educational level is, therefore, the dependent variable measured using the degree categorized as 0,1,2,3 and 4. 

Independent Variables 

The research anticipates that the variable race influences the educational attainment of the sample individuals. As a result, the race is the independent variable, divided into three groups labeled as race 1, 2, and 3. 

Strength of the Effect 

The decision rule is to reject the null hypothesis if the associated p-value < the level of significance. The Pearson Chi-square statistic, is 21.298, p-value 0.006. Since the p-value is less than the assumed level of significance, 0.05, we reject the null hypothesis that there is no association between race and degree. Therefore, we conclude that there is sufficient statistical evidence to support an association between race and degree. 

Explanation 

Association between race and degree means that the percentages of educated persons change significantly among the different races. If there existed no association between race and degree, the proportions of people with the various degree levels would be approximately the same for the different races (Frankfort-Nachmias & Leon-Guerrero, 2016). A p-value less than the level of significance means that the proportions of individuals with various degrees differ significantly across the different racial groups. The results confirm that the level of educational qualifications is affected by racial affiliation. This may imply that there exist possibilities of the discrimination of minority groups. 

References 

Darling-Hammond, L. (2016, July 28).  Unequal opportunity: Race and education . Brookings.  https://www.brookings.edu/articles/unequal-opportunity-race-and-education/ 

Frankfort-Nachmias, C., & Leon-Guerrero, A. (2016). Social statistics for a diverse society. Sage Publications.