Analyzing categorical data using a chi-square test

Categorical Data Analysis
The discussion analyzes categorical data using a chi-square test of independence using the General Social Survey Dataset. According to Table 1, the dataset’s mean Age is 48.62.
Table 1: Descriptive statistics

Research Question and Null Hypothesis
Research Question: is there a statistically significant correlation between homeownership and race?
H0: There is no statistically significant correlation between homeownership and race
H1: There is a statistically significant correlation between homeownership and race
Research Design
A chi-square test of independence used in a correlation research design would align with the research question (Laureate Education (Producer), 2016). To comprehend the nature of a relationship between naturally occurring variables that cannot be altered, researchers apply the correlational design method, according to Burkholder et al. (2020). A chi-square test is a significance test for categorical variables.
Variable
The homeownership of respondents is the dependent variable (DV) in this dataset, which has three levels (1 = owns or is purchasing; 2 = renting, and 3 = other) ((Lavrakas, 2018). The respondents’ race is the independent variable (IV), similarly measured on a nominal scale with three levels (1 = white, 2 = black, and 3 = other).
Significance and Effect Size
To determine whether there is a relationship between homeownership and race, Table 4 presents a chi-square tests. It is statistically significant that the Pearson Chi-Square value is 2 (df = 4)=25.217, p .001. Hence, homeownership varied depending on the race of the respondents. I can therefore reject the null hypothesis that there is no statistically significant correlation between race and homeownership. Table 4 further reveals that more than 20% of the anticipated counts are < 5. The dataset’s strength and effect size are presented in Table 5 through symmetric measures. Since the table is larger than a 2×2 table, I will apply Cramer’s V for this dataset. A weak correlation between respondents’ race and homeownership is indicated by Cramer’s V =.190.
Results
Table 2 summarizes the case processing; this analysis has 351 valid cases and 159 missing cases. As a result, 510 survey respondents total, but a few are missing (Nishisato, 2019). The majority of the respondents owned or were purchasing their home (Count = 228;% Within Race = 65%), paid rent (Count = 116;% Within Race = 33%), and for other (Count = 7;% Within Race = 2%), according to Table 3’s Race of Respondent*Does Respondent own or rent Home Cross tabulation table.
Whites made up the majority of homeowners (Count = 205;% Within Race = 70%), followed by blacks (Count = 15;% Within Race = 48%) and other races (Count = 8;% Within Race = 29%). The other group (Count = 19;% Within Race = 67%), blacks (Count = 16;% Within Race = 52%), and whites (Count = 81;% Within Race = 28%) made up the majority of renters as well (Imrey & Koch, 2014). In addition, there were more white people (Count = 6;% Within Race = 6%), followed by other people (Count = 1;% Within Race =.6%), and finally black people (Count = 0;% Within Race =.6%). Overall, the data showed that whites had easier access to home ownership. The analysis addressed my research question, which found a statistically significant relationship between home ownership and race.
Table 2: Case processing summary

Table 3: Cross tabulation

Table 4: Chi-Square Tests

Table 5: Symmetric measures

References
Burkholder, G. J., Cox, K. A., Crawford, L. M., & Hitchcock, J. H. (2020). Research design and methods: An applied guide for the scholar-practitioner. Sage. https://onesearch.library.rice.edu/discovery/fulldisplay?docid=alma991033242971105251&context=L&vid=01RICE_INST:RICE&lang=en&adaptor=Local%20Search%20Engine&tab=Everything&query=sub%2Cexact%2C%20Research%20methodology%20%2CAND&mode=advanced
Imrey, P. B., & Koch, G. G. (2014). Categorical data analysis. Wiley StatsRef: Statistics Reference Online. https://onlinelibrary.wiley.com/doi/abs/10.1002/9781118445112.stat04856
Laureate Education (Producer). (2016). Bivariate categorical tests [Video file]. Author.
Lavrakas, P. J. (2018). Encyclopedia of survey research methods (Vols. 1-0). Sage Publications, Inc. doi: 10.4135/9781412963947
Nishisato, S. (2019). Analysis of categorical data. In Analysis of Categorical Data. University of Toronto Press. https://www.degruyter.com/document/doi/10.3138/9781487577995/html