Categorical Data: Definition, Types, Analysis, and Examples

Scenario 1 

In this assignment, the Afrobarometer dataset has been used and the research question is: “Is there a relationship between trust in the police and presence of democracy (measured with dichotomous variable) that exist in Africa?”

The null hypothesis to be tested from the research question is: “There is no statistically significant relationship between trust in the police and presence of democracy (measured with dichotomous variable) that exist in Africa.” The alternative hypothesis to be tested from the research question is: “There is a statistically significant relationship between trust in the police and presence of democracy (measured with dichotomous variable) that exist in Africa.”

The quantitative data were analyzed using both descriptive and inferential statistics, ( Mertler, & Reinhart, 2016) . The descriptive statistics were used to describe and summarize the data in form of tables, frequencies, and percentages, ( Greenacre, 2017) . The inferential statistics were used to help make inferences and draw conclusions, ( Bakker, Ben-Zvi, & Makar, 2017) . Statistical tests including bivariate categorical tests (Chi-Square test) were used to test the hypotheses, ( Cox, 2018) . The bivariate table was designed to organize the significant relationship between two variables (provided below) (Frankfort-Nachmias & Leon-Guerrero, 2018).

The dependent variable that was used was “DEMOCRACY (DICHOTOMOUS)” at a nominal measure. The independent variable that was used was “TRUST POLICE” at a ordinal measure.

From the cross-tabulation analysis, it is evidenced that the percentages significantly vary between the two variables, but the relationship is not identified. The Chi-Square test indicates a value of 1242.165 with an associated p (true) value of .001. Because the test is significant and below the .05 threshold, there is a need to reject the null hypothesis that there is no relationship, ( Greenland, et, al, 2016) . In other words, there is some relationship between trust in the police and the presence of democracy in Africa. Additionally, the strength of the relationship as the value of 0 indicates no relationship and a value of 1.0 indicates a perfect relationship is determined by the Cramer’s V correlation, ( Sprague, Phillips, & Ross, 2017) . In this scenario, the symmetric measure of Cramer’s V has a value of .162 indicating that the relationship between the two variables is weak despite being significant at the .001, ( Vogt, & Johnson, 2015) . From the results, the significance/strength of the effect, as well as the answer to the research question, the presence of democracy does impact the trust in the police in Africa.

Scenario 2 

In this assignment, the Afrobarometer dataset has been used and the research question is: “Is there a relationship between trust in the police and Urban or Rural Primary Sampling Unit that exist in Africa?”

The null hypothesis to be tested from the research question is: “There is no statistically significant relationship between trust in the police and Urban or Rural Primary Sampling Unit that exist in Africa.” The alternative hypothesis to be tested from the research question is: “There is a statistically significant relationship between trust in the police and Urban or Rural Primary Sampling Unit that exist in Africa.”

The quantitative data were analyzed using both descriptive and inferential statistics. The descriptive statistics were used to describe and summarize the data in form of tables, frequencies, and percentages. The inferential statistics were used to help make inferences and draw conclusions. Statistical tests including bivariate categorical tests (Chi-Square test) were used to test the hypotheses. The bivariate table was designed to organize the significant relationship between two variables (provided below) (Frankfort-Nachmias & Leon-Guerrero, 2018).

The dependent variable that was used was “URBRUR” at a nominal measure. The independent variable that was used was “TRUST POLICE” at a ordinal measure.

From the cross-tabulation analysis, it is evidenced that the percentages significantly vary between the two variables, but the relationship is not identified. The Chi-Square test indicates a value of 877.477 with an associated p (true) value of .0005. Because the test is significant and below the .05 threshold, there is a need to reject the null hypothesis that there is no relationship. In other words, there is some relationship between trust in the police and Urban or Rural Primary Sampling Unit in Africa. Additionally, the strength of the relationship as the value of 0 indicates no relationship and a value of 1.0 indicates a perfect relationship is determined by the Cramer’s V correlation. In this scenario, the symmetric measure of Cramer’s V has a value of .093 indicating that the relationship between the two variables is not very weak despite being significant at the .0005. From the results, the significance/strength of the effect, as well as the answer to the research question, the Urban or Rural Primary Sampling Unit does impact the trust in the police in Africa.

Scenario 3 

In this assignment, the Afrobarometer dataset has been used and the research question is: “Is there a relationship between presence of democracy (measured with dichotomous variable) and Country's present economic condition that exist in Africa?”

The null hypothesis to be tested from the research question is: “There is no statistically significant relationship between presence of democracy (measured with dichotomous variable) and Country's present economic condition that exist in Africa.” The alternative hypothesis to be tested from the research question is: “There is a statistically significant relationship between presence of democracy (measured with dichotomous variable) and Country's present economic condition that exist in Africa.”

The quantitative data were analyzed using both descriptive and inferential statistics. The descriptive statistics were used to describe and summarize the data in form of tables, frequencies, and percentages. The inferential statistics were used to help make inferences and draw conclusions. Statistical tests including bivariate categorical tests (Chi-Square test) were used to test the hypotheses. The bivariate table was designed to organize the significant relationship between two variables (provided below) (Frankfort-Nachmias & Leon-Guerrero, 2018).

The dependent variable that was used was “DEMOCRACY (DICHOTOMOUS)” at a nominal measure. The independent variable that was used was “COUNTRY'S PRESENT ECONOMIC CONDITION” at an ordinal measure.

From the cross-tabulation analysis, it is evidenced that the percentages significantly vary between the two variables, but the relationship is not identified. The Chi-Square test indicates a value of 1957.056 with an associated p (true) value of .0005. Because the test is significant and below the .05 threshold, there is a need to reject the null hypothesis that there is no relationship. In other words, there is some relationship between presence of democracy (measured with dichotomous variable) and Country's present economic condition that exist in Africa. Additionally, the strength of the relationship as the value of 0 indicates no relationship and a value of 1.0 indicates a perfect relationship is determined by the Cramer’s V correlation. In this scenario, the symmetric measure of Cramer’s V has a value of .115 indicating that the relationship between the two variables is weak despite being significant at the .0005. From the results, the significance/strength of the effect, as well as the answer to the research question, the presence of democracy (measured with dichotomous variable) does impact the country's present economic condition in Africa.

Reference 

Bakker, A., Ben-Zvi, D., & Makar, K. (2017). An inferentialist perspective on the coordination of actions and reasons involved in making a statistical inference.  Mathematics Education Research Journal ,  29 (4), 455-470. 

Cox, D. R. (2018).  Analysis of binary data . Routledge. 

Frankfort-Nachmias, C., & Leon-Guerrero, A. (2018). Social statistics for a diverse society (8th ed.). Thousand Oaks, CA: Sage Publications.

Greenacre, M. (2017).  Correspondence analysis in practice . Chapman and Hall/CRC. 

Greenland, S., Senn, S. J., Rothman, K. J., Carlin, J. B., Poole, C., Goodman, S. N., & Altman, D. G. (2016). Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations.  European journal of epidemiology ,  31 (4), 337-350. 

Mertler, C. A., & Reinhart, R. V. (2016).  Advanced and multivariate statistical methods: Practical application and interpretation . Routledge. 

Sprague, B. N., Phillips, C. B., & Ross, L. A. (2017). Age-varying relationships between physical function and cognition in older adulthood.  The Journals of Gerontology: Series B . 

Vogt, W. P., & Johnson, R. B. (2015).  The SAGE dictionary of statistics & methodology: A nontechnical guide for the social sciences . Sage publications. 

Appendix 1: SPSS for Scenario 1

Case Processing Summary
	Cases
	Valid		Missing		Total
	N	Percent	N	Percent	N	Percent
Democracy (dichotomous) * Q59h. Trust police	47429	91.9%	4158	8.1%	51587	100.0%

Democracy (dichotomous) * Q59h. Trust police Crosstabulation
			Q59h. Trust police				Total
			Not at all	Just a little	Somewhat	A lot
Democracy (dichotomous)	Not a Democracy	Count	2143	1396	1074	756	5369
		% within Democracy (dichotomous)	39.9%	26.0%	20.0%	14.1%	100.0%
		% within Q59h. Trust police	20.1%	11.6%	8.6%	6.1%	11.3%
	Democracy	Count	8516	10588	11370	11586	42060
		% within Democracy (dichotomous)	20.2%	25.2%	27.0%	27.5%	100.0%
		% within Q59h. Trust police	79.9%	88.4%	91.4%	93.9%	88.7%
Total		Count	10659	11984	12444	12342	47429
		% within Democracy (dichotomous)	22.5%	25.3%	26.2%	26.0%	100.0%
		% within Q59h. Trust police	100.0%	100.0%	100.0%	100.0%	100.0%

Chi-Square Tests
	Value	df	Asymp. Sig. (2-sided)
Pearson Chi-Square	1242.165 a	3	.000
Likelihood Ratio	1173.593	3	.000
Linear-by-Linear Association	1125.520	1	.000
N of Valid Cases	47429
a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 1206.61.

Symmetric Measures
		Value	Approx. Sig.
Nominal by Nominal	Phi	.162	.000
	Cramer's V	.162	.000
N of Valid Cases		47429
a. Not assuming the null hypothesis.
b. Using the asymptotic standard error assuming the null hypothesis.

Appendix 2: SPSS for Scenario 2 

Case Processing Summary
	Cases
	Valid		Missing		Total
	N	Percent	N	Percent	N	Percent
Urban or Rural Primary Sampling Unit * Q59h. Trust police	50485	97.9%	1102	2.1%	51587	100.0%

Urban or Rural Primary Sampling Unit * Q59h. Trust police Crosstabulation
			Q59h. Trust police				Total
			Not at all	Just a little	Somewhat	A lot
Urban or Rural Primary Sampling Unit	Urban	Count	5216	5360	5130	3878	19584
		% within Urban or Rural Primary Sampling Unit	26.6%	27.4%	26.2%	19.8%	100.0%
		% within Q59h. Trust police	46.3%	42.5%	38.6%	29.1%	38.8%
		% of Total	10.3%	10.6%	10.2%	7.7%	38.8%
	Rural	Count	5937	7082	7973	9237	30229
		% within Urban or Rural Primary Sampling Unit	19.6%	23.4%	26.4%	30.6%	100.0%
		% within Q59h. Trust police	52.7%	56.1%	60.0%	69.3%	59.9%
		% of Total	11.8%	14.0%	15.8%	18.3%	59.9%
	Semi-Urban	Count	104	178	177	213	672
		% within Urban or Rural Primary Sampling Unit	15.5%	26.5%	26.3%	31.7%	100.0%
		% within Q59h. Trust police	0.9%	1.4%	1.3%	1.6%	1.3%
		% of Total	0.2%	0.4%	0.4%	0.4%	1.3%
Total		Count	11257	12620	13280	13328	50485
		% within Urban or Rural Primary Sampling Unit	22.3%	25.0%	26.3%	26.4%	100.0%
		% within Q59h. Trust police	100.0%	100.0%	100.0%	100.0%	100.0%
		% of Total	22.3%	25.0%	26.3%	26.4%	100.0%

Chi-Square Tests
	Value	df	Asymp. Sig. (2-sided)
Pearson Chi-Square	877.477 a	6	.000
Likelihood Ratio	893.555	6	.000
Linear-by-Linear Association	794.593	1	.000
N of Valid Cases	50485
a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 149.84.

Symmetric Measures
		Value	Approx. Sig.
Nominal by Nominal	Phi	.132	.000
	Cramer's V	.093	.000
N of Valid Cases		50485
a. Not assuming the null hypothesis.
b. Using the asymptotic standard error assuming the null hypothesis.

Appendix 3: SPSS for Scenario 3 

Case Processing Summary
	Cases
	Valid		Missing		Total
	N	Percent	N	Percent	N	Percent
Q3a. Country's present economic condition * Q59h. Trust police	49739	96.4%	1848	3.6%	51587	100.0%

Q3a. Country's present economic condition * Q59h. Trust police Crosstabulation
			Q59h. Trust police				Total
			Not at all	Just a little	Somewhat	A lot
Q3a. Country's present economic condition	Very Bad	Count	4347	3254	2768	2724	13093
		% within Q3a. Country's present economic condition	33.2%	24.9%	21.1%	20.8%	100.0%
		% within Q59h. Trust police	39.1%	26.1%	21.1%	20.9%	26.3%
		% of Total	8.7%	6.5%	5.6%	5.5%	26.3%
	Fairly bad	Count	3214	3961	3924	3458	14557
		% within Q3a. Country's present economic condition	22.1%	27.2%	27.0%	23.8%	100.0%
		% within Q59h. Trust police	28.9%	31.7%	30.0%	26.5%	29.3%
		% of Total	6.5%	8.0%	7.9%	7.0%	29.3%
	Neither good nor bad	Count	1325	2009	2501	2128	7963
		% within Q3a. Country's present economic condition	16.6%	25.2%	31.4%	26.7%	100.0%
		% within Q59h. Trust police	11.9%	16.1%	19.1%	16.3%	16.0%
		% of Total	2.7%	4.0%	5.0%	4.3%	16.0%
	Fairly good	Count	1858	2839	3400	3750	11847
		% within Q3a. Country's present economic condition	15.7%	24.0%	28.7%	31.7%	100.0%
		% within Q59h. Trust police	16.7%	22.8%	26.0%	28.8%	23.8%
		% of Total	3.7%	5.7%	6.8%	7.5%	23.8%
	Very good	Count	382	413	508	976	2279
		% within Q3a. Country's present economic condition	16.8%	18.1%	22.3%	42.8%	100.0%
		% within Q59h. Trust police	3.4%	3.3%	3.9%	7.5%	4.6%
		% of Total	0.8%	0.8%	1.0%	2.0%	4.6%
Total		Count	11126	12476	13101	13036	49739
		% within Q3a. Country's present economic condition	22.4%	25.1%	26.3%	26.2%	100.0%
		% within Q59h. Trust police	100.0%	100.0%	100.0%	100.0%	100.0%
		% of Total	22.4%	25.1%	26.3%	26.2%	100.0%

Chi-Square Tests
	Value	df	Asymp. Sig. (2-sided)
Pearson Chi-Square	1957.056 a	12	.000
Likelihood Ratio	1883.936	12	.000
Linear-by-Linear Association	1443.996	1	.000
N of Valid Cases	49739
a. 0 cells (0.0%) have expected count less than 5. The minimum expected count is 509.78.

Symmetric Measures
		Value	Approx. Sig.
Nominal by Nominal	Phi	.198	.000
	Cramer's V	.115	.000
N of Valid Cases		49739
a. Not assuming the null hypothesis.
b. Using the asymptotic standard error assuming the null hypothesis.