Discussion – Crosstabs

Discussion – Crosstabs

Overall Research Question: Does an individual’s level of education determine their income?

Broad Research Hypothesis: An individual’s education level affects their level of income.

To perform the Crosstabs analysis, the CONRIC variable, which represents the individuals’ income level, was recorded as follows to facilitate analysis;

1=Level 1=0-20000

2=Level 2= 20001-40000

3=Level 3= 40001-60000

4=Level 4= 60001-80000

5=Level 5= 80001-100000

6=Level 6= 100001-120000

7=Level 7= 120001-190000

EDUC variable, which is the highest level of education completed by individuals in years, was recorded as follows;

1=Group 1= Between 0-4years

2= Group 2= Between 5-9years

3= Group 3= Between 10-14years

4= Group 4= Between 15-19years

DV and IV Crosstabs

CONRICRANGE * EDUCRANGE Crosstabulation
			EDUCRANGE				Total
			Group 1	Group 2	Group 3	Group 4
CONRICRANGE	Level 1	Count	24	102	955	406	1487
		% within CONRICRANGE	1.6%	6.9%	64.2%	27.3%	100.0%
		% within EDUCRANGE	96.0%	87.2%	72.7%	49.6%	65.4%
		% of Total	1.1%	4.5%	42.0%	17.9%	65.4%
	Level 2	Count	0	11	238	165	414
		% within CONRICRANGE	0.0%	2.7%	57.5%	39.9%	100.0%
		% within EDUCRANGE	0.0%	9.4%	18.1%	20.2%	18.2%
		% of Total	0.0%	0.5%	10.5%	7.3%	18.2%
	Level 3	Count	1	4	71	106	182
		% within CONRICRANGE	0.5%	2.2%	39.0%	58.2%	100.0%
		% within EDUCRANGE	4.0%	3.4%	5.4%	13.0%	8.0%
		% of Total	0.0%	0.2%	3.1%	4.7%	8.0%
	Level 4	Count	0	0	21	43	64
		% within CONRICRANGE	0.0%	0.0%	32.8%	67.2%	100.0%
		% within EDUCRANGE	0.0%	0.0%	1.6%	5.3%	2.8%
		% of Total	0.0%	0.0%	0.9%	1.9%	2.8%
	Level 5	Count	0	0	16	53	69
		% within CONRICRANGE	0.0%	0.0%	23.2%	76.8%	100.0%
		% within EDUCRANGE	0.0%	0.0%	1.2%	6.5%	3.0%
		% of Total	0.0%	0.0%	0.7%	2.3%	3.0%
	Level 6	Count	0	0	3	10	13
		% within CONRICRANGE	0.0%	0.0%	23.1%	76.9%	100.0%
		% within EDUCRANGE	0.0%	0.0%	0.2%	1.2%	0.6%
		% of Total	0.0%	0.0%	0.1%	0.4%	0.6%
	Level 7	Count	0	0	9	35	44
		% within CONRICRANGE	0.0%	0.0%	20.5%	79.5%	100.0%
		% within EDUCRANGE	0.0%	0.0%	0.7%	4.3%	1.9%
		% of Total	0.0%	0.0%	0.4%	1.5%	1.9%
Total		Count	25	117	1313	818	2273
		% within CONRICRANGE	1.1%	5.1%	57.8%	36.0%	100.0%
		% within EDUCRANGE	100.0%	100.0%	100.0%	100.0%	100.0%
		% of Total	1.1%	5.1%	57.8%	36.0%	100.0%

Symmetric Measures
		Value	Approximate Significance
Nominal by Nominal	Phi	.318	.000
	Cramer’s V	.184	.000
N of Valid Cases		2273

The dependent variable was specified as the row variable. The cross-tabulation explains the relationship between the dependent variable and the independent variable. For an effective depiction of the relationships, the dependent variable was reduced to 7 Categories shown by the number of levels after recoding while the independent variable was reduced to four categories shown by the number of groups forming the columns.

The Crammer’s V and Phi value shows that there is a positive relationship between the level of education in years and the level of income an individual earns in constant dollars. Subtracting the percentages in each row for each variable, it is evident that the rows in each level have at least one epsilon value that is more than 10%, which indicates that the variables are fit for further statistical analyses. The strength of association further confirms that the variables are fit for analysis.

DV and Control Variable Crosstabs

CONRICRANGE * Race of respondent Crosstabulation
			Race of respondent			Total
			WHITE	BLACK	OTHER
CONRICRANGE	Level 1	Count	1080	259	183	1522
		% within CONRICRANGE	71.0%	17.0%	12.0%	100.0%
		% within the Race of respondent	63.8%	67.3%	67.8%	64.8%
		% of Total	46.0%	11.0%	7.8%	64.8%
	Level 2	Count	296	83	48	427
		% within CONRICRANGE	69.3%	19.4%	11.2%	100.0%
		% within the Race of the respondent	17.5%	21.6%	17.8%	18.2%
		% of Total	12.6%	3.5%	2.0%	18.2%
	Level 3	Count	144	25	26	195
		% within CONRICRANGE	73.8%	12.8%	13.3%	100.0%
		% within the Race of the respondent	8.5%	6.5%	9.6%	8.3%
		% of Total	6.1%	1.1%	1.1%	8.3%
	Level 4	Count	49	12	6	67
		% within CONRICRANGE	73.1%	17.9%	9.0%	100.0%
		% within the Race of the respondent	2.9%	3.1%	2.2%	2.9%
		% of Total	2.1%	0.5%	0.3%	2.9%
	Level 5	Count	68	3	4	75
		% within CONRICRANGE	90.7%	4.0%	5.3%	100.0%
		% within the Race of the respondent	4.0%	0.8%	1.5%	3.2%
		% of Total	2.9%	0.1%	0.2%	3.2%
	Level 6	Count	11	2	1	14
		% within CONRICRANGE	78.6%	14.3%	7.1%	100.0%
		% within the Race of respondent	0.6%	0.5%	0.4%	0.6%
		% of Total	0.5%	0.1%	0.0%	0.6%
	Level 7	Count	45	1	2	48
		% within CONRICRANGE	93.8%	2.1%	4.2%	100.0%
		% within Race of respondent	2.7%	0.3%	0.7%	2.0%
		% of Total	1.9%	0.0%	0.1%	2.0%
Total		Count	1693	385	270	2348
		% within CONRICRANGE	72.1%	16.4%	11.5%	100.0%
		% within the Race of respondent	100.0%	100.0%	100.0%	100.0%
		% of Total	72.1%	16.4%	11.5%	100.0%

Symmetric Measures
		Value	Asymptotic Standard Errora	Approximate Tb	Approximate Significance
Ordinal by Ordinal	Gamma	-.100	.039	-2.604	.009
N of Valid Cases		2348
a. Not assuming the null hypothesis.
b. Using the asymptotic standard error assuming the null hypothesis.

After recoding, the cross-tabulation dependent variable retains the categories, while the three columns indicate that the independent variable has three race categories. The relationship between the races and the level of income shown by the Gamma value shows that there is a negative relationship between the dependent variable and the control variable, although the relationship is a weak negative, weak relationship. Considering the 10% crosstab rule, the rule is satisfied since the percentage epsilon values obtained by subtracting the highest and lowest figures in each row have at least one row with 10%. It also confirms that the variables are fit for further analysis.

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This week, we talk about the uses of a crosstabulation (crosstabs) and the benefits of creating this “snapshot” of your data.

For this discussion, provide a brief introduction to your study to remind your classmates what we are reading about here. Include:

1. Your overall research question
2. A broad research hypothesis, that is, the relationship of IV to DV. (For example, educational attainment affects family income in US adults.)

Next, create two crosstabs for variable relationships and include them in the post – one to look at your IV and DV and one to look at your control variable and the DV. Be sure to explain your findings, including a description of the data, a calculation of the epsilons, and a discussion of the 10% rule for each crosstab. The epsilons, in short, are the differences between the highest and lowest column % in any given row. As long as one epsilon makes the 10% threshold, we’ll deem two variables have “enough” going on with each other to warrant further statistical analysis.

Special note:

When a variable is continuous (interval/ratio level of measurement), for example, the age of the respondent, we do not run crosstabs directly because it will result in a really spread-out table with lots of zeros and low-frequency cells. Such a crosstab does not help us understand the data. The correct way is to reduce the level of measurement to either ordinal level or nominal level (group the numbers into categories) by recoding and then running the crosstab. (Please refer to the Lessons for further information.)

When you run your crosstabs, be sure to also include a measure of association. As a reminder, here are the guidelines:

Both DV and IV are nominal variables: Lambda (when it is not a 2X2 table)
Both DV and IV are nominal variables, and it is a 2X2 table: Phi
Both DV and IV are ordinal variables: Gamma
One variable is ordinal, AND the other variable is dichotomous nominal (like Yes/No, male/female, etc.): Gamma
One variable is ordinal, and the other variable is nominal (not dichotomous, but has more than 2 categories): Cramer’s V.
Both DV and IV are I/R variables: Pearson’s r
Be sure to discuss the strength and direction of the potential relationship between the variables. Keep in mind measures of association are a statistical procedure based on Proportional Reduction of Error (PRE). Thus, the format of interpretation will be as follows: Knowing the IV will reduce errors in predicting the DV by *%.