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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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Question 


Discussion - Crosstabs

Discussion – Crosstabs

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 *%.

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