Today’s post is the assignment exercise for week 4 for the Coursera class on Data Visualization Tools from Wesleyan University.
The topic is as below:
Run an ANOVA, Chi-Square Test or correlation coefficient that includes a moderator.
For this round of assignments, I’m using the outlook on life dataset provided for the course, as available here. Today I am going to test the confidence to achieve secure retirement (var = W1_F4_B) based on incomegroup (INCOME, calculated from given var = PPINCIMP). The moderator variable is marital status (MARIT, computed from PPMARIT).
I am using the chi-square test for this assignment.
The hypothesis for this assignment is as follows:
- Ho = No relationship between INCOME and W1_F4_B.
- H1 = There is a significant relation between above two variables.
Procedure for Chi-Square test:
- INCOME variable has 5 levels :
- 20 => income between 0 to 19,999
- 40 => income between 20,000 to 39,999
- 60 => income between 40,000 to 59,999
- 80 => income between 60,000 to 99,999
- 100 => income greater than 99,999
- MARIT variable has 4 levels:
- 1 => Married or living with partner
- 2 => widowed
- 3 => separated or divorced
- 4 => never married.
- W1_F4_B is modified to have only 2 levels :
- 1 = Very hard or somewhat hard
- 4 = Very easy or somewhat easy.
- The code for this program is located at my github SAS folder. The essence of the code is :
- There are 5 levels in INCOME, so we need to make 10 comparisons. Hence Bonferoni adjusted p-value = 0.005.
- Code with moderator in the posthoc test comparisons:
/* comparison set 1 */DATA COMPARISON1; SET temp_chk;TITLE ‘Comparison range 20 & 40’;IF INCOME=20 OR INCOME=40;PROC FREQ; TABLES W1_F4_B*INCOME/chisq; BY MARIT;
- Code without moderator in the posthoc test comparisons:
/* comparison set 1 */DATA COMPARISON1; SET temp_chk;TITLE ‘Comparison range 20 & 40’;IF INCOME=20 OR INCOME=40;PROC FREQ; TABLES W1_F4_B*INCOME/chisq;
Results & Interpretation:
The complete results are also available in thisW4-INCOME-WEALTH-MODVAR-MARIT-POSTHOC-MARIT
Based on the output, the following conclusions can be inferred:
- For the main chi-square test, we see that Ha = TRUE only for MARIT = 1 ( married or living together). So we accept an association between wealth confidence and income only for married couples. The null hypothesis is true for all other marital status.
- The other main trend is that majority of survey respondents show little confidence in achieving their wealth goals and a secure financial retirement status. At lower incomes, this is overwhelmingly so, but even at highest income levels, only about 35-40% respondents remain positive.
- Thus we see that major answer differences between lowest and highest income groups only for marital status MARIT = 1 . (married and those living with their partners)
- Based on adjusted p-value < 0.005, we see a statistical difference for income samples 20&100, 40&100, 60&100.
- I ran the program with posthoc tests both with & without considering marital status as moderator, but the trend again is seen only for marit = 1. If we do not use the moderator variable for posthoc tests, we only see one extra comparison group that is statistically different (income groups 20&80)
Thank you for taking a look at my analysis. Please feel free to add any suggestions for improvement or other feedback in the comments section.