survey data analysis (discrete data)

Question

I did small survey and get such data:

|-------------| Yes | No | Dont_Know |  
|-------------|     |    |           |  
| Employee    | 60  | 5  | 5         |  
| Workers     | 17  | 0  | 1         |  
| Businessmen | 71  | 5  | 10        |  
| Jobless     | 4   | 30 | 0         |  

R code

dt <- data.frame(workers = c("Employee",
                             "Workers", 
                             "Businessmen", 
                             "Jobless"), 
                 yes = c(60,17,71,4), 
                 no = c(5,0,5,30), 
                 dont_know = c(5,1,10,0)
                )

1. What kind of test I must do, if I want to show, that the Jobless people are often choosing No answer?
2. Is the difference between Jobless and Businessmen answers significant?
3. And what is about other groups?
4. What another information I can get from such data or what kind questions I can ask from such data?

Answer 1

Here are some things to try.

1. Plot a bar graph. The bar graph will clearly show jobless people are often choosing NO. Try an 1-way ANOVA test. If the p < delta (i.e. delta=0.05), try a post-hoc test (i.e. Tukey's HSD) to do a pairwise comparison.
2. Like I said earlier, try a multiple comparison test (1-way ANOVA) first, if there is a statistically significant difference, you can try a pairwise comparison test (post-hoc test).
3. Maybe try a clustering algorithm? Be careful, because the marginal sums (by rows or columns) are not equal. Maybe create a similarity matrix by profession? To me, it seems that Employees and Businessmen are in one group (very similar), while Workers and Jobless are each in their own group. If you turn those frequencies into proportions, then you might just have 2 groups; one for employees + workers + businessmen, and one for jobless.
4. Use contingency table analysis to see if the responses (yes/no/don't know) are associated with profession.