I applied a questionnaire to social workers, but the number of completed questionnaires is very low (9). On a item I obtain 4 for option a, 3 for option b and 3 for option c. Bootstrap can be used to estimate the distribution?
I am not sure but here's what is available in RG that you can peruse for certainty:
https://www.researchgate.net/search.Search.html?type=publication&query=bootstrap%20in%20estimating%20answer%20distribution&tabViewId=585174f7217e20480e344c61&previous=researcher
Best regards,
Debra
Bootstrap won't present you the "true" distribution of you variable of interest, except rather an approximation that might be useful in calculating parameters of the true distribution.
The idea is extremely easy: you sample with replacement NN cases from your dataset of NN observations the same way as you sampled your data from the population. In R that would look like this
age
Bootstrap will tell you that there are about 33% more A than B or C. But you already know this.
But why do want to know the "distribution"? What possible answers are you expecting from the question "What is the distribution of these data?"?
I'm not sure the bootstrap is so helpful here. Generally you want more data than this. If I wanted to simulate the distribution I'd probably use a multinomial distribution - but Salvatore's question is appropriate. What are you trying to do with the data?
Thank you for the answers. I will try to expose in other way the problem: In the project where I'm involved, I want to compare observational records obtained in 2010 with observational records in 2015 (from a transit center). But I don't have enough observation records (17 in 2010 and 21 for 2015). For example, on an item I have: single, married, divorced, others. And I want to see whether there are differences on this item 2010 compared with 2015.
In that case you can use a Chi-square test of association or related test (extended Fisher's exact, G-test).
You make a table of counts, where one axis is Year, and one axis is S/M/D.
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