# Applying inferential statistics for census data

Let's assume I have a census data of a population which I would like to study and it has variables such as age, gender, sex, occupation etc and the dependent variable which is community participation of the population is in the form of numerical data (mean score). Is it appropriate to apply inferential statistics such as t test, ANOVA etc. to find out the variance/difference between the independent variables such as age group (such as young,middle, and old), sex (male/female), occupation (four categories), level of education (five categories)?

• Do you have individual data on your dependent variable or not? If not, then you cannot do an analysis of individual observations. Commented Apr 8, 2015 at 21:39
• Yes, I do have individual data on the dependent variavle i.e. separate mean score of the community participation for each individual. Commented Apr 10, 2015 at 4:31

## 2 Answers

You can test hypotheses if you want to generalize your findings beyond the original population; this is the practical meaning of the superpopulation model. This would apply for a causal and predictive modeling study, or for what Deming calls an "analytic" study. For another related thread, with references, see: Adjusting any power analysis with FPC?

Only you know your study goal. However your proposal to test associations with every demographic/personal variable does not describe a study with a focused set of questions. Nor does it describe a predictive analysis. This might be an analytic analysis, but the inferences will not be strong. Go ahead and test hypotheses; be sure to adjust p-values for multiple comparisons.

Reference Deming, W. E. (1966). Some theory of sampling. New York: Dover Publications.

• Yes Steve, it is an analytic analysis. From what I understand. It is is not wise to use inferential statistics when one has data regarding an entire population as there won't be any sample error. Hence, I'll stick to only descriptive statistics from now on while researching on an entire population. Thanks. Commented Apr 15, 2015 at 15:16
• I may not have been clear: it is precisely when you are doing an "analytic", as opposed to doing an "enumerative" or "descriptive" study, that hypothesis testing is okay. Commented Apr 15, 2015 at 22:04

If your census is of the -entire population-, I do not think so. For example, the mean age of NYC in 2011 might be 45. The mean age of SFC in that same year is 46. You can conclude they are not the the same... because you've counted all of them, a full population census count. The question ceases to be statistical.

This depends heavily on a frequentist view of the world, and the idea that it is a full population census, excluding no one. Some Bayesian may be able to argue differently, but their techniques will also be different.

• Actually, you can do an inferential analysis of a census without being a Bayesian by assuming that the population is one sample from a "superpopulation". There is discussion with some references at: stats.stackexchange.com/questions/125058/… Commented Apr 8, 2015 at 21:44
• Thank you Steve, I perfectly understand and appreciate the concept of assuming that the population is one sample from a supersample. However, I'm not a statistician and would like to know what exactly is the Bayesian view in this particular context and how it is different from the frequentist view. Commented Apr 10, 2015 at 5:06
• Sorry-I know nothing about a Bayesian approach to this problem. Commented Apr 11, 2015 at 19:57
• Oh okay. Thanks for the superpopulation idea though. I really appreciate it. Commented Apr 12, 2015 at 3:35