I've had people tell me on numerous occasions that you can / should do tests normally reserved for sample statistics (e.g., difference of means etc.) on census data when you are comparing figures over time. The claim usually made is that this is because each census is a 'sample in time'.
My understanding is that it is not appropriate to extend sampling theory in this way. Specifically, the explanation below (copied from census statistical techniques) describes my view quite well.
When you have a sample you use inferential stats to generalise to the population. When you have a census you already have data for the whole population, so there is no need to generalise.
For example, if you used sampling, and there is a 3% difference between groups, then you have to use inferential stats to decide whether that 3% difference is real, or just due to random chance when you did the sampling.
But if you did a census, and there is a 3% difference between groups, well, then there's definitely a 3% difference. That 3% difference is not due to random chance in sampling, because you have data for the whole population. However, even with a census you will still need to use your own judgement to think about why there is a 3% difference (for reasons other than random chance in sampling), and whether the 3% difference is large enough to have any practical significance for the work you are doing.
So basically, just use descriptive stats. Correlations are fine, but you only need the r value to show the strength of the correlation, not the p value which is related to random chance in sampling.
A lot of people don't get the difference between sample stats and census stats, and will complain that you didn't do the stats properly. I've had cases where I ended up having to do inferential stats on census data just because people complained so much that there were no p values on anything!
If you have a lot of missing data from a census sometimes you need some fancy inferential stats to fill it in. I doubt this will apply to you, but it does apply to the US population census because (for some bizarre libertarian reason) completing the census survey in not mandatory in the US.
However, my question relates to comparisons across time rather than between groups. The argument I've been given is that when you look across time, each census parameter is actually a single-point sample from all possible parameters across time. I have a couple of problems with this:
- differences in census figures across time won't be attributable to chance. They must be attributable to changes in the underlying environment / population and
- even if the 'samples in time' argument is correct, you only ever have very few data points sampled from this 'infinite population'--maybe parameters across four or five censuses you want to compare--which means $n$ is so tiny as to be useless for generating sample statistics.
Surely others have addressed this situation more formally, but I've been unable to find material covering this situation. My question therefore is:
Can anyone here point me in the direction of material discussing this issue or offer an explanation of the 'samples in time' argument that provides a more formal foundation for accepting that it is indeed appropriate to use sample statistical tests on census parameters?