Random Selection and Random Assignment

Randomness is something very important in statistics. Yet I have this opinion that it is not given its due space in statistical courses. Then I've found that usually people have trouble understanding the reason randomness is so important and the possible implications of the lack of it in certain contexts. In two contexts randomness is very important but has a different role - Experimental Design and Sampling. In the former we usually want to assign units randomly to treatments/groups and in the later we want to select units randomly from a given population.

I also think that the lack of understanding randomness, or perhaps only thinking more about it or taking it more seriously is making us to turn a blind eye to the many circumstances where lack of randomness is an issue, specially related to sampling. In that regard I think we need to get better at model based approaches that account for introduced biases, starting by understanding sources and consequences of the non-randmness. Unfortunately the reality is not very friendly and random sample or experiments are the exception, not the rule.

In Sampling, randomness aims at guaranteeing that the conclusions from the small set of units we select, the sample, generalizes to some larger population, because we don't really care about the sampled folks, we care about the population they are supposed sampled from. But sampling in a random way from human populations is next to impossible most of the times. In experimental designs the random assignment allows us to control for concurring causes of what we intend to measure the effect. A randomized experiment allows us to make causal claims about statistical differences, but if the used sample was not selected randomly then the causal claim is in theory only valid for the units participating in the experiment. Here is where both things come together.

Therefore it is important that students have a good understanding of randomness and the difference between assigning randomly (experimental design) and selecting randomly (sampling) and the possible implications when the randomness fail. This is an interesting paper that talks about this and gives an example of how to engage students with real world activities related to the application and interpretation of random selection and random assignment. I thought the idea is cool also because it uses roaches, which are not very much liked in our culture, so I guess it is good for retaining the moment...