Sampling Homework. When Things Start to Fall Apart
We work all time with customers taking stats classes, and usually things start smooth. Descriptive statistics seem to be a breeze, students get it, and everyone is happy. But something happens when the next topics shows its face.
Sampling is a little bit of a tricky subject, because its defined in a specific way that is very mathematical. When the idea of "with replacement" or "without replacement", or when you need to distinguish between "systematic" and "cluster" sampling, things can get murky.
From my experience, it is at the point where students have their sampling homework (which is usually their second homework from Stats), where things start going downhill. Usually, I tell them that random sampling is just a tool to be able to work with hypothesis testing, but panic sets in.
What will you cover in your sampling HW?
Typically your sampling assignment will be a PDF or simply a list of problems from your course textbook. Or at times it comes with a pdf worksheet with activities to complete.
What I think is what throws students off is the concept of sampling distributions. For example, the idea of sampling distribution of sample means, where now the random variable is the sample mean from ALL possible samples, and the purpose is to understand what values those sample means can take.
Or sometimes you have a discrete random variable with 4 values (say 1, 5, 10 and 15) and you are told to get the sampling distribution of sampling means when you take samples of size n = 2. So you have to construct a table with all possible samples of size n = 2 that you can get, compute their means, and see how frequently those different possible means appear.
One part of your sampling HW will likely have to do with different sampling techniques. I find that students do not get too complicated with this. Indeed, this topic is much simpler than the relatively conceptual idea of sampling distributions.
Using simple random sampling, systematic sampling, cluster or stratified are foundational ideas, which are relatively easy to absorb. These different sampling techniques have applicability on different contexts, and ultimately, that is all you need to understand: when to apply each type of sampling.
Lately, instructors have added multi-stage sampling to the list of sampling techniques. This is to give a more modern, real-life approach to sampling.
Homogeneous sampling versus Heterogeneous sampling
Students get confused as to when to use these different kinds of sampling. When to use a homogeneous type of sampling (such a simple random sampling) and when to use a heterogeneous type of sampling (such as stratified sampling). There is not one recipe to know when to use what, but in statistics you will like to deal with homogeneous groups, and if they are not, you will break them down into sub groups that are.
As usual, you will have to play by ear. One way of detecting which type of sampling you need to deal with is to see many examples, with the rationale of why a type of sampling applies. You can always hire a Stats tutor to help you with that.
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