# Stratified SRS vs. probability-proportional-to-size (PPS) sampling - what's the difference?

If my understanding is correct, the key difference is that:

1. In stratified SRS you intentionally draw $$N_h$$ samples from each of your $$k$$ strata ($$h = 1...k$$, $$\sum_{1}^{k}{N_h} = N$$) and are therefore guaranteed to get a certain number, $$N_h$$, from each stratum by design.
2. In PPS you are modifying the probability of selection for each unit to be proportional to the size of the stratum containing that unit, $$p_h = \frac{x_h}{\sum_{i=1}^{k}{x_i}}$$ (where $$x$$ is the number of units in a stratum), but you aren't guaranteed to hit a certain number of samples per unit.

Is this correct?

What I don't understand is why you would use one of these over the other. I haven't been able to find any comparison between the two online, can anyone help? Thanks!

• In PPS, strata aren't (necessarily) involved. Instead, each unit's prob is proportional to the "size" of the unit itself. For example, you might sample companies proportionally to the number of employees at the company, or its gross income, or something. In this example the units are the companies, not employees or dollars. Each unit (company) has its own sampling prob, unlike in stratified sampling. Commented Jan 5 at 21:41