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From what I can gather from lists of "pros and cons" like this one, systematic sampling is roughly equivalent to simple random sampling when the list is randomly sorted. If not, it leads to sampling bias.

With this information, my conclusion would be that systematic sampling had a use before (pseudo)random numbers could be easily generated, but I can think of no practical use nowadays.

Are there situations where systematic sampling is still used? I am curious because it is usually included in all lists of sampling methods, but I'm unsure if it's just some sort of "historical inertia".

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  • $\begingroup$ Some hints in the related questions: stats.stackexchange.com/questions/73741/… stats.stackexchange.com/questions/220998/… $\endgroup$ Jul 15, 2019 at 11:44
  • $\begingroup$ Can you please elaborate? I am not sure how the questions are related. Both obviously refer to situations where systematic sampling is being used (or at least considered), but I don't see any systematic sampling benefits over other sampling methods, nor can I conclude that systematic sampling is not useful from those two examples. $\endgroup$
    – Narciandi
    Jul 15, 2019 at 12:09
  • $\begingroup$ You are correct, this is why i linked them in the comment and not as answer :-). I don't have a better answer. $\endgroup$ Jul 15, 2019 at 12:12
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    $\begingroup$ Sampling at equally spaced intervals in time and/or space has many secondary advantages. $\endgroup$
    – Nick Cox
    Jul 15, 2019 at 13:18
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    $\begingroup$ In Earth and environmental sciences measuring at regular intervals across a transect or down a core is utterly standard. $\endgroup$
    – Nick Cox
    Jul 15, 2019 at 16:31

3 Answers 3

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Systematic sampling has the advantage of not always requiring a frame. Take for example this scenario: you want to survey people at your amusement park about their favourite ride. Your systematic sample could be surveying every fifth person to enter the park until your sample is filled.

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    $\begingroup$ In your scenario, simple random sampling can be accomplished, too (generate the sampling intervals with a geometric distribution), demonstrating that not requiring a frame is not a particular advantage of systematic sampling. $\endgroup$
    – whuber
    Mar 23, 2023 at 13:27
  • $\begingroup$ I don’t follow your reasoning can you explain further $\endgroup$
    – astel
    Mar 24, 2023 at 20:12
  • $\begingroup$ See Method (3) at stats.stackexchange.com/a/134245/919. $\endgroup$
    – whuber
    Mar 24, 2023 at 22:09
  • $\begingroup$ If I adjust my answer to remove the part where I say until your sample is filled your comment holds no weight. In order to do what you are suggesting you need to have endpoints an and b, ie an idea of how many people will enter your park that day. How does your method draw a 20% sample without knowing how many people are in the park? $\endgroup$
    – astel
    Mar 24, 2023 at 23:08
  • $\begingroup$ No, I don't need endpoints, just as your systematic sample doesn't need any. You have to determine the sampling rate. When you select samples according to iid draws of a geometric distribution with the same rate, then you get the equivalent of a uniformly random subsample of the process. You can find an explicit code example in the link I provided. The procedure is incredibly simple: in your example with a rate of $1/5,$ you could obtain a simple random sample by choosing each park entrant independently with a probability of $1/5.$ $\endgroup$
    – whuber
    Mar 24, 2023 at 23:10
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Systematic sampling is still quite useful. In fact, it’s used today in several of the largest surveys in the United States, such as the American Community Survey (ACS). Systematic sampling is typically useful because it leads to more precise estimates than simple random sampling, if it’s implemented a certain way. Rather than sort the sampling frame randomly, survey samplers sort the frame according to available variables such as age or geographic location, pick a random starting point on the frame, and then select every, say, 10 units on the frame. Doing it this way still uses randomization, but it also introduces an “implicit stratification” which leads to less variation in the kinds of samples it will yield and hence results in more precise estimates.

This blog post provides a simple, visual explanation and references for why systematic sampling is useful:

https://www.practicalsignificance.com/posts/systematic-sampling-as-implicit-stratification/

Here’s an illustration of a systematic sample of size $n=5$ from a frame of $20$ individuals, sorted by their age.

enter image description here

In the following illustration, we can see how this sampling method has created implicit stratification:

enter image description here

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    $\begingroup$ +1 A similar discussion about pseudo-randomization as a way of balancing covariates discusses the pros and cons and similarity to this approach. stats.stackexchange.com/questions/54450/… $\endgroup$
    – AdamO
    Mar 24, 2023 at 13:24
  • $\begingroup$ Thanks, that is a quite similar discussion, and one of those answers does a good job of explaining the connection to systematic sampling $\endgroup$
    – bschneidr
    Mar 24, 2023 at 13:47
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In a prospective, randomized medical study, patients enroll to the trial in a non-systematic fashion. The panel of eligible participants is actually a moving window of time in which subjects are convenience sampled: an offer to enter the trial is made to the first people who stroll up until the trial is fully enrolled. It's well known that this sample is not at all representative of the total patient population - and that's hardly the chief concern of medical research today! This drift exacerbates for each conditional step of the study: performing a screening visit, signing informed consent, and - for non-randomized set analyses - complying with study procedures.

But simple random sampling is just not possible in research. Consider cancer patients. At this moment, say there are 1 million people with a subtype of relapsed/refractory multiple myeloma in the world. I cannot cold-call every single number to identify them, and even if I did, the timeline for my drug approval is 5-10 years after which nearly every living person with this disease will die - the point of my drug is to treat the next 20-40 years of patients with this disease on the assumption that something even better will come along at that point. "Time stops for no one."

We cannot assume that the time-series of patients in the sampling window are random or independent. As I mentioned, all individuals with a condition will be invited to participate, and they are screened and enrolled on a first-come-first-serve basis until target recruitment is achieved. The biases of a convenience sample are prevalent case bias and lead time bias. Both of these scenarios are instances where subjects merely show up more often to the hospital/clinic where recruitment is performed because a. they already had the condition and were receiving care for it, or b. they are more cautious and show up more often.

Randomization does not eliminate these biases. Randomization can balance covariates so there is no confounding of intent-to-treat analyses. However, the actual treatment effect may remain unknown. Even so the study may be well motivated, we chose time invariant analyses and assess the assumption of undetected interactions so that, even if the estimate is biased, there's little if any chance that the effect is actually reversed. In this case, the inference on the central hypothesis of "no effect" is well conserved. For example, a drug may confer a 0.50 risk reduction for an adverse outcome in the population, but because of healthy participant bias, the trial estimates a 0.75 risk reduction, however the upper bound of the 97.5% CI does not include 1 so we can conclude that the drug is beneficial at the one-sided 0.025 alpha level.

So this example contributes to a "no" response to the question. When SRS can be done, it is preferred in all respects. But cost, time, and other considerations don't always permit. In fact, complex sampling procedures can only be said to make the sample less random yet more efficient. This extends all the way to the above example where the sampling is entirely deterministic.

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    $\begingroup$ Would you say this process is actually systematic sampling or rather some sort of convenience sampling? $\endgroup$
    – Narciandi
    Jul 16, 2019 at 9:02
  • $\begingroup$ @Narciandi yes, I completely rewrote my answer based on this comment. $\endgroup$
    – AdamO
    Mar 23, 2023 at 13:27

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