I've taken many samples, large and small, simple and complex, over the years. My conclusion: Simple random sampling (SRS) alone is almost *never* the choice for a real-world problem.


On the other hand the *theory* of SRS is  important, because it underlies the theory of other techniques. 

The alternatives to SRS: stratified sampling, systematic sampling, in some instances, unequal probability sampling, or a combination of these.  It is okay to take an SRS within strata.

In my comments, I quoted Cochran as saying stratified sampling isn't always more precise than SRS. However increased precision is not the only, or even the main, reason for choosing a stratifed design.


**Reasons to stratify**

Look for stratifying factors for at five reasons (Lohr (2009) p. 74; Valliant, Dever, & Kreuter, 2013, p. 44):

1. To avoid selecting a sample that badly misrepresents the population. I've seen many instances of such SRSs. In some  reweighting the sample was a partial fix . In others, no recovery was possible. One such  was the object of a question to Statalist. A senior public health official wanted to study prevalence of infection in patients attending medical clinics in a city.  There were 40 clinics, in the city and 10 were drawn by SRS. Unfortunately, two of the clinics (5% of the totoal number) were in large hospitals and, together, saw about 30% of all outpatients, often the sickest. Unsurprisingly, the SRS did not include either clinic (the chance of this was about 44%). Thus the *patients* in the selected clinics did not represent the target population.  At a minimum, the two large hospital clinics should have been selected with certainty before taking the simple random sample.

2. Closely related: stratify to "cover" the entire population.  This is also a reason to do stratified sampling

3. To guarantee a minimum sample size for group that are going receive separate analyses. For a study of occupational health and safety in California farms, for example, farms were stratified by size and major crop.

4. To control costs.  Example: charts were to be abstracted in a sample of California hospitals.  Rural hospitals were placed in a separate stratum and sampled at a lower rate than urban hospitals. Why? Experienced abstractors lived in urban areas and could study 1-2 hospitals per day, then  go home at night. To study a rural hospital  took one abstractor two days and incurred the cost of an overnight stay.

5. To improve sample efficiency (i.e. get smaller standard errors) by grouping together observations with similar means and variances.   Some national surveys stratify as finely as possible and  draw a SRS with $n= 1$ unit from each stratum. Because a minimum of $n = 2$ observations per stratum is needed to compute standard errors, such designs are *analyzed* by combining neighboring strata.  The "true" standard errors for the design are then likely to be smaller than the estimated standard errors, clearly a good thing. 

6. To approximate more complex designs like sampling with probability proportional to size. In a study of farm safety for a certain crop, the number of farm workers was not known for each farm, but was approximately proportional to  number of acres, a quantity known from a census  After sorting the list of farms by acreage, I created strata with equal total acreage, except of the largest farms, which were taken with certainty.   Ten farms were taken at random from each of the other  strata, so that that each sampled farm "represented", on the average, the same number of acres, therefore the same number of workers. 

**Systematic sampling**


In many studies, sampling frames are naturally ordered. Date ordering is common, for example.  It is possible form strata from such frames, but systematic samples will sometimes be superior, because they cover the entire frame. 

In other situations, the frame isn't ordered but is in list format. It is easier to take a systematic sample of the list than to take a random sample. One example was a sample of a very large multipage spreadsheet that recorded innformation certain kinds of equipment. Some lines contained no asset information and some assets had information on several lines. I drew a 1 in 40 sample of lines. If the information for an asset began on the selected line, that asset was studied.  Otherwise, the selected line was ignored (became a "blank")  This rule assured that the sampling rate for *assets* was 1 in 40.

Many stratified samples are analyzed *as if* they were SRS, with the expectation that the true standard errors will be smaller (see point 5, above).  However, a good design is to take  say $k = 10$ several systematic samples, not just one.  Deming (1960) has many examples.

**References**

WE Deming, 1960, Sampling Design in Business Research, Wiley, NY

Lohr, Sharon L. 2009. Sampling: Design and Analysis. Boston, MA: Cengage Brooks/Cole.

Valliant, Richard, Jill A. Dever, and Frauke Kreuter. 2013. Practical Tools for Designing and Weighting Survey Samples. Statistics for Social and Behavioral Sciences. Springer.