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1. To avoid selecting a sample that badly misrepresents the population. I've seen many instances of such SRSs. In some, reweighting 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 total 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 studied 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 systematic 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, including travel, 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 an agricultural 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, roughly the same number of workers.

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. Dividing the date range into strata would be somewhat arbitrary, because neighboring dates would be in different strata. With a large enough sample, many narrow strata could be created. However in a moderately sized sample, many degrees of freedom might be lost.

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 information about 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. In fact to calculate standard errors, I created $k = 10$ 1 in 400 systematic samples, not just one. Deming (1960) has many examples.

Many systematic samples are analyzed as if they were SRS, with the expectation that the true standard errors will be smaller (see point 5, above).

References

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

1. To avoid selecting a sample that badly misrepresents the population. I've seen many instances of such SRSs. In some, reweighting 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 estimate characteristics of an epidemic by studying tf patients who attended medical clinics during that time. There were 40 clinics in the city, and 10 were drawn by SRS. Unfortunately, the 10 did not include the two very large hospital clinics in the city, which between them saw over 30% of all outpatients, usually the sickest. This bias made the sample useless for the satisfying its original purpose. 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 systematic 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, including travel, 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 sample with probability approximately proportional to size.

Many frames have a natural ordering, for example date of event. Systematic samples capture the natural stratification contained in this ordering.

References

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 total 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.

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.

1. To avoid selecting a sample that badly misrepresents the population. I've seen many instances of such SRSs. In some, reweighting 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 total 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 studied 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 systematic 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, including travel, 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 an agricultural 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, roughly the same number of workers.

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. Dividing the date range into strata would be somewhat arbitrary, because neighboring dates would be in different strata. With a large enough sample, many narrow strata could be created. However in a moderately sized sample, many degrees of freedom might be lost.

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 information about 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. In fact to calculate standard errors, I created $k = 10$ 1 in 400 systematic samples, not just one. Deming (1960) has many examples.

Many systematic samples are analyzed as if they were SRS, with the expectation that the true standard errors will be smaller (see point 5, above).

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.

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 total 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.