Multiple frame agricultural surveys. v. 1: Current surveys based on area and list sampling methods. (FAO Statistical Development Series - 7) (1996)
 PART II: AREA SAMPLE DESIGNS WITH SEGMENTS THAT HAVE IDENTIFIABLE PHYSICAL BOUNDARIES
 CHAPTER 3 GENERAL CHARACTERISTICS OF THE SURVEY DESIGN
 3.2 Criteria for Area Frame Construction and Determination of the Main Parameters of the Survey Design
 (introduction...) 3.2.1 Frame Boundaries 3.2.2 Land-Use Strata Definitions 3.2.3 Strata Boundaries and Minimum Block Size 3.2.4 Target Segment Size in Each Strata 3.2.5 Sample Size and Allocation to Strata 3.2.6 Subdivision of Strata into PSUs. Size of PSUs, Strata and Total Frame Size 3.2.7 Ordering of PSUs within Strata 3.2.8 Replicated Sampling Selection Methods 3.2.9 Special Sampling Frames

### 3.2.8 Replicated Sampling Selection Methods

The use of a replicated sample allows the overall sample size to be increased or decreased by adding or deleting replicates. It also facilitates the preparation of samples for special surveys and allows for rotation of a portion of the sample in successive survey rounds in order to avoid respondent fatigue.

Replicated sampling can be carried out with the use of either systematic or random sampling. A number of smaller independent samples (called replicates) are selected to represent the population or universe rather than selecting one large sample. Care must be taken to ensure that each of the replicas is an unbiased representation of the universe. For example, if it has been decided that a sample of 60 units is sufficient to properly represent a population, with replicated sampling, 4 independent samples (replicates) of 15 units each could be selected from the population instead of one single sample of 60 units. Other possibilities are: 5 replicates of 12 units each; 3 replicates of 20 units; and 10 replicates of 6 units each (this may be the best). At the time of sample selection, additional replicates are selected for sample rotation and management. Replicated sampling for periodic, large-scale, agricultural surveys is recommended for the following reasons:

* The existence of replicates makes sample management easier. The sample size can be readily increased or decreased by adding or taking out replicates in order to achieve a desired precision. Additional replicates or retired replicates can be used for special one time or repetitive surveys.

* Sample rotation to ease respondent burden caused by repeated interviewing is greatly facilitated. The number of replicates in the sample can be coordinated with the desired sample rotation. If the desired level of sample rotation is 25% each year, four (or a multiple of 4) active replicates are selected. One replicate (or 2 when using 8 replicates etc.) would be retired each year and a new replicate (or replicates) rotated in, resulting in a complete rotation every four years. The replicates that are rotated out after less than four years of service can be rotated back in later in order to bear their share of the survey burden. The number of replicates can be adjusted to coincide with a complete rotation every three years or every five years. This procedure also ensures that a significant portion of the sample will be the same from one year to the next, so that a stable measure of change can be calculated by using ratios of current estimates to those for the previous year for units surveyed in both years. The fact that sample rotation is facilitated by the existence of replicates does not mean that rotation is required with a replicated sample. As long as respondent fatigue is not a problem, sample rotation can be delayed.

* Replicated sampling provides the means to test different survey procedures. For example, half the replicates could be assigned to a new approach; the other half would be surveyed using the established method; the test could be between versions of a questionnaire and/or interviewing techniques. The test of difference would be derived using the means and/or totals from each replicate for each approach.

* Quality control is assisted by a quick comparison of replicate totals. A significant deviation by one or more replicates from the others indicates the need for an additional detailed check of data entered for those replicates. It does not mean that the data are incorrect. It simply means that a check should be made before allowing the data to go on to final summary.

* Replicated sampling provides a simple unbiased method for estimating sample variance (even where systematic sampling is used) and population parameters (expansions) using replicate means or totals. This is particularly important where computer power is not available. However, the variance estimate for an individual stratum is unstable due to the reduced degrees of freedom, but it gains stability as strata are added.

Assume that a sample of n segments has been allocated to the land-use strata (size nh in each stratum) and that the PSUs were measured and ordered within each land-use strata.

Let rh denote the number of replicates in the land-use stratum h. The number of sample replicates in a land-use stratum is dictated by the degrees of freedom in the variance of the estimates and by the desired sample rotation procedure to reduce respondent burden caused by repeated interviewing. Suppose that 5 sample replicates (rh = 5) are selected in the stratum.

For selecting the desired number of replicates (each with nh/5 segments) in a given land-use stratum, the stratum should be completely subdivided into non-overlapping substrata with an equal number of segments called also zones, in order to select 5 segments in each zone, one for each replicate.

For each land-use stratum (with Nh segments), the number of substrata (Lh) is given by the size (number of segments) of each replicate (Lh = nh/5).

At this point, the allocated sample size in the land-use strata, nh, should be adjusted, so that nh is proportional to rh, the number of replicates. For example, if 5 sample replicates are selected, the nh values, resulting from the allocation of the sample, are adjusted to multiples of 5.

Within each land-use stratum, the determination of zones, is done by following the established order of the PSUs. For that purpose, in each land-use stratum a list should be prepared with the accumulated measures of size of the ordered PSUs.

The sample selection within each stratum can be done by selecting a random sample in each zone (random replicated sampling) or systematically by selecting replicates with identical selection intervals equal to the size of a substrata (systematic replicated sampling). The mechanics of these two selection procedures are described in chapter 7. Although random replicated sampling within each zone is recommended, systematic sampling is often used due to its simplicity and because it ensures a geographical spread of the sample if the PSUs were ordered in a serpentine fashion, as explained earlier. Systematic sampling can cause a serious bias if the sampling interval should happen to coincide with a certain periodicity in the arrangement of the segments, but such periodicity is rare in area frame segment listings.