Multistage Sampling Techniques

Multistage Sampling: Two-Stage Equal Cluster Sampling

• Multi-stage sampling selects the sample in stages.
• Sampling units in each stage are subsamples from larger units chosen in the previous stages.
• Appropriate methods of selection are adopted at each stage (e.g., simple random, systematic, probability proportional to size).

Multi-Stage Sampling: Reasons

• Sampling frames may not be available for all units in the population, making it laborious and costly to create a complete frame.
• Multi-stage sampling is often more convenient and less expensive than single-stage sampling, especially in large-scale surveys.
• Multi-stage sampling can reduce response errors and improve sampling efficiency by reducing intra-class correlation in natural sampling units (e.g., households, villages).
• In crop surveys, villages are the first-stage units, fields within villages are the second-stage, and plots within fields are the third-stage units.

Two-Stage Sampling Scheme

• The population is divided into clusters.
• Clusters are the first-stage sampling units.
• A sample of clusters is selected from the population.
• Each selected cluster is then divided into subunits (sub-clusters).
• A sample of subunits is selected from each cluster.

Mean and Variance of Two-Stage Sampling

• The population consists of N clusters, each with M subunits.
• Y_ij is the value of a characteristic for the j^th subunit in the i^th cluster.
• The population mean (Y) is calculated as (1/NM) * Σ_i=1^N Σ_j=1^M Y_ij.

Sampling Frame Definition

• A sampling frame is a listing of the units from which a sample is selected.

• It should accurately represent the population.

• It includes materials, procedures, and devices to identify, distinguish, and access population elements.

• Rules for linking frame units to population elements are part of the frame.

• Auxiliary information (e.g., size, demographic information) is typically included for use in special sampling techniques (e.g., stratification, probability proportional to size, ratio or regression estimation).

• Multi-stage designs need a frame for each stage of selection.

Frames in Multi-Stage Designs

• In multi-stage sampling, the sampling units used at the first stage are called primary sampling units (PSUs).
• For subsequent stages, units are called secondary sampling units (SSUs), or third-stage units, etc.
• The final-stage units are called ultimate sampling units (USUs).
• For example, in a household survey, districts may be PSUs, enumeration areas (EAs) could be SSUs, and housing units could be USUs.

Types of Sampling Frames

• Area frames: Units are geographically defined areas.
• List frames: Units are listed as items on a list.
• Master sample frames: Used for repeated surveys over time to ensure stability.
• Clustered frames: Are used when no good population frame exists.
• The existence of a complete frame or master frame is not always viable.

Desirable Properties of Frames

• Quality related properties: Minimize nonsampling errors (e.g., coverage error).

  • Units should be well-defined (with clear boundaries on maps/definitions).
  • Units should have unique identifiers (numerical, and other identifiers).
  • The frame should be complete (including all target population elements).
  • The frame should be up-to-date.
  • Units should be stable over the time period.

• Efficiency related properties: Balance sampling error and cost.

  • Choose sampling units that work in a hierarchical fashion.
  • The frame should be in a format suitable for use in computer-assisted processing.
  • A good quality map should be available with the frame.

• Cost related properties: Frame preparation costs should be considered at the planning stage.

  • Aim for a frame that is maintainable in low cost, and should be efficient in use.
  • Consider how data from different stages can be combined.

Sample Design-Selection Process

• Defining sample objectives is needed before choosing a suitable sample design.
• The method of selecting a sample should be chosen carefully as each design produces different levels of precision for a given sample size.

Sample Size Calculation

• The sample size (n) depends on several factors:
• The required level of precision (margin of error & confidence level)
• The acceptable estimate of the key proportion (or 50% when unsure).
• The sample design that will be used.

Estimation Procedure

• Population estimates are computed from sample data, reported together with an indication of the estimate's precision.
• The specific estimation procedure depends on the sample design used.
• Population estimates are often based on proportions, calculating an estimate of a small sample and multiplying by the inverse of the sampling fraction.

Methods of Data Collection

• Primary data: Collected directly by or on behalf of the researcher.
• Primary data methods: Questionnaires, interview methods, observation methods.
• Secondary data: Collected for a different purpose by someone else.
• Secondary data sources: Published materials (journals, books), databases, and other sources.

Ethical Considerations

• Honesty in data reporting, methodological descriptions, and publication status.
• Avoid bias and disclose potential conflicts of interest.
• Maintain integrity, keep commitments, and be careful in research.
• Minimize harm and maximize benefits of research.
• The ethical treatment of human study participants through informed consent (which can be implemented through the provision of information, comprehension, and individual autonomy).
  • Providing the respondent with all applicable information (objectives, selection criteria, risks, compensation details).
• The researcher’s responsibility to the respondents and ensure all applicable research guidelines are in place to minimize negative impact from study participants.
• Ethical review committees (ERBs) are responsible for determining scientific soundness and resolving ethical concerns.

Instrument of Data Collection

• A data collection instrument (e.g., a questionnaire) is used to collect and record data.
• Structured questionnaires: contain pre-determined questions in a prescribed order
• Unstructured questionnaires: Contain open-ended questions that allow for more diverse answers
• Combining various methods is common

Questionnaires

• Open-ended questions allow free-form answers.
• Closed-ended questions use predetermined answer choices.
• Questions should be organized logically; based on a natural sequence.
• Questions should be phrased clearly for every individual completing the questionnaire.
• Sensitive topics and time reference periods should also be considered during survey design. Multiple questions (soluble-barreled) may combine two or more distinct questions.
• Ambiguous questions can lead to inaccurate interpretations and should be avoided. The language needs to be suitable across varied audiences.