Untitled Quiz

Multistage Sampling: Two-Stage Equal Cluster Sampling

• Multi-stage sampling selects a sample in stages.
• Sampling units in each stage are sub-sampled from previous stages.
• Selection methods include simple random sampling, systematic sampling, and probability proportional to size.

Multistage Sampling - Reasons

• Sampling frames may not be available for all units.
• Multi-stage sampling is more practical when frames are incomplete or expensive to construct.
• Multi-stage sampling can be more convenient, especially in large-scale surveys.
• Reduced response errors and improved sampling efficiency by lowering intra-class correlation in groups like villages and households.

Multistage Sampling - Example

• In a crop survey, villages are first-stage units.
• Fields within villages are second-stage units.
• Plots within fields are third-stage units.

Multistage Sampling - Population Diagram

• Population includes a large number of units categorized into clusters.
• First-stage: select a small number of clusters.
• Second-stage: sample a number of units (e.g., m units) from each selected cluster.

Multistage Sampling - Equations

• Population Mean: Y = (1/NM) Σ_i=1^N Σ_j=1^M Y_ij
• Mean per first-stage unit (fsu): (1/NM) Σ_i=1^N Σ_j=1^M Y_ij
• Mean per second-stage unit in the population: (1/NM) Σ_i=1^N Σ_j=1^M Y_ij.

Multistage Sampling - Calculation Average

• Average the estimator over all second-stage selections from a fixed set of n units.
• Then average over all possible selections of n units by the plan.

Multistage Sampling - Variance Calculation

• Two-stage variance: Var(θ) = E[E₂(θ-θ̂)²]
• Includes the variance of the estimator and the average over the second-stage selections.

Multistage Sampling - Three-stage Variance

• Variance of three-stage sampling: Var(θ) = V₁[E₂(θ₃)] + E₁[V₂(θ₃)] + E[E₂{V₃(θ₃)}].

Stratified Multistage Sampling

• Stratified multistage designs combine advantages of stratification and multi-stage sampling.
• Strata should be internally homogeneous but heterogeneous with respect to each other.
• First-stage units should be internally heterogeneous but homogeneous relative to each other.

Sampling Frames - Definition

• A listing of units from which a sample will be selected in any stage of sampling.
• Accurate representation of the target population.
• Contains materials, procedures, and devices to identify, distinguish, and allow access to population elements.

Sampling Frames - Content

• Auxiliary information is included (measure of size, demographic information).
• Used for special sampling techniques (stratification, probability proportional to size, etc.).
• Needed for each stage of selection in multi-stage sample designs.

Frames in Multi-stage Design

• Primary Sampling Units (PSUs) are used at the first sampling stage.
• Secondary Sampling Units (SSUs), Third-stage units, etc. are for intermediate sampling stages.
• Ultimate Sampling Units (USUs) refer to the sampling units at the final stage, often the ultimate units of interest.

Sampling Frames - Examples

• In a three-stage household survey, districts could be PSUs, enumeration areas SSUs, and households USUs.

Types of Sampling Frames

• Area frames: County, district, tract, etc.
• List frames: Lists of target units.
• Master Sample frames: Stable frames for multiple survey rounds.
• Clustered frames: Used when no good or inexpensive population frame is available.

Desirable Properties of Sampling Frames

• Quality related: completeness (coverage), up-to-date, and stable units.
• Efficiency related: choice of sampling units, hierarchical structure, and good quality maps and easy manipulation.

Cost Related Properties

• Frame development, maintenance, and updates.
• Cost should be considered and budgeted in the survey's planning stages.
• The frame source with the lowest development, use, and maintenance cost is preferred when equivalent in quality and efficiency.

Sample Design

• The goal of sampling is representative target population.
• Prior knowledge of the population is needed for reasonable estimations.
• Sampling method affects sampling estimate precision and accuracy.

Sample Design - Choice of Design

• Survey statisticians and experts collaborate for a design.
• Issues like objectives, variables to be measured, required estimates, reliability, validity, timeliness, and costs need agreement.

Sample Design - Objectives and Prelim Investigation

• Define the problem clearly.
• Define the population to be studied, including geographic area, economic or social classification.
• Specify desired information in statistical terms.

Sample Design - Level of Breakdown and Timeliness

• Specify breakdown levels (regions, age, sex) for tabulated results.
• Specify the accuracy level or the tolerated error rate.
• Determine the required timeliness of the results.

Sample Design - Selection Process

• Choose sample design after survey objective, coverage, and issue assessments.
• Various sample designs may be suitable for different survey types and circumstances.

Sample Size Calculation - Population Proportion

• Formula for sample size: n = (Z_α/2)² * p(1-p) / w²
• p: Estimate of population proportion; reasonable estimate or 0.50 if unknown.
• w: acceptable width of confidence interval.
• Z_α/2: Z-value related to confidence level; often 1.96 for 95% confidence.

Sample Size Estimation - Factors

• Required precision in the estimate: specify desired margin of error and confidence level.
• Sample design: different designs affect precision for the same sample size.

Sample Size Estimation - Calculation Basis

• Minimum sample size is required for acceptable precision.
• Accurate implementation is essential for sample representation and reliable estimates.
• Varied precision requirements across variables lead to different sample size needs.

Estimation Procedure

• Purpose of surveys is estimated population characteristics.
• Estimates along with precision from sampling variance are reported.
• Calculation of estimates depends on the sampling design.

Data Collection Methods

• Primary data: data collected directly for the survey.
• Typical methods are questionnaires, interview methods, and observation method.
• Secondary data: data collected previously for a different purpose.

Data Collection - Secondary Data Sources

• Published sources (journals, books, historical documents).
• Other sources of published information.

Ethical Considerations

• Systematic study of values (good, bad, right, wrong).
• Focus on principles and conduct standards.

Codes & Policies for Research Ethics

• Professional associations set ethical codes for research practices.
• Specific ethical principles include honesty, objectivity, integrity; respect for persons, beneficence, and justice.
• Ethical review boards ensure research's scientific merit and ethical concerns' resolution.

Informed Consent

• Process where participants make voluntary choices to be in the study.
• Goal is for participants to understand and freely choose to participate or continue.
• Essential elements are information, comprehension, and participant autonomy.
• Considers objectives, voluntary participation and withdrawal, details of discomfort, and risk, expected costs and benefits.

Chapter 6 - Instruments of Data Collection

• Data collection instrument is used to gather data.
• Two types exist: structured and unstructured questionnaires.

Type of Questionnaires

• Structured questionnaires: Written questions, respondents respond directly.
• Unstructured questionnaires (checklist of topics) : Used for qualitative surveys.

Questionnaire Design Principles

• Questions should be clear, unambiguous, same meaning for all.
• Neutral phrasing is crucial; avoid leading questions.
• Use simple language that aligns with respondents' native language.

Questionnaire Design Principles - Sensitive Topics

• Awareness of sensitive topics that may hinder open answers.
• Proper structure and design are essential to ensure reliability.

Types of Questions

• Closed-ended questions: Pre-determined answers (dichotomous, multiple choice).
• Open-ended questions: Unstructured, respondents answer freely in their own words.

Question Layout

• Logical order for questionnaires.
• Common layouts: verbatim listing, question listing, tabular row and column format, and checklist of topics.

Common Problems of Question Phrasing

• Use clear, unambiguous wording and appropriate meaning to all parties.
• Avoid wording questions that lead respondents to specific answers.

Multiple Questions

• Multiple questions combine two or more distinct questions in one.
• Avoid ambiguity in the construction of questions.
• The wording needs to be precise and accurately reflect the intended meaning for all respondents.

Choice of Reference Period

• Accurate time reference period in questionnaire design is important.
• Time-reference period refers to the specified time frame for gathering information on events.