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Topics Covered

Population & Sample Parameter / Statistic Sampling Distribution Steps in a Survey Principles Sampling vs Non-sampling Errors Types of Sampling
On this page
  1. 1. Population, Sample, Parameter and Statistic
  2. 2. Census vs Sample Survey
  3. 3. Principal Steps in a Sample Survey
  4. 4. Principles of Sample Survey
  5. 5. Sampling and Non-sampling Errors
  6. 6. Types of Sampling
  7. Key Take-aways

1. Population, Sample, Parameter and Statistic

DEFINITIONS
Population (N) Parameter: μ, σ², P (usually unknown) Sample (n) Statistic: x̄, s², p̂ draw sample infer / estimate
Fig 1.1 — A sample is drawn from a population; statistics are used to estimate parameters

2. Census vs Sample Survey

AspectCensusSample Survey
CoverageEvery unit of populationSubset only
CostVery highLow
TimeLong (years)Short (weeks/months)
AccuracyHigh in principle but error-prone in practiceStatistical accuracy with quantified error
Use caseDecennial population censusPolls, market research, NSSO surveys

Advantages of Sampling over Census

  1. Cost-effective.
  2. Saves time.
  3. Often more accurate (better trained staff, fewer non-response errors).
  4. Necessary when population is infinite or testing is destructive.
  5. Provides a measure of reliability via the standard error.

Limitations of Sampling

  1. Sampling error is unavoidable.
  2. Requires specialised knowledge to design well.
  3. Inadequate sample size may give misleading conclusions.
  4. Not suitable when individual-level data on every unit is needed (e.g., voter rolls).

3. Principal Steps in a Sample Survey

  1. Statement of objectives — what is to be estimated and why.
  2. Definition of population — clearly demarcate the units (geographic, time, characteristic).
  3. Choice of sampling units & frame — list of all units (e.g. household list).
  4. Method of data collection — interview, mailed questionnaire, observation.
  5. Questionnaire design — short, unambiguous, pre-tested.
  6. Selection of sampling scheme & sample size — based on cost and precision.
  7. Pilot survey — small-scale dry run to refine the design.
  8. Field work — training enumerators, collecting data.
  9. Analysis & estimation — compute estimates & standard errors.
  10. Report writing — clear, transparent presentation.

4. Principles of Sample Survey

FOUR PRINCIPLES
  1. Statistical regularity — a moderately sized random sample is likely to have characteristics similar to those of the population.
  2. Inertia of large numbers — large samples are more stable; results vary less.
  3. Validity — selection should permit valid estimation of sampling error.
  4. Optimization — design should attain maximum precision for given cost (or minimum cost for given precision).

5. Sampling and Non-sampling Errors

Sampling Error

Error arising solely because we observe only a sample, not the whole population. Decreases as \(n\) grows; vanishes for a complete census.

Measured by standard error: \(\text{SE}(\bar X) = \sigma/\sqrt n\) for SRSWR.

Non-sampling Error

Error arising from sources other than sampling. Present in both sample surveys and censuses, often larger than sampling error in censuses.

Sources include:

AspectSampling ErrorNon-sampling Error
CauseUse of a sampleMistakes in design/execution
Census present?NoYes
Effect of large nDecreasesMay increase
Quantifiable?Yes (SE)Hard to quantify

6. Types of Sampling

Sampling Methods Probability (Random) Sampling Simple random (SRSWR / SRSWOR) Stratified random Systematic Cluster Multistage Probability proportional to size Non-probability (Purposive) Sampling Convenience Judgement (purposive) Quota Mixed Sampling Some stages random, others purposive
Fig 1.1 — Classification of sampling methods. Every method is either probability (random) sampling — where each unit has a known, non-zero chance of selection, so error can be quantified — or non-probability (purposive) sampling, which relies on judgement and permits no valid error estimate; mixed sampling combines both across stages. The subsections below expand each branch.

6.1 Subjective (Non-random / Purposive) Sampling

Units are selected based on the personal judgement of the investigator. No probability mechanism is used.

Examples: convenience sampling, judgement sampling, quota sampling.

EXAMPLE 1

A reporter interviews the first 20 voters who exit a polling booth — convenience sampling.

EXAMPLE 2

An economist hand-picks 10 "typical" villages to study tribal economy — judgement sampling.

6.2 Probability (Random) Sampling

Every unit has a known, non-zero probability of selection. Allows valid statistical inference and quantification of error.

Main schemes:

  1. Simple Random Sampling (SRSWR / SRSWOR) — Unit 2.
  2. Stratified Random Sampling — Unit 3.
  3. Systematic Sampling — Unit 4.
  4. Cluster Sampling, Multistage Sampling — Unit 4.
EXAMPLE 1

The NSSO selects households by stratified multistage sampling — every household has a known probability of inclusion.

EXAMPLE 2

Lottery draws are SRSWR — each ticket has equal probability of being drawn.

6.3 Mixed Sampling

Combination of probability and non-probability methods. E.g., the first stage units chosen by judgement, second stage chosen at random.

EXAMPLE 1

An exit poll selects polling booths purposively (close to investigator's office) and then samples voters at random within each booth.

EXAMPLE 2

A market researcher chooses 5 cities by judgement and then surveys a random sample of households in each.

Key Take-aways

← Course Home Next: Unit 2 — Simple Random Sampling →