NSS Sampling Design in India: Two-Stage Stratified Sampling, Multipliers and Exam Questions for ISS

Almost every large household survey number in India, from consumption expenditure to employment, is an estimate from a sample. The National Sample Survey (NSS) is the standard example, and its design is a favourite of Indian Statistical Service (ISS) paper setters because it puts sampling theory to real use. It also appears in RBI, NABARD, SSC and university statistics exams. This guide gives you the design, the estimation logic and three exam-style questions.

1. What is the National Sample Survey?

The NSS was launched in 1950 under the guidance of P. C. Mahalanobis and is now conducted by the National Statistics Office (NSO), MoSPI. It collects household-level data on consumption expenditure, employment, health, education and other social and economic themes, using sample surveys instead of a complete count.

2. The design in one view

NSS surveys generally use a stratified multi-stage design. The exact details change from round to round, so treat this as the standard pattern.

3. Estimation and the multiplier

With PPSWR at the first stage and SRSWOR of households at the second stage, the estimate of a population total is a weighted sum. Each surveyed household carries a multiplier, roughly the inverse of its overall selection probability.

Here n is the number of first-stage draws, p_i is the selection probability of the i-th village in a single draw, H_i households are listed, h_i are surveyed, and y_ij is the value of the character for household j. Adjustments for non-response and sub-samples are applied on top.

• Strength: unbiased estimates with sound theory at a manageable field cost.
• Weakness: sampling error is unavoidable, and non-sampling errors such as non-response and recall lapse can bias results.
• Property to remember: the first-stage factor is 1/(n × p_i), not 1/p_i.

4. The interpenetrating sub-sample (IPNS) idea

Mahalanobis introduced IPNS: the whole sample is split into two or more independent sub-samples, each drawn with the same design and each able to give an estimate on its own.

• Two sub-samples give two estimates, Y₁ and Y₂. The combined estimate is their average.
• The variance estimate is ( Y₁ − Y₂ )² / 4, so no complex variance formula is needed.
• Different sub-samples can go to different investigators, which helps detect investigator (non-sampling) errors.
• Results from a single sub-sample are available early, before the full sample is processed.

5. Census vs sample survey: the comparison that keeps coming up

6. Common mistakes students make

• Saying NSS is conducted by the Registrar General. It is NSO, MoSPI (NSSO was merged into NSO in 2019).
• Using 1/p as the first-stage factor when n draws are made. It is 1/(n × p_i).
• Mixing up FSU and USU. The village or block is the FSU; the household is the USU.
• Thinking IPNS means overlapping samples. The sub-samples are independent, and each covers the same area.
• Forgetting the divisor 4 in the IPNS variance estimate ( Y₁ − Y₂ )² / 4.

7. Three important questions on NSS sampling

Try each one on your own first, then tap the answer.

Key takeaways

• The NSS uses a stratified multi-stage design: strata, then villages or blocks (FSU), then households (USU).
• With PPSWR, the first-stage factor is 1/(n × p_i), and the second-stage factor is H/h.
• IPNS gives a simple variance estimate: (Y₁ − Y₂)²/4 for two sub-samples.
• Design details vary by round, so read the technical note before quoting specifics.