OFFICIAL STATISTICS SPECIALLY DESIGNED FOR INDIAN STATISTICAL SERVICE (ISS) AND OTHER GOVERNMENT & PRIVATE SECTOR STATISTICAL EXAMINATIONS
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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.
Why examiners love this topic
The NSS design combines stratification, unequal probability sampling (PPSWR), two-stage estimation and interpenetrating sub-samples. One question can test the theory, the numerical multiplier or the reasoning behind the design.
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.
Strata
Districts (or groups of districts) form basic strata. Rural strata are split by population size, and large cities usually form separate urban strata.
First-stage units
Census villages in rural areas and Urban Frame Survey (UFS) blocks in urban areas.
Ultimate units
Households, chosen from the listed households, usually by SRSWOR within second-stage strata.
Exam tip
Villages are typically selected with probability proportional to population (PPSWR), while urban blocks are usually drawn by simple random sampling without replacement. Write “in the standard NSS design” and check the technical note of the specific round before quoting details.
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, pi is the selection probability of the i-th village in a single draw, Hi households are listed, hi are surveyed, and yij 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 × pi), not 1/pi.
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
| Basis | Census (complete enumeration) | NSS (sample survey) |
|---|---|---|
| Coverage | Every unit in the population | Only a selected sample |
| Cost and time | High and slow | Lower and faster |
| Errors | Mainly non-sampling errors | Sampling plus non-sampling errors |
| Best for | Small-area counts and building frames | National and state-level estimates |
| Example | Population Census | Household consumption expenditure survey |
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 × pi).
- 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.
What are interpenetrating sub-samples, and how do they help in estimating the variance?
Show answer
The full sample is divided into independent sub-samples, each selected by the same design and each able to estimate the parameter. If two sub-samples give Y1 and Y2, the combined estimate is (Y1 + Y2)/2 and its variance is estimated by (Y1 − Y2)2/4. For example, with 52 and 48 (in lakh), the estimate is 50 and the variance estimate is 4, so the standard error is 2 lakh.
In a rural stratum the total population is 60,000. A village of population 1,200 is selected as one of n = 8 first-stage units by PPSWR. In this village 40 households are listed and 8 are surveyed. Find the selection probability of the village per draw and the multiplier for each surveyed household (ignore non-response).
Show answer
p = 1,200 / 60,000 = 0.02.
First-stage factor = 1 / (n × p) = 1 / (8 × 0.02) = 6.25.
Second-stage factor = H / h = 40 / 8 = 5.
Overall multiplier = 6.25 × 5 = 31.25. Each surveyed household represents about 31 households of the stratum.
Describe the sampling design used in the National Sample Survey and discuss the advantages of interpenetrating sub-samples.
Show answer
Write your answer in four parts. (a) Stratification: districts or groups of districts form basic strata, with rural and urban sub-strata based on population size. (b) Stages: first-stage units are villages (selected with probability proportional to population) or urban blocks (usually SRSWOR); households are selected at the second stage after listing and second-stage stratification. (c) Estimation: each household gets a multiplier equal to the inverse of its selection probability, adjusted for non-response. (d) IPNS advantages: the sample is split into independent sub-samples, which gives a simple variance estimate, helps compare investigators and detect non-sampling errors, and allows quick early estimates. Conclude that the design balances precision, cost and speed.
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 × pi), 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.
Everything on Official Statistics, in one book
NSS sampling design is just one chapter of the syllabus. If you want the complete picture, this book is built for you.
- Indian official statistical system: MoSPI, NSO, NSC and the data they produce
- National accounts, GDP, IIP, price indices and labour statistics
- NSS surveys, sampling designs and data quality concepts
- Written specially for the ISS exam, and useful for other government and private sector statistical exams
- Concept-focused notes to revise quickly before the exam
Official Statistics for ISS and other Government & Private Sector Statistical Examinations