Simple Random Sampling — SRS
Simple Random Sampling · Also known as: SRS, unrestricted random sampling, equal-probability sampling, EPSEM
Simple random sampling (SRS) is the foundational probability sampling method in which every unit in the population has an equal and independent chance of being selected. Because selection is governed purely by chance, SRS eliminates systematic bias, supports unbiased estimation of population parameters, and provides the statistical baseline against which all more complex probability designs are evaluated.
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When to use it
Use SRS when a complete and accurate sampling frame is available, the population is relatively homogeneous, and budget allows for the sample size required to achieve target precision. It is the preferred baseline design when no auxiliary information about the population structure exists. Do not use SRS when the population is highly heterogeneous by groups you care about (stratified sampling is more efficient), when the frame is incomplete or impossible to construct (consider systematic or cluster designs), when some subgroups are rare and must be over-represented (stratified oversampling), or when logistical constraints make a dispersed random sample prohibitively costly to contact (cluster sampling is cheaper). SRS is also unsuitable for qualitative or purposive goals where representativeness is defined by theoretical relevance rather than equal probability.
Strengths & limitations
- Unbiased: every unit has the same known probability of selection, eliminating systematic bias in estimation.
- Theoretically tractable: standard errors, confidence intervals, and hypothesis tests follow directly from probability theory.
- Simplicity: the design is easy to explain, audit, and replicate.
- Serves as the statistical baseline: design effects for all complex sampling designs are measured relative to SRS.
- Software support: virtually every statistical package (R, Stata, SPSS, SAS) includes functions for SRS estimation.
- Requires a complete sampling frame — impossible to use if the population cannot be enumerated.
- Statistically inefficient for heterogeneous populations: stratified sampling achieves the same precision with a smaller sample.
- Can be logistically costly when selected units are geographically or organizationally dispersed.
- Rare subgroups may be under-represented by chance, limiting subgroup analysis without oversampling.
Frequently asked
What is the difference between sampling with replacement (SRSWR) and without replacement (SRSWOR)?
In sampling with replacement a selected unit is returned to the frame before the next draw, so it can be chosen again. In sampling without replacement (the standard practice) each selected unit is removed, ensuring each unit appears at most once. SRSWOR is more efficient because no information is wasted on duplicate selections, and it is the design that standard survey estimation formulas assume unless stated otherwise.
When should I prefer stratified over simple random sampling?
Prefer stratified sampling when the population contains identifiable subgroups (strata) that differ substantially in the outcome of interest. Stratification reduces variance by ensuring each stratum is represented and, for a fixed total sample size, typically yields narrower confidence intervals than SRS. SRS is adequate when the population is relatively homogeneous or when no reliable auxiliary variable is available for stratification.
Do I need a very large sample for SRS to be valid?
No. The validity of SRS-based inference rests on the randomness of selection, not on sample size. Small but properly randomized samples are unbiased. However, small samples produce wide confidence intervals. The required n depends on the desired precision (margin of error), confidence level, and variability in the population — use the sample-size formula and plan accordingly.
What is the finite population correction (FPC) and when does it matter?
The FPC is the factor sqrt(1 - n/N) applied to standard errors when the sample constitutes a non-trivial proportion of the population. It reduces the standard error, reflecting the fact that sampling a large share of a finite population provides more information than sampling the same number from an infinite stream. By convention, apply the FPC when the sampling fraction n/N exceeds roughly 0.05 (5%). For most large-scale surveys where n/N is tiny, the FPC is negligible.
Can I use SRS if I do not have a complete list of the population?
No. SRS requires a complete sampling frame. Without one, equal-probability selection is impossible and the statistical guarantees break down. If a complete frame is unavailable, consider cluster sampling (which requires only a frame of clusters, not individuals), or systematic sampling from a partial list with documented coverage assumptions, and acknowledge the resulting coverage limitations transparently.
Sources
- Cochran, W. G. (1977). Sampling Techniques (3rd ed.). John Wiley & Sons. ISBN: 978-0471162407
- Lohr, S. L. (2009). Sampling: Design and Analysis (2nd ed.). Brooks/Cole. ISBN: 978-0495105275
How to cite this page
ScholarGate. (2026, June 3). Simple Random Sampling. ScholarGate. https://scholargate.app/en/survey-methodology/simple-random-sampling
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
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