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Simple Random Sampling
Definition
Simple random sampling is a probability-sampling method. For a fixed-size sample drawn without replacement, every possible group of that size has the same chance of selection. Consequently, every population unit has the same inclusion probability. The sampling frame determines which units can actually be selected.
What it means
Suppose a business wants to review some of its completed support requests. Taking the first hundred, the easiest hundred or the hundred staff remember is not simple random sampling. The selection must follow a random mechanism applied to a defined population list.
For the usual version without replacement, a selected request cannot appear twice. Sampling with replacement is another version, in which independent draws can select the same unit again. The design must state which version is intended.
Random selection supports an assessment of sampling uncertainty. It does not guarantee that one realized sample perfectly matches every population characteristic. Nor does it repair an incomplete list, inaccurate answers or missing responses after selection.
How it works
First define the target population, sampling unit and time window. Build a frame with one appropriate entry per unit and decide the sample size before looking at outcomes. Then use a suitable random selection procedure with or without replacement as specified.
For simple random sampling without replacement of n units from N, each unit's inclusion probability is n/N. Every subset containing n different units must be possible and equally likely. Equal individual inclusion probabilities alone are insufficient: a design can give everyone an equal chance while allowing only particular groups.
Record the frame version, selection method and selected identifiers. A random seed can help reproduce a software draw, but it does not establish that the frame is correct or the algorithm matches the design.
Analyze the data using uncertainty calculations appropriate to that design. When sampling a substantial fraction of a finite population without replacement, the finite-population correction matters.
Three practical examples
- A service team randomly selects completed tickets from a month's complete ticket register for a documented quality review.
- An AI evaluation team randomly samples eligible questions from a defined question bank, while separately assessing whether that bank represents intended users.
- A community organizer samples households from a maintained address list to estimate interest, then tracks which selected households do not respond.
Think of it this way
Think of putting one indistinguishable token for each eligible unit into a well-mixed container and drawing the required number without returning tokens. Each possible group can emerge through the draw.
The analogy illustrates the design, not a recommendation to use a physical lottery for large studies. Tokens missing from the container cannot be selected. A beautifully random draw from the wrong container still answers a question about the wrong population.
Worked example
Why equal chances are not enough
Consider four invented records A, B, C and D, with a required sample size of two. The six possible unordered samples are AB, AC, AD, BC, BD and CD. Under simple random sampling without replacement, each has probability 1/6.
A appears in three of the six samples, so its inclusion probability is 3/6 = 1/2. The same is true for every other record, agreeing with n/N = 2/4.
Now consider a different procedure that flips a fair coin and selects either AB or CD. Each record still has a one-half inclusion probability. However, AC, AD, BC and BD can never be selected. This is not a simple random sample of two from four.
The distinction matters because the selection relationships between units affect sampling variability. Naming only individual probabilities does not fully describe the design.
Illustrative case study
Fictional case: Meadow Services asks an assistant to choose fifty customers for a feedback survey. The assistant randomly selects from customers who opened the latest newsletter because that list is readily available.
The draw can be random within that list, but customers who did not open the newsletter have no chance of selection. The team therefore cannot describe the sample as a simple random sample of all customers.
It rebuilds the frame for the stated customer population, removes duplicate account entries according to the chosen unit and records nonresponse after drawing the sample. If individuals can hold several accounts, the team also decides whether the study concerns accounts or people. Random selection begins only after that distinction is resolved.
Common misconceptions and mistakes
- Random means representative in every respect. A realized sample can differ from the population through chance.
- Equal individual chances automatically establish simple random sampling. The worked example shows why the possible groups also matter.
- A large sample removes frame and response bias. Those problems can persist as sample size grows.
- Replacing nonrespondents with convenient volunteers preserves the original design. Such substitutions change how the observed sample is obtained.
Business use
Simple random sampling is useful when a suitable frame exists and the design's simplicity fits the study. It provides a clear starting point for audits, surveys and model evaluation.
It may be inefficient when important small groups need adequate coverage or when contacting widely scattered units is expensive. Stratified or cluster designs may suit those needs, but they require their own selection and analysis rules. Specify the decision, precision needs and operational constraints before choosing a design merely because a spreadsheet can generate random numbers.
People also ask
Is simple random sampling the same as random assignment?
No. Sampling selects units for observation; assignment allocates selected units to treatments or conditions.
Can it omit a small subgroup by chance?
Yes. Guaranteed subgroup coverage usually requires a different design, such as suitable stratification.
Is every tenth record a simple random sample?
Generally no. Systematic sampling with a random start is a distinct design, even when individual inclusion probabilities are equal.
Check your understanding
A manager randomly chooses one entire team from ten equally sized teams and reviews everyone on it. Is that a simple random sample of employees?
Answer: No. It is a cluster-based selection. Employees may have equal inclusion probabilities, but many employee combinations cannot be selected, and analysis must account for the design.
Related terms
- Selection bias
- Stratified sampling
- Cluster Sampling
- Sampling error
- Probability sampling
- sampling frame
- systematic sampling
Learn next
Read sampling frame and stratified sampling. For a small fictional population, enumerate all samples of a chosen size and compare simple random selection with a procedure that selects only predefined groups.
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Sources
Statistics Canada, Probability sampling: https://www150.statcan.gc.ca/n1/edu/power-pouvoir/ch13/prob/5214899-eng.htm. Statistics Canada, Survey Methods and Practices, simple random sampling chapter: https://www150.statcan.gc.ca/n1/en/pub/12-587-x/12-587-x2003001-eng.pdf. University of Chicago glossary: https://ds1.datascience.uchicago.edu/glossary.html. Scenarios and four-record calculations are original illustrations.
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