Simple Random Sample

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Simple Random Sample

A simple random sample (SRS) is a subset of a population in which each member has an equal probability of being selected. It is designed to provide an unbiased, representative snapshot of the whole population without systematically favoring any subgroup.

Key points

  • Every member of the population has the same chance of selection.
  • Useful when little is known about population structure.
  • Prone to sampling error; the sample may not perfectly reflect the population.
  • Alternatives (stratified, systematic, cluster) can reduce certain types of error.

How it works (brief example)

Imagine a company with 250 employees. To create a simple random sample of 25 employees, assign each employee a unique number from 1 to 250, then randomly select 25 numbers. Each employee’s probability of being chosen is equal, so the resulting sample aims to reflect the broader workforce without deliberate bias.

Six steps to conduct a simple random sample

  1. Define the population: Specify the full group you want to study (e.g., all students at a university, all companies in the S&P 500).
  2. Choose the sample size: Decide how many units you need based on resources and desired precision.
  3. List population units: Create a complete list of every unit in the population.
  4. Assign numerical IDs: Give each unit a unique sequential number.
  5. Select random numbers: Use a random method to pick the required number of IDs.
  6. Identify the sample: Match selected numbers back to the units to form your sample.

Random selection techniques

  • Lottery (draw numbered slips or balls).
  • Physical randomizers (dice, coins, spinning wheels).
  • Random number tables.
  • Online random number generators.
  • Spreadsheet functions (e.g., Excel’s =RANDBETWEEN or RAND-based methods).

Tip: Have an independent person or colleague perform or review the random selection to reduce accidental bias.

How SRS compares with other methods

  • Stratified sampling: Population is divided into non-overlapping strata (e.g., age groups), and random samples are drawn from each. Better when you want proportional representation of known subgroups.
  • Systematic sampling: Choose a random start, then select every k-th unit. Simpler for ordered lists and avoids clustering but can introduce bias if the list has patterns.
  • Cluster sampling: Population is divided into clusters; clusters are randomly chosen and then members within clusters are sampled. Efficient for geographically dispersed populations or multistage designs.

Advantages

  • Conceptually simple and easy to implement for lists or digital datasets.
  • Minimizes selection bias because each unit has equal probability.
  • Straightforward to explain and defend.

Disadvantages

  • Sampling error: Random variation can produce samples that are not representative of some characteristics (e.g., all men).
  • Inefficient for small but important subgroups—stratified sampling may be preferable when subgroup estimates are required.
  • Listing and numbering all population units can be costly or impractical for very large populations.

When to use SRS

  • When you have or can create a complete list of the population.
  • When population heterogeneity is unknown or you only need overall population estimates.
  • When simplicity and transparency are priorities.

Short FAQ

Q: Does SRS guarantee accurate results?
A: No. SRS reduces selection bias but cannot eliminate sampling error; larger samples reduce error.

Q: How do I pick a sample size?
A: Base it on desired confidence, margin of error, variability in the population, and available resources.

Q: When is stratified sampling better?
A: When you need reliable estimates for specific subgroups or when the population contains distinct strata that should be represented proportionally.

Conclusion

Simple random sampling is the most basic probability sampling method and works well when you can list the population and need a straightforward, unbiased sample. For populations with known subgroups or where subgroup precision is important, consider stratified or cluster methods to reduce sampling error and improve efficiency.