Random (Probability) Sampling Methods

In a random (or probability) sampling method, every unit of the population has a known, non-zero, and pre-determined chance of being selected in the sample. This property is what lets us measure sampling error mathematically and generalise sample results to the population with a stated level of confidence. GSHSEB Std 11 Commerce Statistics covers four such methods.

(a) Simple Random Sampling (SRS) — every unit has an equal chance of selection, and every possible sample of the required size has an equal chance of being chosen. Two common techniques:

• Lottery method — each unit is written on an identical slip, the slips are mixed thoroughly, and the required number is drawn blindly.
• Random number tables — units are numbered serially, and a sample is drawn using a table (or computer-generated list) of random numbers.

Sampling may be done with replacement (SRSWR) — a selected unit is returned to the population before the next draw — or without replacement (SRSWOR) — a selected unit is not returned, which is the usual practice in business surveys.

(b) Stratified Random Sampling — the population is first divided into non-overlapping, internally homogeneous groups called strata (e.g., by region, income group, or business size), and a simple random sample is then drawn independently from each stratum. This ensures every important sub-group is represented, which plain SRS cannot guarantee. Under proportional allocation, the sample size drawn from a stratum is kept proportional to that stratum's share of the population:

where $n_i$ is the sample size for stratum $i$, $N_i$ is the population size of stratum $i$, $N$ is the total population size, and $n$ is the total required sample size.

(c) Systematic Sampling — units are arranged in some order (e.g., a numbered list), and every $k$-th unit is selected after a random start, where the sampling interval is:

For example, from a numbered list of 500 employees, to draw a sample of 50, the interval is $k = 500/50 = 10$; a random starting point is chosen between 1 and 10, and then every 10th employee thereafter is included. …