Understanding Sampling Procedures with Equal and Independent Chance

Sampling procedures are methods used to select a subset of individuals or units from a larger population to gather data. The goal is often to make inferences about the entire population based on the sample. A key characteristic differentiating various sampling methods is how the units are selected.

The question asks to identify sampling procedures where units are chosen giving an equal and independent chance. This specific phrase, "equal and independent chance," is the defining characteristic of Simple Random Sampling.

Let's examine each listed sampling procedure:

• A. Quota sampling procedure: This is a non-probability sampling method. Researchers select participants based on predefined characteristics (quotas) until a certain number is reached. The selection is not random; it depends on the researcher's judgment or convenience in finding individuals who fit the criteria. Units do not have an equal or independent chance of being selected.
• B. Stratified sampling procedure: This is a probability sampling method. The population is divided into homogeneous subgroups called strata. Then, units are selected from each stratum using a random sampling method, usually Simple Random Sampling or Systematic Sampling. While the chance of selection might not be equal for all units in the entire population (if strata sizes are disproportionate in the sample), units *within a stratum* typically have an equal and independent chance of being selected from that stratum when Simple Random Sampling is used within strata. This method relies on random selection principles.
• C. Dimensional sampling procedure: Similar to quota sampling, this is a non-probability method. It involves identifying key characteristics (dimensions) and then selecting individuals who meet these dimensions. The selection process is judgmental, not random. Units do not have an equal or independent chance.
• D. Random sampling procedure: This broadly refers to methods where units are selected using random chance. Simple Random Sampling is a type of random sampling where every unit in the population has an equal and independent chance of being selected. This directly matches the description in the question. Other forms of random sampling also involve chance selection with calculable probabilities.
• E. Systematic sampling procedure: This is a probability sampling method. After a random starting point is chosen from the first k units, every k-th unit on a list is selected. While each unit usually has an equal chance of being selected, the selections are not independent (once the first unit is selected, the subsequent units are determined by the interval k). However, it is considered a method based on chance and falls under probability sampling.

Comparing the methods:

Based on the analysis, Quota sampling (A) and Dimensional sampling (C) are non-probability methods that do not involve selecting units with an equal and independent chance. Stratified sampling (B), Random sampling (D - specifically Simple Random Sampling), and Systematic sampling (E) are probability sampling methods that involve selecting units based on chance, providing either equal and independent chance (SRS, Stratified within strata) or at least equal chance (Systematic).

Therefore, the sampling procedures that fit the description of involving chance, particularly highlighting methods like Simple Random Sampling (part of D) and methods related to probability selection like Stratified (B) and Systematic (E), are B, D, and E.

The final answer is $\boxed{B, D \text{ and } E \text{ only}}$.

Revision Table: Key Sampling Concepts

Additional Information on Sampling Procedures

Understanding the difference between probability and non-probability sampling is crucial in research design. Probability sampling methods, like Simple Random Sampling, Stratified Sampling, and Systematic Sampling, are preferred when the goal is to generalize findings from the sample back to the entire population. This is because they minimize selection bias by ensuring that each unit has a calculable chance of being included in the sample.

Non-probability sampling methods, such as Quota Sampling and Dimensional Sampling, are often used in qualitative research or in situations where probability sampling is not feasible or necessary. While easier and less costly to implement, they do not allow for reliable generalizations to the population because the sample selection is not random and thus not representative in a statistically rigorous way. The phrasing "equal and independent chance" is the gold standard of randomness, most purely embodied by Simple Random Sampling, but related principles of chance-based selection apply to other probability methods like Stratified and Systematic sampling.