Which sampling method allows every member of the population an equal chance of selection?

The sampling method that allows every member of the population an equal chance of selection is known as a random sample. This approach is fundamental in research and statistical studies because it ensures that the sample accurately represents the population, thus reducing potential biases. By giving each individual an equal opportunity to be selected, random sampling helps improve the reliability and validity of the conclusions drawn from the results. This method is essential in creating a fair representation of diverse viewpoints within the population, which is crucial in fields such as social sciences, market research, and public opinion polling.

The other methods presented, such as stratified sampling, involve specific criteria or categories to select participants rather than providing equal chances for all. Hasty generalization is a logical fallacy where conclusions are drawn from insufficient evidence, and "variation" does not specifically refer to a method of sampling in the context provided.