It’s clear from Examples 7, 8, and 9, and from the challenges of using the Internet to conduct surveys, that designing samples is a business for experts. Even most statisticians don’t qualify. We won’t worry about such details. The big idea is that good sample designs use chance to select individuals from the population. That is, all good samples are probability samples.
Probability sample
A probability sample is a sample chosen by chance. We must know what samples are possible and what chance, or probability, each possible sample has.
Some probability samples, such as stratified samples, don’t allow all possible samples from the population and may not give an equal chance to all the samples they do allow. As such, not all probability samples are random samples.
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A stratified sample of 300 undergraduate students and 200 graduate students, for example, allows only samples with exactly that makeup. An SRS would allow any 500 students. Both are probability samples. We need only know that estimates from any probability sample share the nice properties of estimates from an SRS. Confidence statements can be made without bias and have smaller margins of error as the size of the sample increases. Nonprobability samples such as voluntary response samples do not share these advantages and cannot give trustworthy information about a population. Now that we know that most nationwide samples are more complicated than an SRS, we will usually go back to acting as if good samples were SRSs. That keeps the big idea and hides the messy details.