What is the difference between a random sample and a simple random sample?

Question

I know what the definition of each is, but I don't know how to figure it out?

For example:

A container holds 1000 thoroughly mixed items, and 100 items are selected for testing.

Answer 1

A simple random sample is a specific kind of random sample. A random sample uses randomization to pick your sample. That can be done in a number of ways. A simple random sample is basically like selecting names from a hat. Every subject in the population has an equally likely chance of being in the sample, and every possible sample has an equally likely chance of being selected.. Other possible ways to take a random sample are systematic sampling (where you randomly select a starting point, and then pick every nth subject), cluster sampling (where subjects are separated into clusters, then all of the subjects in a random sample of clusters are put in the sample), and stratified sampling (where subjects are put into strata, and then a random sample is taken from each strata).

Non random samples do not use randomization. Online polls are an example of a nonrandom sample. The person taking the sample does not take an effort to pick the sample; people choose themselves to be in the sample.

Your example is a simple random sample. It's just like drawing from a hat.

In short, simple random samples are random samples, but random samples are not necessarily simple random samples.

Answer 2

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RE:
What is the difference between a random sample and a simple random sample?
I know what the definition of each is, but I don't know how to figure it out?

For example:

A container holds 1000 thoroughly mixed items, and 100 items are selected for testing.

Answer 3

A "random sample" is a generalized term for all kinds of sampling techniques that ensure the choices of the sampled data are equally likely and unbiased. A "simple" random sample is a specific type of random sample wherein the selection is made out of the population data without special rules of sampling other than the equally likely and unbiased rules.

By contrast, a random sample from groups conforming to certain criteria would not be a simple random sample; it would be a group random sample. A good example of a group random sample can be found in the election exit polls. Here, geographical/demographical groups are defined and randomly selected to ensure a representative distribution of the whole U.S. Then the exit polls are randomly conducted within each randomly selected defined group.

Your example is a simple random sample of the entire container. Had you divided the 1000 items into, say, a dozen containers, randomly selected five containers, and then did a simple random selection in each of the five containers, that would have been a group random sample. In this case, something called Analysis of Variance (ANOVA) would have been the appropriate statistical technique to test if the samples represented the population.

Another non-simple sampling technique is called stratified random sampling. Here we defined levels, i.e., strata, of the population to sample. For example, we might divide a population into age strata and then sample each stratum according to some weighting rules to ensure the results represented the population as a whole.