Talk:Simple random sample

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The following appeared before I edited this article, and is nonsense:

For instance, if I have 10 names in the hat, the probability of

any one name being drawn is 1 out of 10. After the first name is

drawn, there are nine names left in the hat changing the

probability of anyone being selected as the second name is 1 out

of 9. Since different names have different probabilities

depending on the sequence in which the drawing is done, the

resulting sample will not be a simple random sample.

The conditional probability that a certain name will be chosen on the second draw given that it was not chosen on the first draw, is 1/9, not 1/10. But the unconditional probability that a certain name will be the second one chosen, calculated in ignorance of which name was chosen first, is 1/10. Moreover, prior to the experiment, the probability of any particular name's being included in a sample without replacement is no different from the probability that any other particular name will be chosen. Thus there is no discrimination against or in favor of any particular name in sampling without replacement. All of this is covered in elementary statistics courses. -- Mike Hardy

<<You seem to be conflating two ideas, that of conditional probability and that of ignorance. The probability of a name being drawn WITHOUT REPLACEMENT drops from 1 in 10, to 1 in 9, to 1 in 8, and so on, whether we know the drawings are dependent (conditional) or not. Our ignorance does not change the probabilities. Only if the names are REPLACED do the probabilities remain at 1 in 10 for each subsequent drawing. This is the interpretation in elementary statistics texts. B. Moore>>

[edit] Merge suggested with Random sample

Not a good idea, in my opinion. The two articles cover quite different ideas. I have commented in a bit more detail on Talk:Statistics and Talk:Random sample. Avenue 13:48, 23 September 2005 (UTC)

I agree - they aren't the same thing. Simple random samples assign an equal probability to each unit in the sampling frame, whereas they don't have to have equal probabilities of selection in a random sample.

• • I removed the merge tag and added an expert tag. Can you explain in the article the difference between a random and simple random sample? Thatcher131 15:01, 17 February 2006 (UTC)

[edit] Random sampling versus simple random sampling

<<Random sampling refers to the fact that any member of a population has an equal likelihood of being selected. This is what you are using to define a SIMPLE random sample, something that actually refers to the likelihood of any sample of size n in the population having the same chance of being selected. The distinction is critical.

For example, if I have a classroom with 60 students arranged in six rows of 10 students each and I select a sample of 10 students by rolling a die, then select the row corresponding to the outcome, this is a random sample. It is a random sample because each student in the classroom had an equal chance (1 in 6) of being in the row selected. However, it is NOT a "simple random sample" because not all possible samples of size 10 in this classroom have the same chance of being selected. Thus, any stratified or cluster sampling may begin with a random sample but can never be a simple random sample. By the same token, if a sample does NOT begin with a random sample, it cannot be a simple random sample, either. B. Moore>>

[edit] Example distinguishing random and simple random

I added a simple example that should help illustrate the distinction between a random sample and a simple random sample. Steve Simon 04:09, 17 October 2006 (UTC)