I am reading, just for fun, the book Essentials of Statististics of Mario Triola.
I am trying to see the differences between Random Sample and Simple Random Sample.
In the book I found these definitions:
"A simple random sample of n subjects is selected in a such way that every possible sample of the same size n has the same chance of being selected.
In a random sample members from the population are selected in a such way that each individual member in the population has an equal chance of being selected."
I believe, but I am not sure, that in the random sample we need to be careful that the sample represent races, ages, economical situation, geographical location but in the simple random sample we do not consider that.
Am I correct?
Best Answer
Okay, let me try to address your question. I am sorry, I did not have time to read other responses. Here is the deal: In the definition of the random sample Triola is talking about a probability of selecting an object (individual). In the definition of a simple random sample, he talks about the probability of selecting varied samples of size n (groups of objects). That is the difference between the two (individual vs. a group)
Here is an example: You have a class of 50 students, 30 males and 20 females. You are randomly selecting 3 males and 2 females. This is an example of a random sample because each person in the class has the same probability of being selected 3/30=2/20. However, all your samples are going to be the same: 3 males and 2 females. It is not possible to get 2 males and 3 females, or 4 males and 1 female. Therefore, it is not a simple random sample.
I hope this helps )