Random Sample vs Simple Random Sample 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?
 A: 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 )
A: I found this explanation in a website of the University of Texas:
There are some types of Random Sample, one is  Simple Random Sample. There are other types called Probability Samples. One kind of Probability Sample is Stratified Random Sample. Here is the information of the University of Texas.
"A good example about how to select a SIMPLE RANDOM SAMPLE would proceed as follows:
First, obtain or make a list of all hospitals in the U.S. that perform heart bypass surgery. Number them 1, 2, ... up to to the total number M of hospitals in the population. (Such a list is called a sampling frame.)
Then use some sort of random number generating process2 to obtain a simple random sample of size n from the population of integers 1, 2, ...,  M.  The simple random sample of hospitals would consist of the hospitals in the list that correspond to the numbers in the SRS of numbers."
"Other Types of Random Samples
There are other types of random samples (sometimes called probability samples) besides simple random samples. These may be appropriate in some studies. but when they are used, the correct method of statistical analysis will differ from the method for a simple random sample. 1
Examples: 


*

*In a stratified random sample, the population is first classified into groups (called strata) with similar characteristics. Then a simple random sample is chosen from each strata separately. These simple random samples are combined to form the overall sample.


Examples of characteristics on which strata might be based include: gender, state, school district, county, age.
Reasons to use a stratified rather than simple random sample include:

The researchers may be interested in studying results by strata as well as overall. Stratified sampling can help ensure that there are enough observations within each strata to be able to make meaningful inferences by strata.
Statistical techniques can be chosen taking the strata into account to allow stronger conclusions to be drawn.
Practical considerations may make it impossible to take a simple random sample. 
2. In one-stage cluster sampling, the population is also divided into groups, called clusters. But instead of sampling within each cluster, a simple random sample of clusters is selected, and the overall sample consists of all individuals in the clusters that constitute this simple random sample of clusters. For example, if the purpose of the study is to find the average hourly wage of convenience store employees in a city, the researcher might randomly select a sample of convenience stores in the city and find the hourly wages of all employees in each of the stores in the sample.
The results from cluster samples are not as reliable as the results of simple random samples or stratified samples, so it should only be used if practical considerations do not allow a better sample scheme. For example, in the convenience store example, it may be practically speaking impossible to draw up a list of all convenience store employees in the city, but it would be much less difficult to draw up a list of all the convenience stores in the city.


*There are also many adaptive sampling designs2, in which the sampling pattern is updated (by a method depending on the particular design) depending on the data already collected."

