Intro Stats: Islamic Approach -- Part 2: Probability and Statistics -
Lecture 1: Random Samples, Concept 4: Simple Random Samples
S1: SRS is a sequence of repeated Simple Random Draws
As already discussed, a simple random draw from a population picks one element of the population in such a way that all elements have an equal chance of being drawn. Let us name this first draw D1. Now repeat this operation of simple random draw to get a D2, D3, ... D(K). Then this is called a Simple Random Sample of size K. In statistical contexts, the population P is generally very large -- like 132 million people in Pakistan -- and the simple random sample is quite small; for instance 3000 people. If drawing is done randomly, then the random sample is representative of the population of Pakistan, and then it can be used to make inferences about the entire population of Pakistan.
Problem: PIDE current has 650 enrolled student. Create a simple random sample (SRS) of 50 students from this population.
GOAL: If the SRS is representative, then we can take a survey of these students, and expect that this will inform us about the general opinion at PIDE.
Solution: First create an EXCEL spreadsheet which lists all 650 students in the first column. Thus each row R=1,...,650 contains the name of one student at PIDE.
Then, RANDBETWEEN(1,650) will select a random number between 1 and 650. This will be the first Random Draw -- select the student in the indicated row. Repeat this operation 50 times to get a Simple Random Sample with 50 Students
Technicality: Sampling With Replacement. In the procedure described above, there is a chance that student might be selected TWICE. This is because the every draw is made from the same population of 1,2,...,650. Even if a student has been selected before, in a previous draw, he/she is still available for selection, and has a chance of being chosen. There is an alternative, which is used to avoid this problem. This is called Sampling WITHOUT Replacement. Once a student is selected, he/she is TAKEN OUT OF THE POOL of students. So if the first random draw selects student number 77, the name of student 77 is deleted from the pool of students, and can no longer be selected. The next random draw is made from the pool of 649 students, after excluding student 77, One simple way to achieve this effect, following the same procedure as above, is to just reject a repeat. That is, if some random draw repeats a name, just ignore this, and go on until 50 different students have been selected.