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Intro Stats: Islamic Approach -- Part 2: Probability and Statistics -
Lecture 1: Random Samples, Concept 3: Random Draws
S1: Simple Random Draw
Definition: A Simple Random Draw from a population selects one element of the population in such a way that ALL elements of the population have an exactly equal chance of being drawn.
A simple random draw is an IDEALIZATION - in the real world, when we draw one element from a population, it is difficult to ensure exactly equal chances for all elements. We use the idealization to make calculations of probabilities while keeping in mind that the real world situation may not match the theoretical ideals.
If the population has N elements, then each element has 1/N probability of being selected.
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There are 6x9=54-2=52 tickets on the table. If we pick one at random, all should have an equal chance 1/52 of being chosen.
: Common Confusion --
"Random": made, done, or happening without method or conscious decision.
Statistical Term: "Random" -- means all potential selection targets have EQUAL probability of being selected.
Example of ENGLISH random choice:
Close your eyes, and select a student by pointing to someone in the class at random.
Select the next student to walk through the doors of the classroom.
BOTH of these are RANDOM in the sense of being without any particular pattern. BUT THESE ARE NOT RANDOM in statistical sense. We cannot prove that ALL students have equal chance of being chosen.
HOW can we make a choice in such a way that we can PROVE that all students had an equal choice of being chosen? This goal can NEVER be achieved perfectly, but may be achieved with more or less precision.
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