Section 1.3

Simple Random Sampling

To trust the data, we must trust how it was gathered. Randomness is not chaos—it is the only way to defeat bias.

1

The Power of "Simple Random"

Definition: Simple Random Sampling (SRS)

A sample of size from a population of size is obtained such that every possible sample of size has an equally likely chance of occurring.

LogicLens Breakdown: The "Sample" Nuance

Common Mistake: Thinking SRS just means "every person has an equal chance."

Why that's wrong (The Classroom Example):

Imagine a class with 10 boys and 10 girls. I flip a coin:

  • Heads: All boys are the sample.
  • Tails: All girls are the sample.

Every student has a 50% chance. But is it SRS? NO.

Why? Because a mix (1 boy, 9 girls) is impossible. SRS requires that every possible combination is selectable.

2

The Frame & The Notation

The Frame

A list of all the individuals within the population. If the frame doesn't match the population, you have bias.

Example Failure: Using a phone book to survey "All Residents". It misses people with only cell phones or no phones (Undercoverage).

Standard Notation

N
Population Size
The Target Total
n
Sample Size
The Data We Collect
3

The Selection Process

1

Obtain the Frame

List every individual in the population from 1 to N.

2

Randomize

Use a Random Number Table or Technology (RNG) to pick n unique numbers.

3

Match & Select

Correpond the random numbers back to the individuals in the list.

4

With vs. Without Replacement

With Replacement

Once an individual is selected, they are put back into the population and can be selected again.

Prob of 2nd Pick = (Constant)

Without Replacement (Standard)

Once selected, an individual is removed. They cannot be picked twice. This is the default for SRS.

Prob of 2nd Pick = (Increases)
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