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1. Core Definitions

• Population: The entire collection of individuals or items that you want to study.
• Census: An investigation that observes/tests every single member of a population.
  • Pros: Completely accurate.
  • Cons: Time-consuming, expensive, and impossible if the testing destroys the item (e.g., testing the lifetime of lightbulbs).
• Sample: A selection of observations taken from a subset of the population used to find out about the whole population.
  • Pros: Quicker, cheaper, and less data to process.
  • Cons: Data may not be completely accurate or representative.
• Sampling Unit: An individual member of a population that can be sampled.
• Sampling Frame: A distinct list of all sampling units in the population (e.g., a school register or a list of electoral voters).

2. Random Sampling Methods

Every member of the population has an equal or known chance of being selected. Requires a sampling frame.

Simple Random Sampling

Assign a unique number to every item in the sampling frame, then use a random number generator to select your sample.

• Pros: Bias-free; completely fair.
• Cons: Inconvenient for massive populations; you must have a full, accurate list of everyone.

Systematic Sampling

Choose a random starting point from the first $k$ items, then choose every $k$th item after that (e.g., every 10th person on a list).

• Pros: Quick and simple to use.
• Cons: Can introduce bias if the population has a hidden recurring pattern that matches your sampling interval.

Stratified Sampling

The population is split into distinct groups (strata) like age or gender. You sample proportionally from each group.,

$\text{Sample Size for Strata} = \frac{\text{Number in Strata}}{\text{Total Population}} \times \text{Total Sample Size}$

• Pros: Guaranteed to accurately reflect the structure of the population.

• Cons: You must know the exact proportions of the population beforehand; cannot be done if people don’t fit neatly into distinct groups.

3. Non-Random Sampling Methods

Members do not have an equal chance of selection. Does not require a sampling frame.

Quota Sampling

An interviewer is told to find a specific number of people from distinct groups (e.g., “go interview 20 women over 50 and 20 men under 30”).

• Pros: Quick, cheap, and allows easy comparison between groups without needing a master list of the population.
• Cons: The interviewer can introduce bias by choosing who to approach (e.g., avoiding people who look angry).

Opportunity (Convenience) Sampling

Taking samples from members of the population who are available at that exact moment and fit the criteria (e.g., stopping the first 10 people you see outside a supermarket).

• Pros: Easiest and cheapest method by far.
• Cons: Highly unlikely to be representative; heavily biased towards a specific time and place.

Large Data Set Stuff

• The Data: Covers May–October in 1987 and 2015 across 5 UK stations (Leuchars, Leeming, Heathrow, Hurn, Camborne) and 3 overseas stations (Jacksonville, Beijing, Perth).

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