stats lecture 2&3

Sampling Techniques

• Multistage Sampling:

  • Used for national surveys encompassing various subgroups.

  • Involves multiple stages: stratifying by region, then income level within regions, and selecting one cluster per income level.

  • Combines different sampling strategies for complex populations.

• Common Sampling Methods:

  • Simple Random Sample: Basic method where every individual has an equal chance of selection.

  • Stratified Random Sample: Divides the population into subgroups and samples proportionally from each group.

  • Other methods may be appropriate under different circumstances.

• Sampling Examples:

  • Class of 200:

    • 20 rows, 10 students; selecting 3 students from each row is stratified sampling since rows may differ based on placement.

  • Flight Sampling:

    • Surveying all passengers from one randomly selected flight exemplifies cluster sampling.

  • Assembly Line Testing:

    • Every 100th item tested is systematic sampling after a random first selection.

Proportional Representation in Sampling

• For a survey of 700 British students across unis, TAFEs, and private colleges:

  • Total institutions: 5 unis + 25 TAFEs + 5 private colleges = 35

  • Sample size distribution:

    • 100 uni students

    • 500 TAFE students

    • 100 private college students

  • Sampling should be proportional to the number of each type of institution in the population.

Variability in Sampling

• Definition: Variability of a population can be measured to ensure representative sampling.

• Methods may involve complex calculations such as standard deviation, rarely employed in practice due to difficulty.

Data Summary Techniques

• Purpose: After experiment design and data collection, summarizing and visualizing data is crucial.

• Key Concepts:

  • Types of variables: quantitative (continuous measurements) and categorical (group labels).

  • Introduction of histograms and quartiles as methods for data visualization.

Types of Variables

• Quantitative Variables: Numerical values (height, weight).

• Categorical Variables: Group names without numerical meaning (club, gender).

  • Some categorical variables can be coded numerically for convenience, but arithmetic operations are still not valid.

• Ordinal Variables: Categorical with logical ordering (T-shirt sizes, grades).

Data Distribution and Visualization

• Definition: Distribution is the relationship between values a variable can take and the frequency of