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

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