uni/year2/semester1/logseq-stuff/pages/Sampling.md

• #ST2001 - Statistics in Data Science I
• Previous Topic: Exploratory Data Analysis
• Next Topic: Probability
• Relevant Slides:
• What is a Parameter? #card card-last-interval:: -1 card-repeats:: 1 card-ease-factor:: 2.6 card-next-schedule:: 2022-11-23T00:00:00.000Z card-last-reviewed:: 2022-11-22T13:40:14.581Z card-last-score:: 1
  • A parameter is a single value summarising some feature or variable of interest in the population.
  • It is usually unknown.
• What is inference? #card card-last-interval:: 33.64 card-repeats:: 4 card-ease-factor:: 2.9 card-next-schedule:: 2022-11-22T23:24:34.466Z card-last-reviewed:: 2022-10-20T08:24:34.467Z card-last-score:: 5
  • Inference is the process of making decisions about a population based on information in a sample.
• A consequence of natural variation is that two samples drawn form the same population will usually give different estimates of the population parameters.

• Sampling

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  • What is non-probabilistic sampling? #card card-last-interval:: 29.04 card-repeats:: 4 card-ease-factor:: 2.56 card-next-schedule:: 2022-12-13T20:02:44.059Z card-last-reviewed:: 2022-11-14T20:02:44.059Z card-last-score:: 5
    • Non-probabilistic sampling methods are techniques of obtaining a sample that is not chosen at random and may be subject to sampling bias.

  • Simple Random Sample

    • Difficulties:

      • Obtaining a sampling frame (list of all experimental units).
      • Possibly time consuming / expensive.
      • Minority groups, by chance, may not be represented in the sample.

  • Stratified Random Sampling #card

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    • 1. Split entire population into homogeneous groups, called strata.
      2. Take a Simple Random Sample from each stratum.

    • Stratified VS Simple Random Sample

      • Ensure representation from minority groups.
      • Estimates of the population parameters per strata may be of interest.
      • Possible reduction in cost per observation in the survey.
      • Increased accuracy as reduced sampling error (less variation within a stratum).

      • Difficulties

        • Can you correctly allocate each individual to one & only one stratum?
        • Should every group receive equal weight?
        • What if some strata are more varied than others?
        • Take into account mean, variance, and cost to get "optimal allocation".

  • Cluster Sampling #card

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    • Instead of randomly choosing individuals, a Simple Random Sample of collection or groups of individuals is taken.
    • The population is broken up into regions or groups, usually a natural partition, called a cluster.
      • Internally heterogeneous, homogeneous between the clusters.
    • Clusters are assumed representation of the entire population.
    • Small number of clusters are selected at random.
    • Every individual within a cluster is observed.

    • Cluster Over Stratified

      • Sampling frame not necessarily needed.
      • May be more practical and / or economical than Simple or Stratified Random Sampling.
      • Will be biased if the entire cluster is not sampled.
      • Careful if homogeneity within a cluster and heterogeneity between clusters as this can increase sample error.
      • Note: In stratified sampling, all strata are sampled, while in cluster sampling only some clusters are sampled.

• Studies & Experiments

  • Observational Studies & Experiments #card

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    • In an Observational Study, data is collected only be observing what occurs.
      • E.g., surveys, historical records.
    • When researchers want to investigate causal relationships, it's best to conduct an experiment.
      • Usually there will be both an explanatory variable & a response variable.
      • Be wary of confounding variables.

  • Designed (Comparative) Study

    • An experiment allows us to prove a cause-and-effect relationship.
    • The experimenter must identify:
      • at least one explanatory variable, called a factor to manipulate.
      • at least one response variable to measure.
    • The experimenter must also control any other nuisance factors that could influence the response.

      • e.g., weather, day of the week.