100 lines
4.8 KiB
Markdown
100 lines
4.8 KiB
Markdown
- #[[ST2001 - Statistics in Data Science I]]
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- **Previous Topic:** [[Exploratory Data Analysis]]
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- **Next Topic:** [[Probability]]
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- **Relevant Slides:** 
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- What is a **Parameter**? #card
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card-last-interval:: -1
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card-repeats:: 1
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card-ease-factor:: 2.6
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card-next-schedule:: 2022-11-23T00:00:00.000Z
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card-last-reviewed:: 2022-11-22T13:40:14.581Z
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card-last-score:: 1
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- A **parameter** is a single value summarising some feature or variable of interest in the population.
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- It is usually unknown.
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- What is **inference**? #card
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card-last-interval:: 33.64
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card-repeats:: 4
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card-ease-factor:: 2.9
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card-next-schedule:: 2022-11-22T23:24:34.466Z
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card-last-reviewed:: 2022-10-20T08:24:34.467Z
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card-last-score:: 5
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- **Inference** is the process of making decisions about a population based on information in a sample.
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- A consequence of **natural variation** is that two samples drawn form the same population will usually give different estimates of the population parameters.
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- # Sampling
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collapsed:: true
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- What is **non-probabilistic sampling**? #card
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card-last-interval:: 29.04
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card-repeats:: 4
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card-ease-factor:: 2.56
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card-next-schedule:: 2022-12-13T20:02:44.059Z
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card-last-reviewed:: 2022-11-14T20:02:44.059Z
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card-last-score:: 5
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- **Non-probabilistic sampling** methods are techniques of obtaining a sample that is not chosen at random and may be subject to **sampling bias**.
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- ## Simple Random Sample
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- ### Difficulties:
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- Obtaining a sampling frame (list of all experimental units).
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- Possibly time consuming / expensive.
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- Minority groups, by chance, may not be represented in the sample.
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- ## Stratified Random Sampling #card
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card-last-interval:: -1
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card-repeats:: 1
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card-ease-factor:: 2.36
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card-next-schedule:: 2022-11-18T00:00:00.000Z
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card-last-reviewed:: 2022-11-17T20:19:40.391Z
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card-last-score:: 1
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- 1. Split entire population into **homogeneous groups**, called **strata**.
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2. Take a Simple Random Sample from each stratum.
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- ### Stratified VS Simple Random Sample
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- Ensure representation from minority groups.
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- Estimates of the population parameters per strata may be of interest.
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- Possible reduction in cost per observation in the survey.
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- Increased accuracy as reduced sampling error (less variation within a stratum).
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- ### Difficulties
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- Can you correctly allocate each individual to one & only one stratum?
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- Should every group receive equal weight?
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- What if some strata are more varied than others?
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- Take into account mean, variance, and cost to get "optimal allocation".
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- ## Cluster Sampling #card
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card-last-interval:: -1
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card-repeats:: 1
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card-ease-factor:: 2.36
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card-next-schedule:: 2022-11-18T00:00:00.000Z
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card-last-reviewed:: 2022-11-17T20:18:48.138Z
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card-last-score:: 1
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- Instead of randomly choosing individuals, a Simple Random Sample of collection or groups of individuals is taken.
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- The population is broken up into regions or groups, usually a *natural partition*, called a **cluster**.
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- Internally heterogeneous, homogeneous between the clusters.
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- Clusters are assumed representation of the entire population.
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- Small number of clusters are selected at random.
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- Every individual within a cluster is observed.
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- ### Cluster Over Stratified
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- Sampling frame not necessarily needed.
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- May be more practical and / or economical than Simple or Stratified Random Sampling.
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- Will be biased if the entire cluster is not sampled.
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- Careful if homogeneity within a cluster and heterogeneity between clusters as this can increase sample error.
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- **Note:** In stratified sampling, all strata are sampled, while in cluster sampling only some clusters are sampled.
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- # Studies & Experiments
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- ## Observational Studies & Experiments #card
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card-last-interval:: 4.14
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card-repeats:: 2
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card-ease-factor:: 2.56
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card-next-schedule:: 2022-11-27T15:18:34.757Z
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card-last-reviewed:: 2022-11-23T12:18:34.758Z
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card-last-score:: 5
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- In an **Observational Study**, data is collected only be *observing* what occurs.
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- E.g., surveys, historical records.
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- When researchers want to investigate **causal relationships**, it's best to conduct an experiment.
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- Usually there will be both an explanatory variable & a response variable.
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- Be wary of confounding variables.
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- ## Designed (Comparative) Study
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- An experiment allows us to prove a cause-and-effect relationship.
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- The experimenter must identify:
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- at least one **explanatory variable**, called a **factor** to manipulate.
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- at least one **response** variable to measure.
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- The experimenter must also control any other **nuisance factors** that could influence the response.
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- e.g., weather, day of the week.
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