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Statistics 300: Introduction to Probability and Statistics

Statistics 300: Introduction to Probability and Statistics. Section 1-4. Design of Experiments. Definitions Five different approaches to sampling. Recap Scientific Method. Identify hypothesis and popul. Plan for collecting data Collect the data Analyze the data

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Statistics 300: Introduction to Probability and Statistics

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  1. Statistics 300:Introduction to Probability and Statistics Section 1-4

  2. Design of Experiments • Definitions • Five different approaches to sampling

  3. Recap Scientific Method • Identify hypothesis and popul. • Plan for collecting data • Collect the data • Analyze the data • Draw conclusions (revise hypothesis)

  4. Scientific Method Hypothesis about how the world works Revise Hypothesis Design Experiment Analyze Data Collect Data

  5. Definitions • Observational study • Experiment

  6. Definitions • Observational study: observe (measure) items in the population but without manipulating or modifying the subjects under study

  7. Definitions • Cross Sectional Study • Data are observed, measured, and collected at one point in time • A current “snapshot”

  8. Definitions • Retrospective (or Case Control) Study • Data are collected from the past by going back in time • Learn from history

  9. Definitions • Prospective (“Longitudinal” or “Cohort”) Study • Form groups (cohorts) that share common factors • Track cohort members through (future) time to collect informative data

  10. Definitions • Experiment: we “treat” (manipulate / modify) then observe or measure the characteristic of interest. Assess the “effects” of the treatments.

  11. Definitions • Placebo effect • Blinding

  12. Definitions • Placebo effect • A response due to the “belief” that one is receiving a particular treatment

  13. Definitions • Blinding • practice of preventing a subject from “knowing” how they are being treated • practice of preventing the investigator from knowing also (double blind)

  14. Definitions • Blocking • Confounding

  15. Definitions • Blocking • grouping similar items together • powerful and simple practice

  16. Definitions • Confounding • usually undesirable situation in which an extraneous factor is associated with the factor one is studying • cause(s) of the effects is (are) ambiguous

  17. Definitions • Confounding example • Question: Are teachers better at school A than at school B? • School A is a private school for poor kids and school B is a public school in a rich neighborhood.

  18. Definitions • Confounding example • What have you learned when the poor students at school A do better than the rich students at school B? • Is it the teachers, the students, the administration, the families, the curriculum … ?

  19. Definitions • Replication • Randomization

  20. Definitions • Replication • repetition of an experiment • repeating the treatments or conditions to see whether the response is consistent

  21. Definitions • Randomization • Selecting items or assigning items to treatments so all possible selections or all possible assignments are equally likely

  22. Five Sampling Methods • (Simple) Random Sampling • Stratified (Random) sampling • Systematic sampling • Cluster sampling • Convenience sampling

  23. Simple Random Sampling • Every element in the population is • equally likely to be in sample. • And • Every possible sample of size N • (of N items) has the same chance • of being chosen.

  24. Stratified Sampling • Subdivide the population into • two or more subgroups (strata) • Elements in each subgroup • (stratum) usually share some • common feature • Select random samples within • each of the strata

  25. Systematic Sampling • Select a starting point • Then select every kth element in the population, or • some other structured method of selecting the sample

  26. Cluster Sampling • Identify groups of elements in the population that naturally cluster together • Randomly select clusters (not single elements) • Observe / measure ALL • elements in the selected clusters

  27. Convenience Sampling • Observe and measure elements in the population that are • Convenient • Readily available • Cheap to acquire • May occur in combination with other “designs”

  28. Convenience Samplingwith Other Designs • Random selection of potential • survey participants, but only those who “volunteer” will participate • Stratified population, but selection of elements within each stratum is based on convenience

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