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2014-09-11 12:50:08
Math219 Statistics SCC

Math 219 Statistics and Probability at SCC Informed Decisions Using Data, Michael Sullivan
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  1. Population
    The entire group to be studied.
  2. Sample
    Subset of the population that is being studied.
  3. Individual
    Person or object that is a member of the population being studied
  4. Parameter
    A numerical summary of a population
  5. Statistic
    A numerical summary of a sample.
  6. Descriptive statistics
    Consist of organizing and summarizing data. Descriptive statistics describes data through numerical summaries, tables, and graph.
  7. Inferential statistics
    Uses methods that take a result from a sample, extend it to the population, and measure the reliability of the result.
  8. inference statement
    a reliable conclusion developed by extending the results obtained from the sample
  9. The Process of Statistics
    • 1. Identify the research objective.
    • 2. Collect the data needed to answer the question(s).
    • 3. Describe the data.
    • 4. Perform Inference.
  10. variables
    Characteristics of the individuals within the population. e.g. Height, Weight, Age, Gender, Color
  11. Qualitative (categorical) variable
    classifies the individuals in one of two or more categories or groups. (attribute or characteristics)
  12. Quantitative variable
    a variable that provides numerical measures of individuals in which arithmetic operation makes sense. (measurements)
  13. Discrete variable
    A quantitative variable that has either a finite number of possible values or a countable number of possible values.
  14. Continuous variable
    A quantitative variable that has an infinite number of possible values that are not countable.
  15. Data
    the set of observed values for a variable.
  16. Qualitative data
    Observations corresponding to a qualitative variable.
  17. Quantitative data
    Observations corresponding to a quantitative variable.
  18. Discrete data
    Observations corresponding to a discrete variable.
  19. Continuous data
    Observations corresponding to a continuous variable.
  20. Observational study
    a study that measures the value of the response variable without attempting to influence the value either the response or explanatory variable.
  21. Designed experiment
    In this study a researcher assigns the individuals in a study to a certain group, intentionally changes the value of an explanatory variable, and then records the response variable for each group.
  22. Observation vs. Designed Experiment
    • Observational Study
    • • investigators observe subjects
    • • investigators measure variables of interest without assigning treatments to the subjects.
    • treatment that each subject receives is determined beyond the control of the researcher.

    • Designed Experiment 
    • • researchers apply treatments to experimental units
    • • then proceed to observe the effect of the treatments on the experimental units.
  23. Advantages/Disadvantages of Observational Study
    • Advantages
    • It can detect associations between variables where values of the variable have already been determined.

    Can be used to study variables that are impossible or unethical to control.

    • Disadvantages
    • It cannot isolate causes to determine causations.
  24. Advantages/Disadvantages of Designed Experiment
    • Advantages
    • Can analyze causal relationships between variables and responses, because the researcher is able to control variables that influences the responses.

    • Disadvantages
    • Cannot be done when variables cannot be controlled.
    • Cannot apply in some studies for moral or ethical reasons.
  25. Confounding
    Occurs when the effects of two or more explanatory variables are not separated.

    Therefore, any relation that may exist between an explanatory variable and the response variable may be due to some other variable or variables not accounted for in the study.
  26. Lurking variable
    is an explanatory variable that was not considered in a study, but that affects the value of the response variable in the study.
  27. Why is confounding a potentially major problem with observational studies?
    Often, the cause of confounding is a lurking variable.
  28. Three major categories of observational studies
    • 1.  Cross-sectional Studies
    • 2.  Case-control Studies
    • 3.  Cohort Studies
  29. Cross-sectional Studies
    These observational studies collect information about individuals at a specific point in time or over a short period of time.
  30. Case-control Studies
    These studies are retrospective, meaning they require individuals to look back in time or require the researcher to look at existing records.
  31. Cohort Studies
    A cohort study first identifies a group of individuals to participate in the study (the cohort). The cohort is then observed over a long period of time. During this period, characteristics about the individuals are recorded and some individuals will be exposed to certain factors and others will not.

    At the end of the study the value of the response variable is recorded for the individuals.
  32. Census
    A list of all individuals in a population along with certain characteristics of each individual.
  33. Random sampling
    the process of using chance to select individuals from a population to be included in the sample
  34. simple random sample.
    A sample of size n from a population of size N is obtained through simple random sampling if every possible sample of size n has an equally likely chance of occurring
  35. frame
    a list of all the individuals within a population.
  36. How do you obtain a stratified sample?
    obtained by separating the population into nonoverlapping groups called strata and then obtaining a simple random sample from each stratum. The individuals within each stratum should be homogeneous (or similar) in some way
  37. What is an advantage of stratified sampling?
    it may allow fewer individuals to be surveyed while obtaining the same or more information

    guarantees that each stratum is represented in the sample
  38. How is a Systematic Sample obtained?
    obtained by selecting every kth individual from the population. The first individual selected corresponds to a random number between 1 and k
  39. What are the steps in Systematic Sampling?
    1) If possible, approximate the population size, N.

    2) Determine the sample size desired, n.

    3) Compute N/n and round down to the nearest integer. This value is k.

    4) Randomly select a number between 1 and k. Call this number p.

    5) The sample will consist of the following individuals: p,p+k,p+2k,…,p+(n−1)k
  40. Name a sampling technique that does not require a frame.
    Systematic Sampling
  41. How do you obtain a Cluster Sample?
    obtained by selecting all individuals within a randomly selected collection or group of individuals
  42. What are Factors in a Design Experiment?
    explanatory variables
  43. What is Experimental Unit (or Subject) in a Design Experiment?
    a person, object or some other well-defined item upon which a treatment is applied.
  44. What's the purpose of a Control Group?
    serves as a baseline treatment that can be used to compare to other treatments
  45. What is a Placebo?
    an innocuous medication, such as a sugar tablet, that looks, tastes, and smells like the experimental medication
  46. Blinding
    refers to nondisclosure of the treatment an experimental unit is receiving
  47. What are the two types of Blinding?
    Single Blind and Double Blind
  48. Single-Blind
    A single-blind experiment is one in which the experimental unit (or subject) does not know which treatment he or she is receiving.
  49. Double-Blind
    A double-blind experiment is one in which neither the experimental unit nor the researcher in contact with the experimental unit knows which treatment the experimental unit is receiving.
  50. What are the steps in a Design Experiment?
    Step1. Identify the problem to be solved.

    Step2. Determine the factors that affect the response variable.

    Step3. Determine the number of experimental units.

    Step4. Determine the level of each factor

    Step5. Conduct the Experiment

    Step6. Test the claim
  51. Completely Randomized Design
    each experimental unit is randomly assigned to a treatment
  52. Matched-pairs design
    an experimental design in which the experimental units are paired up. The pairs are matched up so that they are somehow related (that is, the same person before and after a treatment, twins, husband and wife, same geographical location, and so on). There are only two levels of treatment in a matched-pairs design.
  53. How are the treatments distributed in a Matched-pairs Design?
    one matched individual will receive one treatment and the other receives a different treatment.
  54. Before-After or Pretest-Posttest Experiment
    One common type of matched-pair designs is to measure a response variable on an experimental unit before and after a treatment is applied. In this case the individual is matched against itself.
  55. Randomized Block Design
    A randomized block design is used when the experimental units are divided into homogeneous groups called blocks. Within each group, the experimental units are randomly assigned to a treatment.
  56. Blocks
    a group of Homogeneous individuals in a Randomized Block Design
  57. What is the goal of a Randomized Block Design?
    Our goal is to remove any variability in the response variable that may be attributable to the block.
  58. What is the goal of an experiment?
    The goal in an experiment is to determine the effect various treatments have on the response variable.

    We want to determine whether a new treatment is superior to an existing treatment (or no treatment at all).