www.jjw3.com > Math1431 OR Math1431H > Math1431 Notes > Sullivan Chapter 1 Notes

Chapter 1: Data Collection

Section 1.1: Introduction to the Practice of Statistics

Knowledge Prerequisites

  1. declarative knowledge (definitions)
    1. none
  2. procedural knowledge
    1. none
  3. conditional knowledge
    1. none

Learning Goals

  1. declarative knowledge (definitions)
    1. statistics
    2. data
    3. population
    4. individuals
    5. sample
    6. statistic
    7. descriptive statistics
    8. inferential statistics
    9. parameter
    10. variable
    11. categorical variable
    12. quantitative variable
    13. discrete variable
    14. continuous variable
    15. margin of error (ME or E)
    16. steps in process of statistics
  2. procedural knowledge
    1. none
  3. conditional knowledge
    1. how to distinguish between a population and a sample
    2. understand the difference between a parameter and a statistic
    3. how to identify the difference between qualitative data and quantitative data
    4. how to identify the difference between discrete quantitative data and continuous quantitative data
    5. identify the steps in process of statistics

Section 1.2: Observational Studies versus Designed Experiments

Knowledge Prerequisites

  1. declarative knowledge (definitions)
    1. none
  2. procedural knowledge
    1. none
  3. conditional knowledge
    1. none

Learning Goals

  1. declarative knowledge (definitions)
    1. explanatory variable
    2. response variable
    3. observational studies
    4. experimental units/subjects/participants
    5. confounding variable
    6. lurking variable
    7. cross-sectional studies
    8. case-control studies
    9. cohort studies
  2. procedural knowledge
    1. none
  3. conditional knowledge
    1. how to identify the difference between an observational study and an experiment from a statistical study
    2. identify possible lurking variables in a statistical study
    3. understand why association does not imply causation
    4. advantages of observational studies over designed experiments
    5. advantages of designed experiments over observational studies
    6. advantages of cross-sectional, case-control, vs. cohort studies

Section 1.3: Simple Random Sampling

Knowledge Prerequisites

  1. declarative knowledge (definitions)
    1. none
  2. procedural knowledge
    1. none
  3. conditional knowledge
    1. none

Learning Goals

  1. declarative knowledge (definitions)
    1. random sampling
    2. simple random sampling (SRS)
    3. frame
    4. sampling without replacement
    5. sampling with replacement
    6. population size, N
    7. sample size, n
  2. procedural knowledge
    1. identify all possible samples of size n from a population
    2. How to find a simple random sample (SRS) using randInt on TI83/84 [ALL steps below MUST be shown]: http://stats.jjw3.com/math1431/ti83srs.htm
      1. Label population with whole numbers from 1 to N
      2. Use TI83/84 (see link above) to select n different random numbers (i.e., sample without replacement)
      3. Write sample as individuals from population
  3. conditional knowledge
    1. explain why a random sample is preferred over a convenient sample
  4. important notes
    1. you are not expected to use the random number table, you are expected to use the TI83/84

Section 1.4: Other Effective Sampling Methods

Knowledge Prerequisites

  1. declarative knowledge (definitions)
    1. Section 1.3:
      • random sampling
      • SRS
      • sampling without replacement
      • N
      • n
  2. procedural knowledge
    1. Section 1.3:
      • how to find SRS
  3. conditional knowledge
    1. none

Learning Goals

  1. declarative knowledge (definitions)
    1. strata
    2. stratified sample
    3. systematic sample
    4. cluster sample
    5. convenient sample
    6. self-selected sample
    7. voluntary sample
    8. multi-stage sampling
  2. procedural knowledge
    1. How to find a stratified sample using randInt on TI83/84 [ALL steps below MUST be shown]:
      1. Label population with whole numbers from 1 to N
      2. Find k
      3. Randomly select 1 number between 1 and k, call it p
      4. The labels for the sample are: k, k+p, k+2p, ...
      5. Write sample as individuals from population
    2. How to find a systematic sample using randInt on TI83/84 [ALL steps below MUST be shown]
  3. conditional knowledge
    1. how to identify the type of sampling used in a statistical
    2. know why systematic sampling and stratified sampling are NOT random samples
    3. explain advantages of each sampling method
  4. important notes
    1. you are not expected to use the random number table, you are expected to use the TI83/84

Section 1.5: Bias in Sampling

Knowledge Prerequisites

  1. declarative knowledge (definitions)
    1. none
  2. procedural knowledge
    1. none
  3. conditional knowledge
    1. none

Learning Goals

  1. declarative knowledge (definitions)
    1. bias
    2. sampling errors
    3. nonresponse bias
    4. response bias
    5. undercoverage
    6. interview errors
    7. misrepresented answers
    8. wording of questions
    9. ordering of questions or words
    10. open question
    11. closed question
    12. data entry error
    13. nonsampling errors
    14. sampling errors
  2. procedural knowledge
    1. none
  3. conditional knowledge
    1. how to construct a survey question that will not result in a bias
    2. how to identify the type of error/bias in surveys
    3. how to identify a strongly worded question in a survey

Section 1.6: The Design of Experiments

Knowledge Prerequisites

  1. declarative knowledge (definitions)
    1. Section 1.1:
      • inferential statistics
    2. Section 1.2:
      • designed experiment
      • explanatory variables
      • response variables
  2. procedural knowledge
    1. none
  3. conditional knowledge
    1. Section 1.3:
      • explain why a random sample is preferred over a convenient sample

Learning Goals

  1. declarative knowledge (definitions)
    1. experiment
    2. factors
    3. treatment
    4. experimental unit
    5. subject [participant]
    6. control group
    7. placebo
    8. single-blind experiment
    9. double-blind experiment
    10. designed experiment
    11. replication
    12. double blind
    13. completely randomized design
    14. matched-pairs design
  2. procedural knowledge
    1. list the steps in a statistical study
  3. conditional knowledge
    1. identify the difference between factors and treatments
    2. how to identify the various steps of experimental design from a statistical study
    3. how to identify research objective, identify the sample, list the descriptive statistics, and state conclusions of statistical studies
    4. explain the advantage(s) of well-designed experiments over observations
    5. explain the importance of randomization of group assignment
    6. explain statistical significance
  4. important notes
    1. you are not expected to sketch the diagram of an experiment

Chapter 1: Required Formulas – Need to Know for Tests

  1. k needed for Systematic Sampling: formula to calculate k needed for Systematic Sampling [rounded down to previous integer, i.e., truncated], where N is population size and n is sample size