Descriptive Statistics - Graphical Displays

  • What is the goal of Descriptive Statistics?
  • advice for good statistical practice: Don't neglect descriptive methods!
  1. Populations vs. Samples
  2. define population
  3. define sample
  4. What is the term for a sample which comprises the entire population?
  5. define parameter
  6. define statistic
  7. EXAMPLE: dataset indicated on page 15...
  8. What is the population?
  9. What is the sample?
  10. Name two parameters which might be of interest.
  11. Name two statistics which might be computed.
  12. Types of Variables & Descriptive Goals
  13. What are the 3 types of variables and what distinguishes each?
  14. EXAMPLE:Suppose that the students surveyed for page 15 were also asked their major. Would that be a legitimate categorical variable? Why or why not?
  15. Descriptive Goals:
  16. one categorical variable [SEE Ford Explorers dataset]
  17. What number/percentage fall into each category?
  18. How are individuals distributed amongst the categories?
  19. two categorical variables [SEE Ford Explorers dataset]
  20. Is the prevalence of one category related to the prevalence of another?
  21. Are there special combinations of categories?
  22. one quantitative variable [SEE 2000 BayState Marathon dataset]
  23. What patterns are there?
  24. shape
  25. center
  26. spread
  27. Are there "outliers"?
  28. one categorical & one quantitative variable [SEE 2000 BayState Marathon dataset]
  29. Does the quantitative variable tend to differ across categories?
  30. If the categories are ordinal, is there a relationship to the quantitative variable?
  31. two quantitative variables [SEE 2000 BayState Marathon dataset]
  32. Are the two variables "correlated"? If so, positively or negatively?
  33. Are there individuals whose combination of variables is an "outlier"?
  34. Match each term in #1 below with the appropriate term in #2 below:
  35. explanatory variable response variable
  36. predictED predictOR
  1. Describing Categorical Variables
  2. numerical summaries: good ole percentages!
  3. For a single variable, the percentages are obvious.
  4. For two (or more), percentages can be computed...
  5. row-wise, as Utts shows
  6. column-wise
  7. table-wise
  8. EXAMPLE:
  9. Compute the column-wise percentages for Table 2.3 (page 22).
  10. Compute the table-wise percentages for Table 2.3 (page 22).
  11. EXAMPLE:
  12. Ford Explorers summary
  13. graphical displays:
  14. pie charts - limited utility
  15. bar graphs - Minitab, SPSS
  16. QUESTION: How will the look of a bar graph change if every individual were to "clone itself" (with the same category for its datum)?
  1. Intro to Describing Quantitative Variables
  2. 5-number summary
  3. What are the 5 numbers in the summary?

  • What percentage of the data lie between...
  • min & Q1?
  • Q1 & median?
  • median & Q3?
  • Q3 & max?
  • Q1 & Q3?
  • How are the median & Q1 & Q3 calculated? Stay tuned...
  • OUTLIERS
  • How are they detected?
  • How should they be handled? See text's discussion on pages 45-46; it's very wise.
  • EXAMPLE: sample from 2000 BayState Marathon dataset
  1. Graphical Displays for Quantitative Variables
  2. stem-and-leaf plots: We'll leave these to your reading; they look very similar to histograms.
  3. dotplots:We'll leave these to your reading; they also look very similar to histograms.
  4. histograms:
  5. These are best suited to revealing shape. Options for "shape" are:
  6. symmetric, e.g. bell-shaped
  7. skewed, either to the right or left
  8. METHOD:
  9. by hand - see page 30
  10. with graphing calculator - explore on your own
  11. usingMinitab - [graphs/histogram]
  12. EXAMPLE: sample from 2000 BayState Marathon dataset
  1. boxplots: stay tuned ...
  1. COMPARISON: Read the advice on pages 35-36 and remember it for your project.