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Sociology 549, Lecture 3

Sociology 549, Lecture 3. Graphs by Paul von Hippel. Common graphs for frequency distributions. Pie chart Line chart (frequency polygon) Bar chart Histogram. Other common graphs. Time series Statistical map. Common distortions. False perspective e.g., tilting a pie chart

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Sociology 549, Lecture 3

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  1. Sociology 549,Lecture 3 Graphs by Paul von Hippel

  2. Common graphs for frequency distributions • Pie chart • Line chart (frequency polygon) • Bar chart • Histogram

  3. Other common graphs • Time series • Statistical map

  4. Common distortions • False perspective • e.g., tilting a pie chart • Shortening an axis; e.g., • not starting the vertical at 0 • breaking the vertical • squishing the horizontal • Reasons • Add visual interest • Make small differences look big, • Or make big differences look small

  5. Shapes of distributions • Symmetric • Skewed • Positively skewed • Negatively skewed • Modal • unimodal • bimodal • multimodal

  6. Pie chart • Rare in research • Common in media • Hard to compare wedges (different orientations) • Can’t show order • Restrict to nominal variables

  7. Perspective distortion • Add a meaningless 3rd dimension • Tilt pie away • Edge adds to front • Perspective shrinks back • Comparisons even harder

  8. Pie Charts in politics • Federal budget, from the website of the War Resisters’ League • Redrawn

  9. Bar chart(column chart) • In research,more common than pie • Can show order • Appropriate for ordinal and interval • (as well as nominal) • Easy to compare vertical distances

  10. Axis distortion • Start vertical above zero • Exaggerates all differences • Similar distortion: • Break vertical axis

  11. Perspective distortion • Add meaningless 3rd dimension • Reduces differences(caps same size)

  12. Perspective distortion (continued) • Add 3rd dimension and overlap • Exaggerates differences • Hides side of smaller bars • Also hides part of top • Rotation would make it worse

  13. Line chart(frequency polygon) • Common in research • Can show order • Appropriate for ordinal and interval variables

  14. Axis distortions • Start vertical above zero • Or break vertical

  15. Perspective distortion • Add meaningless 3rd dimension • Tilt horizontal • Exaggerates trend

  16. Bar vs. line: similarities • Bar and line charts almost equivalent • Start with a bar chart • Connect tops • remove bottoms • You get a line chart!

  17. Bar vs. line: Differences • Line suggests trend more strongly • Helpful with ordinal or interval variables • Misleading with nominal

  18. Line eases comparison of groups Bar vs. line: Differences

  19. Histograms • Like bar chart, except • Variable typically continuous • Bars touch • usually • Horizontal can represent equal class intervals (“bins”) • Bin shown by center value (e.g. 35.0) • Or by ends of class interval (e.g. 33.75-36.25)

  20. Summary: Graphical display of distributions

  21. Shape of distributions: Positive or right skew • Positive or right skew • Characteristics: • Peak on left • Long right tail • Stretched (Skewed) to the right • A few large values • Common cause • Floor but no ceiling

  22. Negative or left skew • Negative or left skew • Characteristics mirror positive skew: • Peak on right • Long left tail • Stretched (Skewed) to the left • A few small values • Common cause • Ceiling but no floor

  23. Symmetry • Symmetry, no skew • Two tails, or no tails • Important example: • The normal curve

  24. Dummy variables • Describe the shape of this distribution.

  25. Unimodal distributions • Mode • peak • most common value • Unimodal • one peak • e.g., starting salaries • mode around $27K • Interpretation • the most common salaries • are in the high $20s

  26. Bimodal distributions • Bimodal • two modes • e.g., # children • modes at 0 and 2 • Interpretation?

  27. Multimodal distributions • Multimodal • more than 2 modes • e.g., hours worked by OSU sociology students • modes at 0, 20, 40 (primary) mode secondary modes

  28. Review of shape • Shapes • Symmetric • Skewed • Positive (right) • Negative (left) • Unimodal, bimodal, multimodal

  29. Time series:don’t show distributions,show change over time

  30. Axis distortion:start (or break) vertical above zero

  31. Axis distortion:Squeeze vertical or stretch horizontal

  32. Axis distortion:Squeeze horizontalor stretch vertical

  33. Axis distortion in business • NASDAQ stock index, reported by Yahoo! • Redrawn

  34. Graphical distortion: Summary • Axis distortion • Squeeze one axis • Honest aspect ratio is 3:2 (Tufte) • Start or break vertical axis above zero • Perspective distortion • Add disproportionate areas in a meaningless 3rd dimension • Use blocking & tilting

  35. Graphics: Good advice • Keep it simple • Don’t stretch axes • Don’t start or break axes above zero • Don’t use 3-D • If you have to use 3D, avoid abuses • With just a few numbers,consider a table instead of a graph

  36. Graphics: Evil advice • Use every trick (3D, distorted axes) • Maximize differences that serve your purpose • Minimize differences that work against you

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