Overviews levels of measurement and graphical approaches to analysis of univariate data.

1. James Neill, 2011 Visualisation of quantitative information

3. Approaching data

4. Levels of measurement

5. Principals of graphing

6. Univariate graphs

7. Graphical integrity

8. Visualisation “ Visualization is any technique for creating images, diagrams, or animations to communicate a message.” - Wikipedia

9. Is Pivot a turning point for web exploration? (Gary Flake) ( TED talk - 6 min. )

10. Approaching data

11. Approaching data Entering & screening Exploring, describing, & graphing Hypothesis testing

12. Describing & graphing data THE CHALLENGE: to find a meaningful, accurate way to depict the ‘ true story’ of the data

13. Get your fingers dirty with data

14. Get intimate with your data

15. Clearly report the data's main features

16. Levels of Measurement = Type of Data Stevens (1946)

18. O rdinal

19. I nterval

20. R atio

21. Discrete vs. continuous Discrete - - - - - - - - - - Continuous ___________

22. Each level has the properties of the preceding levels, plus something more!

26. Ordinal / ranked example: Ranked importance Rank the following aspects of the university according to what is most important to you (1 = most important through to 5 = least important) __ Quality of the teaching and education __ Quality of the social life __ Quality of the campus __ Quality of the administration __ Quality of the university's reputation

29. Interval example: 8 point Likert scale

32. Ratio scale: Time

33. Why do levels of measurement matter? Different analytical procedures are used for different levels of data. More powerful statistics can be applied to higher levels

34. Principles of graphing

37. Explore

38. Tabulate

41. Avoid distortion

42. Focus on substance rather than method

43. Present many numbers in a small space

44. Make large data sets coherent

46. Encourage the eye to make comparisons

47. Reveal data at several levels/layers

48. Closely integrate with statistical and verbal descriptions

50. Select which type of graph to use

51. Draw a graph

52. Modify the graph to be clear, non-distorting, and well-labelled.

53. Disseminate the graph (e.g., include it in a report)

55. Univariate graphs

57. Pie chart

58. Data plot

59. Error bar

60. Stem & leaf plot

61. Box plot (Box & whisker)

62. Histogram

64. X-axis: Collapse if too many categories

65. Y-axis: Count or % or mean?

66. Consider whether to use data labels

69. Rotation / position influences perception Pie chart

70. Data plot & error bar Data plot Error bar

72. Use for ordinal, interval and ratio data

73. May look confusing to unfamiliar reader

75. Collapses tails Stem & leaf plot Frequency Stem & Leaf 7.00 1 . & 192.00 1 . 22223333333 541.00 1 . 444444444444444455555555555555 610.00 1 . 6666666666666677777777777777777777 849.00 1 . 88888888888888888888888888899999999999999999999 614.00 2 . 0000000000000000111111111111111111 602.00 2 . 222222222222222233333333333333333 447.00 2 . 4444444444444455555555555 291.00 2 . 66666666677777777 240.00 2 . 88888889999999 167.00 3 . 000001111 146.00 3 . 22223333 153.00 3 . 44445555 118.00 3 . 666777 99.00 3 . 888999 106.00 4 . 000111 54.00 4 . 222 339.00 Extremes (>=43)

77. Represents min., max, median, quartiles, & outliers

79. Useful for screening

80. Useful for comparing variables

81. Can get messy - too much info

82. Confusing to unfamiliar reader Box plot

84. X-axis needs a happy medium for # of categories

85. Y-axis matters (can exaggerate)

86. Histogram of male & female heights

87. Non-normal distributions

88. Non-normal distributions

89. Histogram of weight

90. Histogram of daily calorie intake

91. Histogram of fertility

92. Example ‘normal’ distribution 1

93. Example ‘normal’ distribution 2

94. Example ‘normal’ distribution 2

95. Effects of skew on measures of central tendency

97. Implies continuity e.g., time

98. Can show multiple lines Line graph

99. NOIR Bar chart & pie chart NOI Histogram IR Stem & leaf IR Data plot & box plot IR Error-bar IR Line graph IR Summary: Graphs & levels of measurement

100. Graphical integrity (part of academic integrity)

101. Graphing can be like a bikini. What they reveal is suggestive, but what they conceal is vital. (aka Aaron Levenstein)

102. Graphical integrity "Like good writing, good graphical displays of data communicate ideas with clarity, precision, and efficiency. Like poor writing, bad graphical displays distort or obscure the data, make it harder to understand or compare, or otherwise thwart the communicative effect which the graph should convey." Michael Friendly – Gallery of Data Visualisation

103. Cleveland’s hierarchy

105. Position along identical, non aligned scales

106. Length

107. Angle-slope

108. Area

109. Volume

110. Color hue - color saturation - density

112. Lie Factor = size of effect in graph size of effect in data

113. Misleading uses of area

114. Misleading uses of perspective

115. Leaving out important context

116. Lack of taste and aesthetics

118. Over the last century, the performance of the best baseball hitters has declined. Does this imply that the overall performance of baseball batters has decreased? Review questions

119. Can you complete this table? Level Properties Examples Descriptive Statistics Graphs Nominal /Categorical Ordinal / Rank Interval Ratio Answers: http://wilderdom.com/research/Summary_Levels_Measurement.html

121. A Periodic Table of Visualisation Methods - http://www.visual-literacy.org/periodic_table/periodic_table.html

122. Gallery of Data Visualization - http://www.math.yorku.ca/SCS/Gallery/

123. Univariate Data Analysis – The Best & Worst of Statistical Graphs - http://www.csulb.edu/~msaintg/ppa696/696uni.htm

124. Pitfalls of Data Analysis – http://www.vims.edu/~david/pitfalls/pitfalls.htm

125. Statistics for the Life Sciences – http://www.math.sfu.ca/~cschwarz/Stat-301/Handouts/Handouts.html

127. Jones, G. E. (2006). How to lie with charts . Santa Monica, CA: LaPuerta.

128. Tufte, E. (1983). The visual display of quantitative information . Cheshire, CT: Graphics Press.

130. Free and open source software.

131. http://www.openoffice.org/product/impress.html