1. 1 Subjective Probability Information Design Scott Matthews Courses: 12-706 / 19-702/ 73-359

2. 12-706 and 73-3592 Admin Issues  HW 5 (due next wed)  Next project schedule  Case studies coming

3. 12-706 and 73-3593 Subjective Probabilities  Main Idea: We all have to make personal judgments (and decisions) in the face of uncertainty (Granger Morgan’s career)  These personal judgments are subjective  Subjective judgments of uncertainty can be made in terms of probability  Examples:  “My house will not be destroyed by a hurricane.”  “The Pirates will have a winning record (ever).”  “Driving after I have 2 drinks is safe”.

4. 12-706 and 73-3594 Outcomes and Events  Event: something about which we are uncertain  Outcome: result of uncertain event  Subjectively: once event (e.g., coin flip) has occurred, what is our judgment on outcome?  Represents degree of belief of outcome  Long-run frequencies, etc. irrelevant - need one  Example: Steelers* play AFC championship game at home. I Tivo it instead of watching live. I assume before watching that they will lose.  *Insert Cubs, etc. as needed (Sox removed 2005)

5. 12-706 and 73-3595 Next Steps  Goal is capturing the uncertainty/ biases/ etc. in these judgments  Might need to quantify verbal expressions (e.g., remote, likely, non-negligible..)  What to do if question not answerable directly?  Example: if I say there is a “negligible” chance of anyone failing this class, what probability do you assume?  What if I say “non-negligible chance that someone will fail”?

6. 12-706 and 73-3596 Merging of Theories  Science has known that “objective” and “subjective” factors existed for a long time  Only more recently did we realize we could represent subjective as probabilities  But inherently all of these subjective decisions can be ordered by decision tree  Where we have a gamble or bet between what we know and what we think we know  Clemen uses the basketball game gamble example  We would keep adjusting payoffs until optimal

7. 12-706 and 73-3597 Probability Wheel  Mechanism for formalizing our thoughts on probabilities of comparative lotteries  You select the area of the pie chart until you’re indifferent between the two lotteries  Quick 2-person exercise. Then we’ll discuss p-values.

8. 12-706 and 73-3598 Continuous Distributions  Similar to above, but we need to do it a few times.  E.g., try to get 5%, 50%, 95% points on distribution  Each point done with a “cdf-like” lottery comparison

9. 12-706 and 73-3599 Danger: Heuristics and Biases  Heuristics are “rules of thumb”  Which do we use in life? Biased? How?  Representativeness (fit in a category)  Availability (seen it before, fits memory)  Anchoring/Adjusting (common base point)  Motivational Bias (perverse incentives)  Idea is to consider these in advance and make people aware of them

10. 12-706 and 73-35910 Asking Experts  In the end, often we do studies like this, but use experts for elicitation  Idea is we should “trust” their predictions more, and can better deal with biases  Lots of training and reinforcement steps  But in the end, get nice prob functions

11. 12-706 and 73-35911 Information Design  What is it? Idea of carefully linking what data you have with what you want to say  “God” of the field: Edward Tufte (.com)  Quotes from his books (mostly his first)  The eye can recognize 150 Mbits of information  And is connected to our brain, a great processor  Perhaps most important: don’t just blindly use built- in graph/graphic tools when you have a significant point to make  a.k.a. Excel and Powerpoint are not friends!  They create simplistic graphs that dumb us down  Your graphics say a lot about your perceived command

12. 12-706 and 73-35912 Some pre-thoughts  In statistics, plotting raw data is useful - because it can show outliers (easy to see)  Analytical results need same treatment

13. 12-706 and 73-35913 Strive for “Graphical Excellence” z"consists of complex ideas communicated with clarity, precision, and efficiency zis that which gives to the viewer the greatest number of ideas in the shortest time with the least “ink” in the smallest space zis nearly always multivariate z“requires telling the truth about the data."

14. 12-706 and 73-35914 Graphics/Viz should: z"show the data zinduce viewer to think about the substance rather than about methodology, graphic design, the technology, etc. zavoid distorting what the data have to say zpresent many numbers in a small space zmake large data sets coherent zencourage the eye to compare different pieces of data zreveal the data at several levels of detail, from a broad overview to the fine structure zserve a reasonably clear purpose: description, exploration, tabulation, or decoration zbe closely integrated with the statistical and verbal descriptions of a data set."

15. 12-706 and 73-35915 Visualization goals zcontent focus zcomparison rather than mere description zIntegrity zhigh resolution zutilization of classic designs and concepts proven by time.

16. 12-706 and 73-35916 Content Focus z“Above all else show the data." The focus should be on the content of the data, not the visualization technique. This leads to design transparency. zThe success of a visualization is based on deep knowledge and care about the substance, and the quality, relevance and integrity of the content zAssume that the viewer is just as smart as you and cares just as much zNever `dumb-down' a visualization.

17. 12-706 and 73-35917 Comparison vs. Description zAt the heart of quantitative reasoning is a single question: Compared to what? zMost visualizations today are descriptive rather than comparative. The xy-plot invites reasoning about causality in a way that even the most impressive isosurface does not. zWe should strive for relational, rather than merely descriptive, visualizations. zAvoid relying on the viewer's memory to make visual comparisons; a weak facility in most of us.

18. 12-706 and 73-35918 Integrity - Misleading visualizations are common zTo help limit unintentional visualization lies: y"The representation of numbers, as physically measured on the surface of the graphic itself, should be directly proportional to the numerical quantities represented yClear, detailed, and thorough labeling should be used to defeat graphical distortion and ambiguity yWrite out explanations of the data on the graphic itself. Label important events in the data yShow data variation, not design variation yThe number of information-carrying (variable) dimensions depicted should not exceed the number of dimensions in the data yGraphics must not quote data out of context

19. 12-706 and 73-35919 “Lie Factor” zLie-factor = size-of-effect-shown-in- visualization / size-of-effect-in-data

20. 12-706 and 73-35920 Design Guidelines zVisualizations "are paragraphs about data and should be treated as such." Words, pictures, and numbers are all part of the information to be visualized, not separate entities y"have a properly chosen format and design yuse words, numbers, and drawing together yreflect balance, proportion, sense of relevant scale ydisplay an accessible complexity of detail yoften have a narrative quality, a story to tell about the data yavoid content-free decoration, including “chartjunk” (miscellaneous graphics that have nothing to do with the data)

21. 12-706 and 73-35921 Examples, and what’s wrong?  Think of Tufte’s “rules” above. Specify.

22. 12-706 and 73-35922 Nice attempt gone bad.. Graphic was bad before scan made it worse ;-) Source: NY Times, Aug 9, 1978, p. D-2 Caption says “Fuel Economy Standards for Autos, set by Congress And supplemented by DOT, in miles per gallon”

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29. 12-706 and 73-35929 What’s wrong? What could we do better?

30. 12-706 and 73-35930 Sorted by 5-yr Formatted nicer (big small) Source:http://edwardtufte.com

31. 12-706 and 73-35931 Consistent scale in this case Causes lots of crossover and Clutter.

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33. 12-706 and 73-35933 Labels on both sides!

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35. 12-706 and 73-35935 How far we’ve come!